02_neural_network_classification_in_tensorflow.ipynb

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        "# 02. Neural Network Classification with TensorFlow\n",
        "\n",
        "Okay, we've seen how to deal with a regression problem in TensorFlow, let's look at how we can approach a classification problem.\n",
        "\n",
        "A [classification problem](https://en.wikipedia.org/wiki/Statistical_classification) involves predicting whether something is one thing or another.\n",
        "\n",
        "For example, you might want to:\n",
        "* Predict whether or not someone has heart disease based on their health parameters. This is called **binary classification** since there are only two options.\n",
        "* Decide whether a photo of is of food, a person or a dog. This is called **multi-class classification** since there are more than two options.\n",
        "* Predict what categories should be assigned to a Wikipedia article. This is called **multi-label classification** since a single article could have more than one category assigned.\n",
        "\n",
        "In this notebook, we're going to work through a number of different classification problems with TensorFlow. In other words, taking a set of inputs and predicting what class those set of inputs belong to.\n",
        "\n",
        "## What we're going to cover\n",
        "\n",
        "Specifically, we're going to go through doing the following with TensorFlow:\n",
        "- Architecture of a classification model\n",
        "- Input shapes and output shapes\n",
        "  - `X`: features/data (inputs)\n",
        "  - `y`: labels (outputs) \n",
        "    - \"What class do the inputs belong to?\"\n",
        "- Creating custom data to view and fit\n",
        "- Steps in modelling for binary and mutliclass classification\n",
        "  - Creating a model\n",
        "  - Compiling a model\n",
        "    - Defining a loss function\n",
        "    - Setting up an optimizer\n",
        "      - Finding the best learning rate\n",
        "    - Creating evaluation metrics\n",
        "  - Fitting a model (getting it to find patterns in our data)\n",
        "  - Improving a model\n",
        "- The power of non-linearity\n",
        "- Evaluating classification models\n",
        "  - Visualizng the model (\"visualize, visualize, visualize\")\n",
        "  - Looking at training curves\n",
        "  - Compare predictions to ground truth (using our evaluation metrics)\n",
        "\n",
        "## How you can use this notebook\n",
        "\n",
        "You can read through the descriptions and the code (it should all run, except for the cells which error on purpose), but there's a better option.\n",
        "\n",
        "Write all of the code yourself.\n",
        "\n",
        "Yes. I'm serious. Create a new notebook, and rewrite each line by yourself. Investigate it, see if you can break it, why does it break?\n",
        "\n",
        "You don't have to write the text descriptions but writing the code yourself is a great way to get hands-on experience.\n",
        "\n",
        "Don't worry if you make mistakes, we all do. The way to get better and make less mistakes is to **write more code**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ucRDjFFCJ92X"
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      "source": [
        "## Typical architecture of a classification neural network \n",
        "\n",
        "The word *typical* is on purpose.\n",
        "\n",
        "Because the architecture of a classification neural network can widely vary depending on the problem you're working on.\n",
        "\n",
        "However, there are some fundamentals all deep neural networks contain:\n",
        "* An input layer.\n",
        "* Some hidden layers.\n",
        "* An output layer.\n",
        "\n",
        "Much of the rest is up to the data analyst creating the model.\n",
        "\n",
        "The following are some standard values you'll often use in your classification neural networks.\n",
        "\n",
        "| **Hyperparameter** | **Binary Classification** | **Multiclass classification** |\n",
        "| --- | --- | --- |\n",
        "| Input layer shape | Same as number of features (e.g. 5 for age, sex, height, weight, smoking status in heart disease prediction) | Same as binary classification |\n",
        "| Hidden layer(s) | Problem specific, minimum = 1, maximum = unlimited | Same as binary classification |\n",
        "| Neurons per hidden layer | Problem specific, generally 10 to 100 | Same as binary classification |\n",
        "| Output layer shape | 1 (one class or the other) | 1 per class (e.g. 3 for food, person or dog photo) |\n",
        "| Hidden activation | Usually [ReLU](https://www.kaggle.com/dansbecker/rectified-linear-units-relu-in-deep-learning) (rectified linear unit) | Same as binary classification |\n",
        "| Output activation | [Sigmoid](https://en.wikipedia.org/wiki/Sigmoid_function) | [Softmax](https://en.wikipedia.org/wiki/Softmax_function) |\n",
        "| Loss function | [Cross entropy](https://en.wikipedia.org/wiki/Cross_entropy#Cross-entropy_loss_function_and_logistic_regression) ([`tf.keras.losses.BinaryCrossentropy`](https://www.tensorflow.org/api_docs/python/tf/keras/losses/BinaryCrossentropy) in TensorFlow) | Cross entropy ([`tf.keras.losses.CategoricalCrossentropy`](https://www.tensorflow.org/api_docs/python/tf/keras/losses/CategoricalCrossentropy) in TensorFlow) |\n",
        "| Optimizer | [SGD](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/SGD) (stochastic gradient descent), [Adam](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adam) | Same as binary classification |\n",
        "\n",
        "***Table 1:*** *Typical architecture of a classification network.* ***Source:*** *Adapted from page 295 of [Hands-On Machine Learning with Scikit-Learn, Keras & TensorFlow Book by Aurélien Géron](https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/)*\n",
        "\n",
        "Don't worry if not much of the above makes sense right now, we'll get plenty of experience as we go through this notebook.\n",
        "\n",
        "Let's start by importing TensorFlow as the common alias `tf`. For this notebook, make sure you're using version 2.x+."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IPWQMjYwKpCH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "13cc3a30-b1c5-4e19-feb6-f97bc32aebdd"
      },
      "source": [
        "import tensorflow as tf\n",
        "print(tf.__version__)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.7.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PEAjPGv8J2K0"
      },
      "source": [
        "## Creating data to view and fit\n",
        "\n",
        "We could start by importing a classification dataset but let's practice making some of our own classification data.\n",
        "\n",
        "> 🔑 **Note:** It's a common practice to get you and model you build working on a toy (or simple) dataset before moving to your actual problem. Treat it as a rehersal experiment before the actual experiment(s).\n",
        "\n",
        "Since classification is predicting whether something is one thing or another, let's make some data to reflect that.\n",
        "\n",
        "To do so, we'll use Scikit-Learn's [`make_circles()`](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_circles.html#sklearn.datasets.make_circles) function.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7dT80sWqLYPf"
      },
      "source": [
        "from sklearn.datasets import make_circles\n",
        "\n",
        "# Make 1000 examples\n",
        "n_samples = 1000\n",
        "\n",
        "# Create circles\n",
        "X, y = make_circles(n_samples, \n",
        "                    noise=0.03, \n",
        "                    random_state=42)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CclQDWU8c69i"
      },
      "source": [
        "Wonderful, now we've created some data, let's look at the features (`X`) and labels (`y`)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gf47AUmxLYMj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e00986b4-62d5-4722-cde4-b0f5a72fcef6"
      },
      "source": [
        "# Check out the features\n",
        "X"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.75424625,  0.23148074],\n",
              "       [-0.75615888,  0.15325888],\n",
              "       [-0.81539193,  0.17328203],\n",
              "       ...,\n",
              "       [-0.13690036, -0.81001183],\n",
              "       [ 0.67036156, -0.76750154],\n",
              "       [ 0.28105665,  0.96382443]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FkgZlGstK572",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9d20a0b1-3c94-4c9f-bfd0-2e5bd0fd83f6"
      },
      "source": [
        "# See the first 10 labels\n",
        "y[:10]"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1, 0, 1, 1, 1, 1, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DcBi6A1PeC4s"
      },
      "source": [
        "Okay, we've seen some of our data and labels, how about we move towards visualizing?\n",
        "\n",
        "> 🔑 **Note:** One important step of starting any kind of machine learning project is to [become one with the data](https://karpathy.github.io/2019/04/25/recipe/). And one of the best ways to do this is to visualize the data you're working with as much as possible. The data explorer's motto is \"visualize, visualize, visualize\".\n",
        "\n",
        "We'll start with a DataFrame."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SzQ7X9QgMGpq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "b96c6902-04fa-4c9f-a9fc-5cd6aee44106"
      },
      "source": [
        "# Make dataframe of features and labels\n",
        "import pandas as pd\n",
        "circles = pd.DataFrame({\"X0\":X[:, 0], \"X1\":X[:, 1], \"label\":y})\n",
        "circles.head()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<div>\n",
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              "    .dataframe tbody tr th:only-of-type {\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X0</th>\n",
              "      <th>X1</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
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              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.754246</td>\n",
              "      <td>0.231481</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.756159</td>\n",
              "      <td>0.153259</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.815392</td>\n",
              "      <td>0.173282</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.393731</td>\n",
              "      <td>0.692883</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.442208</td>\n",
              "      <td>-0.896723</td>\n",
              "      <td>0</td>\n",
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            "text/plain": [
              "         X0        X1  label\n",
              "0  0.754246  0.231481      1\n",
              "1 -0.756159  0.153259      1\n",
              "2 -0.815392  0.173282      1\n",
              "3 -0.393731  0.692883      1\n",
              "4  0.442208 -0.896723      0"
            ]
          },
          "metadata": {},
          "execution_count": 5
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ngNwBOxevcv"
      },
      "source": [
        "What kind of labels are we dealing with?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cfgZGtMGe0XB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "61e9b64e-abdf-4a1c-efd6-9c4763978426"
      },
      "source": [
        "# Check out the different labels\n",
        "circles.label.value_counts()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1    500\n",
              "0    500\n",
              "Name: label, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ajz7TdQPesKt"
      },
      "source": [
        "Alright, looks like we're dealing with a **binary classification** problem. It's binary because there are only two labels (0 or 1).\n",
        "\n",
        "If there were more label options (e.g. 0, 1, 2, 3 or 4), it would be called **multiclass classification**.\n",
        "\n",
        "Let's take our visualization a step further and plot our data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KIPTzrETMemP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "0daa7302-a55d-4a15-921b-be7ac6988e5d"
      },
      "source": [
        "# Visualize with a plot\n",
        "import matplotlib.pyplot as plt\n",
        "plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdYlBu);"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Jty66H6cbJp"
      },
      "source": [
        "Nice! From the plot, can you guess what kind of model we might want to build?\n",
        "\n",
        "How about we try and build one to classify blue or red dots? As in, a model which is able to distinguish blue from red dots.\n",
        "\n",
        "> 🛠 **Practice:** Before pushing forward, you might want to spend 10 minutes playing around with the [TensorFlow Playground](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.03&regularizationRate=0&noise=0&networkShape=2,2&seed=0.93799&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&regularizationRate_hide=true&batchSize_hide=true). Try adjusting the different hyperparameters you see and click play to see a neural network train. I think you'll find the data very similar to what we've just created."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cv4fEHihOAq4"
      },
      "source": [
        "## Input and output shapes\n",
        "\n",
        "One of the most common issues you'll run into when building neural networks is shape mismatches.\n",
        "\n",
        "More specifically, the shape of the input data and the shape of the output data.\n",
        "\n",
        "In our case, we want to input `X` and get our model to predict `y`.\n",
        "\n",
        "So let's check out the shapes of `X` and `y`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lZxjjmsHNt_K",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d8fba016-ddb3-4905-daaf-7866c84b4550"
      },
      "source": [
        "# Check the shapes of our features and labels\n",
        "X.shape, y.shape"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((1000, 2), (1000,))"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5BSq58RogJMa"
      },
      "source": [
        "Hmm, where do these numbers come from?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SPr81SsKgHvZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "61acc9cb-adaf-473f-8f6b-9eca7d10a40c"
      },
      "source": [
        "# Check how many samples we have\n",
        "len(X), len(y)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1000, 1000)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XCBbrNaOgPWC"
      },
      "source": [
        "So we've got as many `X` values as we do `y` values, that makes sense.\n",
        "\n",
        "Let's check out one example of each."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hwrSEVubgZNb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "41066f0c-2ff8-4fe4-ff09-a71c20544195"
      },
      "source": [
        "# View the first example of features and labels\n",
        "X[0], y[0]"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.75424625, 0.23148074]), 1)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OMeqY8JSgg4L"
      },
      "source": [
        "Alright, so we've got two `X` features which lead to one `y` value.\n",
        "\n",
        "This means our neural network input shape will has to accept a tensor with at least one dimension being two and output a tensor with at least one value.\n",
        "\n",
        "> 🤔 **Note:** `y` having a shape of (1000,) can seem confusing. However, this is because all `y` values are actually scalars (single values) and therefore don't have a dimension. For now, think of your output shape as being at least the same value as one example of `y` (in our case, the output from our neural network has to be at least one value)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vSjUbiCBN9fc"
      },
      "source": [
        "## Steps in modelling\n",
        "\n",
        "Now we know what data we have as well as the input and output shapes, let's see how we'd build a neural network to model it.\n",
        "\n",
        "In TensorFlow, there are typically 3 fundamental steps to creating and training a model.\n",
        "\n",
        "1. **Creating a model** - piece together the layers of a neural network yourself (using the [functional](https://www.tensorflow.org/guide/keras/functional) or [sequential API](https://www.tensorflow.org/api_docs/python/tf/keras/Sequential)) or import a previously built model (known as transfer learning).\n",
        "2. **Compiling a model** - defining how a model's performance should be measured (loss/metrics) as well as defining how it should improve (optimizer). \n",
        "3. **Fitting a model** - letting the model try to find patterns in the data (how does `X` get to `y`). \n",
        "\n",
        "Let's see these in action using the Sequential API to build a model for our regression data. And then we'll step through each."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lt4pbcZ7OEif",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7db4804a-a44e-48f0-dbc2-a0af27576788"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# 1. Create the model using the Sequential API\n",
        "model_1 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1)\n",
        "])\n",
        "\n",
        "# 2. Compile the model\n",
        "model_1.compile(loss=tf.keras.losses.BinaryCrossentropy(), # binary since we are working with 2 clases (0 & 1)\n",
        "                optimizer=tf.keras.optimizers.SGD(),\n",
        "                metrics=['accuracy'])\n",
        "\n",
        "# 3. Fit the model\n",
        "model_1.fit(X, y, epochs=5)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/5\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 2.8544 - accuracy: 0.4600\n",
            "Epoch 2/5\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7131 - accuracy: 0.5430\n",
            "Epoch 3/5\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6973 - accuracy: 0.5090\n",
            "Epoch 4/5\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6950 - accuracy: 0.5010\n",
            "Epoch 5/5\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6942 - accuracy: 0.4830\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fc85e277590>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oa8Tcv9ePRq6"
      },
      "source": [
        "Looking at the accuracy metric, our model performs poorly (50% accuracy on a binary classification problem is the equivalent of guessing), but what if we trained it for longer?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GqVVD_IqPHm5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bddc17e3-f254-4619-d153-b332e3140ec9"
      },
      "source": [
        "# Train our model for longer (more chances to look at the data)\n",
        "model_1.fit(X, y, epochs=200, verbose=0) # set verbose=0 to remove training updates\n",
        "model_1.evaluate(X, y)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.5000\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.6934829950332642, 0.5]"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-qaMmKrPegL"
      },
      "source": [
        "Even after 200 passes of the data, it's still performing as if it's guessing.\n",
        "\n",
        "What if we added an extra layer and trained for a little longer?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TED0ZkOuPklW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a738c2fe-6b8a-485a-cbec-7aad38e1c0bc"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# 1. Create the model (same as model_1 but with an extra layer)\n",
        "model_2 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1), # add an extra layer\n",
        "  tf.keras.layers.Dense(1) \n",
        "])\n",
        "\n",
        "# 2. Compile the model\n",
        "model_2.compile(loss=tf.keras.losses.BinaryCrossentropy(),\n",
        "                optimizer=tf.keras.optimizers.SGD(),\n",
        "                metrics=['accuracy'])\n",
        "\n",
        "# 3. Fit the model\n",
        "model_2.fit(X, y, epochs=100, verbose=0) # set verbose=0 to make the output print less"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fc85b003a10>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qFWWlhByirLa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "37cb10f2-258b-4106-f908-24930dd71cec"
      },
      "source": [
        "# Evaluate the model\n",
        "model_2.evaluate(X, y)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5000\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.6933314800262451, 0.5]"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HC7vhAHKQQRY"
      },
      "source": [
        "Still not even as good as guessing (~50% accuracy)... hmm...?\n",
        "\n",
        "Let's remind ourselves of a couple more ways we can use to improve our models."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wyTs6QgijF6_"
      },
      "source": [
        "## Improving a model\n",
        "\n",
        "To improve our model, we can alter almost every part of the 3 steps we went through before.\n",
        "\n",
        "1. **Creating a model** - here you might want to add more layers, increase the number of hidden units (also called neurons) within each layer, change the activation functions of each layer.\n",
        "2. **Compiling a model** - you might want to choose a different optimization function (such as the [Adam](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adam) optimizer, which is usually pretty good for many problems) or perhaps change the learning rate of the optimization function.\n",
        "3. **Fitting a model** - perhaps you could fit a model for more epochs (leave it training for longer).\n",
        "\n",
        "![various options you can use to improve a neural network model](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-improving-a-model-from-model-perspective.png)\n",
        "*There are many different ways to potentially improve a neural network. Some of the most common include: increasing the number of layers (making the network deeper), increasing the number of hidden units (making the network wider) and changing the learning rate. Because these values are all human-changeable, they're referred to as [hyperparameters](https://en.wikipedia.org/wiki/Hyperparameter_(machine_learning)) and the practice of trying to find the best hyperparameters is referred to as [hyperparameter tuning](https://en.wikipedia.org/wiki/Hyperparameter_optimization).*\n",
        "\n",
        "How about we try adding more neurons, an extra layer and our friend the Adam optimizer?\n",
        "\n",
        "Surely doing this will result in predictions better than guessing...\n",
        "\n",
        "> **Note:** If you're using TensorFlow 2.7.0+ the original code from the following cells may have caused some errors. They've since been updated to fix those errors. You can see explanations on what happened at the following resources:\n",
        "* [Example Colab Notebook](https://colab.research.google.com/drive/1_dlrB_DJOBS9c9foYJs49I0YwN7LTakl?usp=sharing)\n",
        "* [TensorFlow for Deep Learning GitHub Discussion on TensorFlow 2.7.0 breaking changes](https://github.com/mrdbourke/tensorflow-deep-learning/discussions/278)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "46pebMB4Qeth",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "73fe9b05-449a-4598-b8fb-acbf04891224"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# 1. Create the model (this time 3 layers)\n",
        "model_3 = tf.keras.Sequential([\n",
        "  # Before TensorFlow 2.7.0\n",
        "  # tf.keras.layers.Dense(100), # add 100 dense neurons\n",
        "\n",
        "  ## After TensorFlow 2.7.0 ##\n",
        "  tf.keras.layers.Dense(100, input_shape=(None, 1)), # add 100 dense neurons with input_shape defined (None, 1) = look at 1 sample at a time\n",
        "  tf.keras.layers.Dense(10), # add another layer with 10 neurons\n",
        "  tf.keras.layers.Dense(1)\n",
        "])\n",
        "\n",
        "# 2. Compile the model\n",
        "model_3.compile(loss=tf.keras.losses.BinaryCrossentropy(),\n",
        "                optimizer=tf.keras.optimizers.Adam(), # use Adam instead of SGD\n",
        "                metrics=['accuracy'])\n",
        "\n",
        "# 3. Fit the model\n",
        "model_3.fit(X, y, epochs=100, verbose=0) # fit for 100 passes of the data"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fc85e0eb950>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TJJL0YT7RVzv"
      },
      "source": [
        "Still! \n",
        "\n",
        "We've pulled out a few tricks but our model isn't even doing better than guessing.\n",
        "\n",
        "Let's make some visualizations to see what's happening.\n",
        "\n",
        "> 🔑 **Note:** Whenever your model is performing strangely or there's something going on with your data you're not quite sure of, remember these three words: **visualize, visualize, visualize**. Inspect your data, inspect your model, inpsect your model's predictions.\n",
        "\n",
        "To visualize our model's predictions we're going to create a function `plot_decision_boundary()` which:\n",
        "* Takes in a trained model, features (`X`) and labels (`y`).\n",
        "* Creates a [meshgrid](https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html) of the different `X` values.\n",
        "* Makes predictions across the meshgrid.\n",
        "* Plots the predictions as well as a line between the different zones (where each unique class falls).\n",
        "\n",
        "If this sounds confusing, let's see it in code and then see the output.\n",
        "\n",
        "> 🔑 **Note:** If you're ever unsure of what a function does, try unraveling it and writing it line by line for yourself to see what it does. Break it into small parts and see what each part outputs."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MuwGjU_XR0aG"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "def plot_decision_boundary(model, X, y):\n",
        "  \"\"\"\n",
        "  Plots the decision boundary created by a model predicting on X.\n",
        "  This function has been adapted from two phenomenal resources:\n",
        "   1. CS231n - https://cs231n.github.io/neural-networks-case-study/\n",
        "   2. Made with ML basics - https://github.com/GokuMohandas/MadeWithML/blob/main/notebooks/08_Neural_Networks.ipynb\n",
        "  \"\"\"\n",
        "  # Define the axis boundaries of the plot and create a meshgrid\n",
        "  x_min, x_max = X[:, 0].min() - 0.1, X[:, 0].max() + 0.1\n",
        "  y_min, y_max = X[:, 1].min() - 0.1, X[:, 1].max() + 0.1\n",
        "  xx, yy = np.meshgrid(np.linspace(x_min, x_max, 100),\n",
        "                       np.linspace(y_min, y_max, 100))\n",
        "  \n",
        "  # Create X values (we're going to predict on all of these)\n",
        "  x_in = np.c_[xx.ravel(), yy.ravel()] # stack 2D arrays together: https://numpy.org/devdocs/reference/generated/numpy.c_.html\n",
        "  \n",
        "  # Make predictions using the trained model\n",
        "  y_pred = model.predict(x_in)\n",
        "\n",
        "  # Check for multi-class\n",
        "  if len(y_pred[0]) > 1:\n",
        "    print(\"doing multiclass classification...\")\n",
        "    # We have to reshape our predictions to get them ready for plotting\n",
        "    y_pred = np.argmax(y_pred, axis=1).reshape(xx.shape)\n",
        "  else:\n",
        "    print(\"doing binary classifcation...\")\n",
        "    y_pred = np.round(y_pred).reshape(xx.shape)\n",
        "  \n",
        "  # Plot decision boundary\n",
        "  plt.contourf(xx, yy, y_pred, cmap=plt.cm.RdYlBu, alpha=0.7)\n",
        "  plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.RdYlBu)\n",
        "  plt.xlim(xx.min(), xx.max())\n",
        "  plt.ylim(yy.min(), yy.max())"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OgekXFM2clQW"
      },
      "source": [
        "Now we've got a function to plot our model's decision boundary (the cut off point its making between red and blue dots), let's try it out."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XIyCVjolTmy4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "a91282d9-2185-4956-dd2f-8c190ea4cac8"
      },
      "source": [
        "# Check out the predictions our model is making \n",
        "plot_decision_boundary(model_3, X, y)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "doing multiclass classification...\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XIzcQrknUJPK"
      },
      "source": [
        "Looks like our model is trying to draw a straight line through the data.\n",
        "\n",
        "What's wrong with doing this?\n",
        "\n",
        "The main issue is our data isn't separable by a straight line.\n",
        "\n",
        "In a regression problem, our model might work. In fact, let's try it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7d9O9subUshC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0a5c124c-60d8-4a8d-a6b0-4428902839d7"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create some regression data\n",
        "X_regression = np.arange(0, 1000, 5)\n",
        "y_regression = np.arange(100, 1100, 5)\n",
        "\n",
        "# Split it into training and test sets\n",
        "X_reg_train = X_regression[:150]\n",
        "X_reg_test = X_regression[150:]\n",
        "y_reg_train = y_regression[:150]\n",
        "y_reg_test = y_regression[150:]\n",
        "\n",
        "# Fit our model to the data\n",
        "# Note: Before TensorFlow 2.7.0, this line would work\n",
        "# model_3.fit(X_reg_train, y_reg_train, epochs=100)\n",
        "\n",
        "# After TensorFlow 2.7.0, see here for more: https://github.com/mrdbourke/tensorflow-deep-learning/discussions/278\n",
        "model_3.fit(tf.expand_dims(X_reg_train, axis=-1), \n",
        "            y_reg_train,\n",
        "            epochs=100)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 2/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 3/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 4/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 5/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 6/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 7/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 8/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 9/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 10/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 11/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 12/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 13/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 14/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 15/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 16/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 17/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 18/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 19/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 20/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 21/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 22/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 23/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 24/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 25/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 26/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 27/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 28/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 29/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 30/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 31/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 32/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 33/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 34/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 35/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 36/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 37/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 38/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 39/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 40/100\n",
            "5/5 [==============================] - 0s 7ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 41/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 42/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 43/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 44/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 45/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 46/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 47/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 48/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 49/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 50/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 51/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 52/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 53/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 54/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 55/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 56/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 57/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 58/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 59/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 60/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 61/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 62/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 63/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 64/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 65/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 66/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 67/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 68/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 69/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 70/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 71/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 72/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 73/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 74/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 75/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 76/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 77/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 78/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 79/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 80/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 81/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 82/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0166 - accuracy: 0.0000e+00\n",
            "Epoch 83/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 84/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 85/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0166 - accuracy: 0.0000e+00\n",
            "Epoch 86/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 87/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 88/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 89/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 90/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 91/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 92/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 93/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 94/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 95/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 96/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0151 - accuracy: 0.0000e+00\n",
            "Epoch 97/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 98/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 99/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n",
            "Epoch 100/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: -7190.0156 - accuracy: 0.0000e+00\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fc85cd5bcd0>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lFGjyziVn_Zh",
        "outputId": "d737b50b-9e49-4c91-aba6-eaaeeeec544d"
      },
      "source": [
        "model_3.summary()"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_2\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense_3 (Dense)             (None, None, 100)         200       \n",
            "                                                                 \n",
            " dense_4 (Dense)             (None, None, 10)          1010      \n",
            "                                                                 \n",
            " dense_5 (Dense)             (None, None, 1)           11        \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 1,221\n",
            "Trainable params: 1,221\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SMu37fayVEZI"
      },
      "source": [
        "Oh wait... we compiled our model for a binary classification problem.\n",
        "\n",
        "No trouble, we can recreate it for a regression problem."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OUJtmMPZVOZ9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6f7906c3-4452-473e-f1c1-b3d085fc3eaf"
      },
      "source": [
        "# Setup random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Recreate the model\n",
        "model_3 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(100),\n",
        "  tf.keras.layers.Dense(10),\n",
        "  tf.keras.layers.Dense(1)\n",
        "])\n",
        "\n",
        "# Change the loss and metrics of our compiled model\n",
        "model_3.compile(loss=tf.keras.losses.mae, # change the loss function to be regression-specific\n",
        "                optimizer=tf.keras.optimizers.Adam(),\n",
        "                metrics=['mae']) # change the metric to be regression-specific\n",
        "\n",
        "# Fit the recompiled model\n",
        "model_3.fit(tf.expand_dims(X_reg_train, axis=-1), \n",
        "            y_reg_train, \n",
        "            epochs=100)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 248.2155 - mae: 248.2155\n",
            "Epoch 2/100\n",
            "5/5 [==============================] - 0s 2ms/step - loss: 138.9005 - mae: 138.9005\n",
            "Epoch 3/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 53.1039 - mae: 53.1039\n",
            "Epoch 4/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 73.5170 - mae: 73.5170\n",
            "Epoch 5/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 71.2358 - mae: 71.2358\n",
            "Epoch 6/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 47.0040 - mae: 47.0040\n",
            "Epoch 7/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 45.9386 - mae: 45.9386\n",
            "Epoch 8/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 42.3638 - mae: 42.3638\n",
            "Epoch 9/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 43.6831 - mae: 43.6831\n",
            "Epoch 10/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 42.6198 - mae: 42.6198\n",
            "Epoch 11/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 42.4797 - mae: 42.4797\n",
            "Epoch 12/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.5537 - mae: 41.5537\n",
            "Epoch 13/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 42.0972 - mae: 42.0972\n",
            "Epoch 14/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 41.8647 - mae: 41.8647\n",
            "Epoch 15/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 41.5342 - mae: 41.5342\n",
            "Epoch 16/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.4028 - mae: 41.4028\n",
            "Epoch 17/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.6887 - mae: 41.6887\n",
            "Epoch 18/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.6137 - mae: 41.6137\n",
            "Epoch 19/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.2796 - mae: 41.2796\n",
            "Epoch 20/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.1947 - mae: 41.1947\n",
            "Epoch 21/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.2130 - mae: 41.2130\n",
            "Epoch 22/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.0893 - mae: 41.0893\n",
            "Epoch 23/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 41.2019 - mae: 41.2019\n",
            "Epoch 24/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.9989 - mae: 40.9989\n",
            "Epoch 25/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.0131 - mae: 41.0131\n",
            "Epoch 26/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 41.0654 - mae: 41.0654\n",
            "Epoch 27/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.8764 - mae: 40.8764\n",
            "Epoch 28/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 41.0545 - mae: 41.0545\n",
            "Epoch 29/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 41.0480 - mae: 41.0480\n",
            "Epoch 30/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.8807 - mae: 40.8807\n",
            "Epoch 31/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.2695 - mae: 41.2695\n",
            "Epoch 32/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.9949 - mae: 40.9949\n",
            "Epoch 33/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.0760 - mae: 41.0760\n",
            "Epoch 34/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.2471 - mae: 41.2471\n",
            "Epoch 35/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.6102 - mae: 40.6102\n",
            "Epoch 36/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.1093 - mae: 41.1093\n",
            "Epoch 37/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.8191 - mae: 40.8191\n",
            "Epoch 38/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.2485 - mae: 40.2485\n",
            "Epoch 39/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.0625 - mae: 41.0625\n",
            "Epoch 40/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.5311 - mae: 40.5311\n",
            "Epoch 41/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.5497 - mae: 40.5497\n",
            "Epoch 42/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.4322 - mae: 40.4322\n",
            "Epoch 43/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.5367 - mae: 40.5367\n",
            "Epoch 44/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.2487 - mae: 40.2487\n",
            "Epoch 45/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.5152 - mae: 40.5152\n",
            "Epoch 46/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.3702 - mae: 40.3702\n",
            "Epoch 47/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.4769 - mae: 40.4769\n",
            "Epoch 48/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.1532 - mae: 40.1532\n",
            "Epoch 49/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.7291 - mae: 40.7291\n",
            "Epoch 50/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.1536 - mae: 40.1536\n",
            "Epoch 51/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 40.2711 - mae: 40.2711\n",
            "Epoch 52/100\n",
            "5/5 [==============================] - 0s 6ms/step - loss: 40.6572 - mae: 40.6572\n",
            "Epoch 53/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.6573 - mae: 40.6573\n",
            "Epoch 54/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 40.6894 - mae: 40.6894\n",
            "Epoch 55/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 41.2771 - mae: 41.2771\n",
            "Epoch 56/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 41.8519 - mae: 41.8519\n",
            "Epoch 57/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.7903 - mae: 40.7903\n",
            "Epoch 58/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.3128 - mae: 40.3128\n",
            "Epoch 59/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.7198 - mae: 40.7198\n",
            "Epoch 60/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.1478 - mae: 40.1478\n",
            "Epoch 61/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.1116 - mae: 40.1116\n",
            "Epoch 62/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.7800 - mae: 40.7800\n",
            "Epoch 63/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.7242 - mae: 39.7242\n",
            "Epoch 64/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.1465 - mae: 40.1465\n",
            "Epoch 65/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.6887 - mae: 39.6887\n",
            "Epoch 66/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.2840 - mae: 40.2840\n",
            "Epoch 67/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.5541 - mae: 39.5541\n",
            "Epoch 68/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.7378 - mae: 39.7378\n",
            "Epoch 69/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.9784 - mae: 39.9784\n",
            "Epoch 70/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 40.0016 - mae: 40.0016\n",
            "Epoch 71/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 40.0913 - mae: 40.0913\n",
            "Epoch 72/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.2547 - mae: 39.2547\n",
            "Epoch 73/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.6828 - mae: 39.6828\n",
            "Epoch 74/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.5373 - mae: 39.5373\n",
            "Epoch 75/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.6265 - mae: 39.6265\n",
            "Epoch 76/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.3110 - mae: 39.3110\n",
            "Epoch 77/100\n",
            "5/5 [==============================] - 0s 5ms/step - loss: 39.1599 - mae: 39.1599\n",
            "Epoch 78/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.7550 - mae: 39.7550\n",
            "Epoch 79/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.2542 - mae: 39.2542\n",
            "Epoch 80/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.6968 - mae: 38.6968\n",
            "Epoch 81/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.5442 - mae: 39.5442\n",
            "Epoch 82/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.8686 - mae: 39.8686\n",
            "Epoch 83/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.1693 - mae: 39.1693\n",
            "Epoch 84/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 38.8840 - mae: 38.8840\n",
            "Epoch 85/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 38.8887 - mae: 38.8887\n",
            "Epoch 86/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 38.6614 - mae: 38.6614\n",
            "Epoch 87/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.8399 - mae: 38.8399\n",
            "Epoch 88/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 38.6604 - mae: 38.6604\n",
            "Epoch 89/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.7559 - mae: 38.7559\n",
            "Epoch 90/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.5442 - mae: 38.5442\n",
            "Epoch 91/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.3247 - mae: 38.3247\n",
            "Epoch 92/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 38.8431 - mae: 38.8431\n",
            "Epoch 93/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 39.1137 - mae: 39.1137\n",
            "Epoch 94/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.1463 - mae: 38.1463\n",
            "Epoch 95/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.3998 - mae: 38.3998\n",
            "Epoch 96/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.5599 - mae: 38.5599\n",
            "Epoch 97/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 38.1038 - mae: 38.1038\n",
            "Epoch 98/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 39.0081 - mae: 39.0081\n",
            "Epoch 99/100\n",
            "5/5 [==============================] - 0s 4ms/step - loss: 38.3056 - mae: 38.3056\n",
            "Epoch 100/100\n",
            "5/5 [==============================] - 0s 3ms/step - loss: 37.9976 - mae: 37.9976\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fc85cd32ed0>"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FYHvt7fRWBUL"
      },
      "source": [
        "Okay, it seems like our model is learning something (the `mae` value trends down with each epoch), let's plot its predictions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qUf5DL_fWMZA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 428
        },
        "outputId": "57e72e13-e55b-44ed-a3d0-5a9e50bb933d"
      },
      "source": [
        "# Make predictions with our trained model\n",
        "y_reg_preds = model_3.predict(y_reg_test)\n",
        "\n",
        "# Plot the model's predictions against our regression data\n",
        "plt.figure(figsize=(10, 7))\n",
        "plt.scatter(X_reg_train, y_reg_train, c='b', label='Training data')\n",
        "plt.scatter(X_reg_test, y_reg_test, c='g', label='Testing data')\n",
        "plt.scatter(X_reg_test, y_reg_preds.squeeze(), c='r', label='Predictions')\n",
        "plt.legend();"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V-LGK_jQYUcA"
      },
      "source": [
        "Okay, the predictions aren't perfect (if the predictions were perfect, the red would line up with the green), but they look better than complete guessing.\n",
        "\n",
        "So this means our model must be learning something...\n",
        "\n",
        "There must be something we're missing out on for our classification problem."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RZqShArhUh6d"
      },
      "source": [
        "## The missing piece: Non-linearity\n",
        "\n",
        "Okay, so we saw our neural network can model straight lines (with ability a little bit better than guessing).\n",
        "\n",
        "What about non-straight (non-linear) lines?\n",
        "\n",
        "If we're going to model our classification data (the red and clue circles), we're going to need some non-linear lines.\n",
        "\n",
        "> 🔨 **Practice:** Before we get to the next steps, I'd encourage you to play around with the [TensorFlow Playground](https://playground.tensorflow.org/#activation=linear&batchSize=1&dataset=circle&regDataset=reg-plane&learningRate=0.01&regularizationRate=0&noise=0&networkShape=1&seed=0.09561&showTestData=false&discretize=false&percTrainData=70&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularizationRate_hide=true&discretize_hide=true&regularization_hide=true&dataset_hide=true&noise_hide=true&batchSize_hide=true) (check out what the data has in common with our own classification data) for 10-minutes. In particular the tab which says \"activation\". Once you're done, come back.\n",
        "\n",
        "Did you try out the activation options? If so, what did you find?\n",
        "\n",
        "If you didn't, don't worry, let's see it in code.\n",
        "\n",
        "We're going to replicate the neural network you can see at this link: [TensorFlow Playground](https://playground.tensorflow.org/#activation=linear&batchSize=1&dataset=circle&regDataset=reg-plane&learningRate=0.01&regularizationRate=0&noise=0&networkShape=1&seed=0.09561&showTestData=false&discretize=false&percTrainData=70&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularizationRate_hide=true&discretize_hide=true&regularization_hide=true&dataset_hide=true&noise_hide=true&batchSize_hide=true).\n",
        "\n",
        "![simple neural net created with TensorFlow playground](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-tensorflow-playground-simple-net-linear-activation.png)\n",
        "*The neural network we're going to recreate with TensorFlow code. See it live at [TensorFlow Playground](https://playground.tensorflow.org/#activation=linear&batchSize=1&dataset=circle&regDataset=reg-plane&learningRate=0.01&regularizationRate=0&noise=0&networkShape=1&seed=0.09561&showTestData=false&discretize=false&percTrainData=70&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularizationRate_hide=true&discretize_hide=true&regularization_hide=true&dataset_hide=true&noise_hide=true&batchSize_hide=true).*\n",
        "\n",
        "The main change we'll add to models we've built before is the use of the `activation` keyword.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p54Sk5WeYue9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2c0e291b-3cb1-435b-e117-88b1f2cec8fd"
      },
      "source": [
        "# Set the random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model\n",
        "model_4 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1, activation=tf.keras.activations.linear), # 1 hidden layer with linear activation\n",
        "  tf.keras.layers.Dense(1) # output layer\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_4.compile(loss=tf.keras.losses.binary_crossentropy,\n",
        "                optimizer=tf.keras.optimizers.Adam(lr=0.001), # \"lr\" is short for \"learning rate\"\n",
        "                metrics=[\"accuracy\"])\n",
        "\n",
        "# Fit the model\n",
        "history = model_4.fit(X, y, epochs=100)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n",
            "  super(Adam, self).__init__(name, **kwargs)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "32/32 [==============================] - 1s 1ms/step - loss: 4.2380 - accuracy: 0.5000\n",
            "Epoch 2/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 4.0223 - accuracy: 0.5000\n",
            "Epoch 3/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 3.8296 - accuracy: 0.5000\n",
            "Epoch 4/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 3.7654 - accuracy: 0.5000\n",
            "Epoch 5/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 3.6464 - accuracy: 0.5000\n",
            "Epoch 6/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 3.4960 - accuracy: 0.5000\n",
            "Epoch 7/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 3.3804 - accuracy: 0.5000\n",
            "Epoch 8/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 3.2279 - accuracy: 0.5000\n",
            "Epoch 9/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 2.7024 - accuracy: 0.5000\n",
            "Epoch 10/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 2.4002 - accuracy: 0.5000\n",
            "Epoch 11/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 2.1984 - accuracy: 0.5000\n",
            "Epoch 12/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 1.3257 - accuracy: 0.5000\n",
            "Epoch 13/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.0542 - accuracy: 0.5000\n",
            "Epoch 14/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.0261 - accuracy: 0.5000\n",
            "Epoch 15/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.0069 - accuracy: 0.5000\n",
            "Epoch 16/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9914 - accuracy: 0.5000\n",
            "Epoch 17/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.9776 - accuracy: 0.5000\n",
            "Epoch 18/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.9656 - accuracy: 0.5000\n",
            "Epoch 19/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9549 - accuracy: 0.5000\n",
            "Epoch 20/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9448 - accuracy: 0.5000\n",
            "Epoch 21/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9357 - accuracy: 0.5000\n",
            "Epoch 22/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9269 - accuracy: 0.5000\n",
            "Epoch 23/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.9190 - accuracy: 0.5000\n",
            "Epoch 24/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.9115 - accuracy: 0.5000\n",
            "Epoch 25/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9046 - accuracy: 0.5000\n",
            "Epoch 26/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8976 - accuracy: 0.5000\n",
            "Epoch 27/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8912 - accuracy: 0.4990\n",
            "Epoch 28/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8850 - accuracy: 0.4960\n",
            "Epoch 29/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8790 - accuracy: 0.4950\n",
            "Epoch 30/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8732 - accuracy: 0.4950\n",
            "Epoch 31/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8678 - accuracy: 0.4870\n",
            "Epoch 32/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8623 - accuracy: 0.4790\n",
            "Epoch 33/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8573 - accuracy: 0.4750\n",
            "Epoch 34/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8525 - accuracy: 0.4730\n",
            "Epoch 35/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8477 - accuracy: 0.4650\n",
            "Epoch 36/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8432 - accuracy: 0.4590\n",
            "Epoch 37/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8388 - accuracy: 0.4560\n",
            "Epoch 38/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8347 - accuracy: 0.4470\n",
            "Epoch 39/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8305 - accuracy: 0.4420\n",
            "Epoch 40/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8266 - accuracy: 0.4380\n",
            "Epoch 41/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8227 - accuracy: 0.4340\n",
            "Epoch 42/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8189 - accuracy: 0.4290\n",
            "Epoch 43/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8151 - accuracy: 0.4280\n",
            "Epoch 44/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.8116 - accuracy: 0.4280\n",
            "Epoch 45/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8082 - accuracy: 0.4200\n",
            "Epoch 46/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8049 - accuracy: 0.4160\n",
            "Epoch 47/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8018 - accuracy: 0.4150\n",
            "Epoch 48/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7986 - accuracy: 0.4130\n",
            "Epoch 49/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7956 - accuracy: 0.4140\n",
            "Epoch 50/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7926 - accuracy: 0.4170\n",
            "Epoch 51/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7897 - accuracy: 0.4200\n",
            "Epoch 52/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7870 - accuracy: 0.4210\n",
            "Epoch 53/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7843 - accuracy: 0.4280\n",
            "Epoch 54/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7817 - accuracy: 0.4350\n",
            "Epoch 55/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7791 - accuracy: 0.4480\n",
            "Epoch 56/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7766 - accuracy: 0.4510\n",
            "Epoch 57/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7742 - accuracy: 0.4530\n",
            "Epoch 58/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7718 - accuracy: 0.4530\n",
            "Epoch 59/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7696 - accuracy: 0.4550\n",
            "Epoch 60/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7674 - accuracy: 0.4570\n",
            "Epoch 61/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7654 - accuracy: 0.4560\n",
            "Epoch 62/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7634 - accuracy: 0.4600\n",
            "Epoch 63/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7613 - accuracy: 0.4610\n",
            "Epoch 64/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7595 - accuracy: 0.4640\n",
            "Epoch 65/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7577 - accuracy: 0.4590\n",
            "Epoch 66/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7558 - accuracy: 0.4630\n",
            "Epoch 67/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7541 - accuracy: 0.4620\n",
            "Epoch 68/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7524 - accuracy: 0.4640\n",
            "Epoch 69/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7507 - accuracy: 0.4660\n",
            "Epoch 70/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7491 - accuracy: 0.4660\n",
            "Epoch 71/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7475 - accuracy: 0.4680\n",
            "Epoch 72/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7460 - accuracy: 0.4710\n",
            "Epoch 73/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7445 - accuracy: 0.4720\n",
            "Epoch 74/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7430 - accuracy: 0.4740\n",
            "Epoch 75/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7416 - accuracy: 0.4730\n",
            "Epoch 76/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7403 - accuracy: 0.4750\n",
            "Epoch 77/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7390 - accuracy: 0.4730\n",
            "Epoch 78/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7377 - accuracy: 0.4720\n",
            "Epoch 79/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7365 - accuracy: 0.4730\n",
            "Epoch 80/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7353 - accuracy: 0.4760\n",
            "Epoch 81/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7341 - accuracy: 0.4740\n",
            "Epoch 82/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7330 - accuracy: 0.4750\n",
            "Epoch 83/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7320 - accuracy: 0.4790\n",
            "Epoch 84/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7309 - accuracy: 0.4790\n",
            "Epoch 85/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7299 - accuracy: 0.4810\n",
            "Epoch 86/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7290 - accuracy: 0.4820\n",
            "Epoch 87/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7280 - accuracy: 0.4850\n",
            "Epoch 88/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7271 - accuracy: 0.4850\n",
            "Epoch 89/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7263 - accuracy: 0.4870\n",
            "Epoch 90/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7254 - accuracy: 0.4880\n",
            "Epoch 91/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7246 - accuracy: 0.4900\n",
            "Epoch 92/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7238 - accuracy: 0.4890\n",
            "Epoch 93/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7230 - accuracy: 0.4890\n",
            "Epoch 94/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7223 - accuracy: 0.4860\n",
            "Epoch 95/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7215 - accuracy: 0.4860\n",
            "Epoch 96/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7208 - accuracy: 0.4860\n",
            "Epoch 97/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7202 - accuracy: 0.4880\n",
            "Epoch 98/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7195 - accuracy: 0.4870\n",
            "Epoch 99/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7188 - accuracy: 0.4870\n",
            "Epoch 100/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7181 - accuracy: 0.4850\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TTNzKBvwf2uJ"
      },
      "source": [
        "Okay, our model performs a little worse than guessing.\n",
        "\n",
        "Let's remind ourselves what our data looks like."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RcwI7-s1f2a4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "e26867ca-50ab-49b3-ae69-840ca57fdb2e"
      },
      "source": [
        "# Check out our data\n",
        "plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdYlBu);"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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exfq/j3ldNxgk5vxxG7ExFh+9qgZVVVFl2etluW7Usxz+aaaXgNaFhxLTvjmnVm0MOEBONBowVYulONXbwC2ZTaiKUhoNrMoynX98h5grWpK/9xBhDWoTWqdmmePn7thH4ZF0olo3IaRmYkBrutzQvHQuEXJ3HWBhp+GlnjG2E5msvvkJ2o5/mgb33uzVXlVVVt/8hKfuuEQgq04XOZt3407lWPa8crGNvG37fN6L7daOlq+PZW7jQWW+NARRRGc2YYqPwRQfQ1i9WuV+3vOJ0yWjk8QKeahUhpMnfbtn6nUiWVnF51XgCyXqtXNp/tKDpM1YhKuwGLUk2EyymGg7/hnqjbqBzDWb2Tfhf5xa/jeOnDx3G19/a1FEZzFhTT/pc/4zthPlrGRwq296DHSSW8Vmc5DQswM9Zn7hVYTGkZPHssGjyd2+H1EnITucJN98FR2/eUPz9w8CTeBfRGx/6WMvN0i52MrWpz/AVC2enE07sSRVo9aIwRgiwig8lIb9dLb/AYM43dlP5/i8nrV2C4e+nYpSzg5QNOhJvuXqgOcDt3D8beoO9u7NpEnjOG66sQXx8ZVTASxdfojxH63m+IkCwkKN3HF7G+68rU3Agv/kyUKOHM2ldq0IqiWEBT1/h/Y1OJaeh8vl+btXVBVZVliy9CB1kqOoW/ffM26GJicxeOtMdr35JSeX/42lZiLNnhlDtX5dAIjv2o74EvVP5upNLBt4j5cBGsBSuzq2k6dLXxqBoMoKyAquEpXhiUVrmBLRjriubWn27L0kDugGwNo7nyFn824Uh5Mzo6f+/ieRrRrT+NE7KvHpLy80lc5FxPTq3bAd95FUThSQTEbkYhuSxYyo19Fvxc8YoiOY03CgX9e5KkEUqXPbUA7/+Ifv2wY9iCKt3niMJo8HHmB9ICWLUaOn43DKOJ0Ker2EwSDy/cTrqF8vJqAx8vNtzFtwgKNpubRoVg1LiI5nnluEzf7Py8lk0nHHbW24954OZY7ldMq8OG4Jy1cexmCQcDhk2rapTnSUiWPp+bRvW4ObR7Qkppwd+omTBdx062SKihzIsvu7ZzRKJMSHcupUEZJOQHaptG6dyPh3B2EyXVh7MlVVWdTtZrI37y41QAuShC48BNXh8vkiqCiSxUSb95+mzq1DmRbbyad7b2i9WgxNCc7D6FJH0+FfIizodCNZ67cH1Da8cV2G7JnHjFo9saad8N9QENyGuSB2ZWcT27k19e+9iY0Pvur1ZRf0epo9O4b6o4d7eI4Ewt33zmDLVu90S6EhBtq0TmT4Dc3p2qW23/4pB7MYNWY6LpeKzebCYtbjkhUcDu/PabHoWbZoFHqd7xKAsqzw+FPzWLU61e98Br2IxWLg1//d6HPnX1TkICu7mMRqYZzOKuab7zby98Z04mIshIQa2LAx3WNtBoPE9dc05aknuuNwyAgiftf3b+MqKmb7yxM4/OMfKE4X0R2ac3r15vOSRkMyGxm8cw6zGwz0GXdgjI/m+pNrq3zeixlN4F8ipM9Zxl8jHvMMg/eTbl0yGRm0bSZzWwxBdfhXt+ijwnHmFbq/TIKAqNe51TMBPBe6sBAGrJ5EWINk/mw1lKLUjFL9rGQxUX1QT7pPnVDOKN6oqkqHLl+687j4wWTScdstrbh/jHfhtD9m7eaNt1eU7qDLw2iUmD3jH4Op0yWzYGEKS5YeRFEU0jPyOXTYf176M0iSwOBBjXjlxT6l1/buz+ThsXPIyrKWtnng3o7cdUfb0jZdenztceo4g9mso3GjOLZtP4EgQJdOtXjp+V7ExIQE9Ln+LRZ0Hk7Wum3nbfzqw/qSMWuJz+e8zh3X0PmHd87b3BcjZQl8zdpxEVFjSG/affQc+shwJIsJ0WREF+5fp5236wCqs4ydu+AOgy/dOakqgiQS162tO3WCTiKqXTME/TlqBVEkrls7rt6/gMgWjZBMRgaun0KjsXcQUieJ8Cb1aP32k3T9bXxAn8vhkJHPcv0TBAGjsezdrM3m4sf/bSUry/NUMWvOXt55f1XAwh7cO+fICLeR8PCRHG6+dTJvvL2cFauOsGr10YCEPYAsq8ybv5+J324gN89GZmYRt981rVTYn2nz6RfrWLDwAMXFTqZO3+lT2ANYrS62bD2OoqjIssqq1alcefVPLFqS4r5vc/Ln/P38PGkbu/ecCvjzVjVFh729jqqS43OX+3UsaPDAyPM696XGhaUg1CiX+qOHU/eu67BmnMIQHcH+z35h5yufeh6nBYHQBrXd+vOyduoqXnpR2e7EUjOREUvd5Yn3ffI/tm73TGUsSCLtJryAuVpc6TVDZDht3n6SNm8/GfBn2b7jBG+8vYKDh7KRJIF6daMxm3XUrhVJQnwoR1LLFrR6ncjWbcfp26de6bUvvv4buz1w9ZQkCSQlhbNsxSHmLzzAqr+OeBlUg8HlUvj2h838PmUnffvUw+XyVkOoKrz57nJ043VYrYGnnQD3C+P5lxaRk2Plsy/XI8sqTqeMJIl07VyLt98YgCR57uMKCx0sXprCxs0ZHDyYjcul0LNHMreNbE1EhMnPTIET1bopxxes8n0ziMyh/vBnBBbNRozRkZUa+3JDU+lcJOTuOsCuN74ge8seIps1oNnz9xHdpil5ew8yv/31pZGo4PafHrhuMttfmkDa1Pl+x5QsZp9ZEqPbN+fKDdOQHQ6mxXbyTtolCNS4ujc9Z35R7rpdLoUVqw6zdl0aMTEWhg1pTPXq4RxNy+PmW3/HavORGC1AGWGx6Pno/cE0axpPekY+CfGh9Or/bVDy5cxckiSgqqq/9DRBI0kC0VFmMk9XnRGzPAwGiaef7M61w5oC7tPKzl0neff9VdjsLo9TjygKhIYY+PXnG6leLbxS82Zv2smiHrd4ZEyVLGYaj72DwsPHOLXibwzx0RjCQslavy2o3EplYalVnWFHlv7rrrUXOpof/kVO1obtLO59O4rVjqooFOw7TMa8FfSc/RXrRz3nlZpYcTpx5BWQNm2B3zGbPX8fe97/zuu6aNAT38P9rFiPnfSdV0d1J94qD4dDZswDf3AgJQur1YVeJ/K/n7fyzpsD+GtNKg4/6qZABLYgQEiIntlz9nLfQ7MQBfdFk0mH1Rp4Fa0zcwWjAgoEWVYpKgoul31lcThkxn+8mjatE3nqmQWkZ+Rj8/FCBVAUlfwCO9fe8Asvv9AXvV6kWrUwwkIN1EyK8DollEV0u+b0XfoTW59+j+zNu7FUj6fZiw9Q55ahXm1tp7KY3XAgzvzC0l++oNf59+33hSAgmox0+v6tMoW94nJxYtFqrMczie3ShojG9fy2vVzQdvgXAQu73sTpNVu8rock18Celeu1Axf0OsLq1yZ/z0Gf40lmE8OLtrLlqXc58OWk0tOBIIrowkO4audcLDUScBYWMT2us0+3zrhu7ei/6tcy1z156g4+mrDWS0cdFmqgXr1otm4rw3vIDyEhehQFYqLNJCSEsGlz8IXTRAEknYjTWUXbeT/UrBlB5qkivzr684EgQFiYkcJCR5lG73P7CIKAoqhIknvn/8Jzvejb+/wIyLzdKfx970tkrtmCqJOoNWIwCX07sfHBV1GcLtQATwCi2UTjx+6g1WtjvYKvClJS3dXXCopAUVAVhZrXD6Tzj+9c8oFa2g7/IiZ//2GyNuzwea/oSDpSqLfft+p0kb/vsN8xa1zdC0EQaPPe/xHeqA57PvgOR3YeCX060frNx7HUSABAHxpC3VHXc+iH6ecc1000f/GBMte9aEkKH3y02qdQVVSVaglh6PWnghK6LVsk8PCDnQmx6MnJtfLgI3MC7ns2zZrFc/BQdlBzSxKoqns3GaggPXWykKFXN2b7jpPs23+6QmsNFlWFggJ7UGotVXV7RoH7ZJKXb+fFcUtIqhFBo4axVb7GiKb16b/qVxSXC0EUSwVw7eGDyVq/DUQRuaiYldc9hGLzf0pSrDb2ffQT+hALzZ67z+Peyuse8qrAljZ9EQm9O1Jv1A1V/pkuFi7tV91Fij0rh52vf870al35s+VQ/3lMRNGdFvfcyxZTmcfjVm88Drh3dfVHD+fqvfO5/tRauv32IaF1PXOZtPvoOeqPGeH2CirJk9Jx4uulEZBnyMjI50BKlltnv/IwL7+y1K9AVRW4alBDjMbA9xuCAI8/2pXWLavxw0+beejRigl7UYTeveoiCr4ffZ3OfV0nCeh1Im1aJdKhfQ3uv7cjSxfcxTdfDiNQlbHdITN77j6aNonj+Wd6XnBBVGXhcMj8Mun8uVoCiDqdx25bZzaR0KsjCT06cPrvHWUn7CtBLray+/1vPa4VHk6jMOWo13dALrZy4PNJVbP4i5SL5wm8TDi1cgPLrxoTWCUpRUGUJDCbUErylIgmI6G1qqMLtfjUs8f37EBYff8BS+ci6vW0+/A5Wr/zJM78QozRkR5f0mPpeYwaPYPTJe6RogiRkeYy1RiWED1dOtfi1Zf78vhT8wJah0EvERZm5I9Ze1i89FCFHT8EQSAhLpQJH17FI4/Pde9sVXC6FO4e1Q6HzcWu3ado0CCWm4a3ILGaZxDVwsW+1WT+sNlczJ23n/vHXMGatUdZuz4NWXZHDkuSQEFB1er5DQYJZ1muuAGiKCoZx/M9rjmdMq++sYyFi1NwuRT0ehGXS8FiMXDt0KbcNKIF3/2wieUrj2Ax6xl+Q3NuGt4iKHsAQPbmXex5d2LAOn1nbgGOgkLSpi4ga/129FFh+Hsru6z/QSnOCwhN4F8AOAsK2f7ixxz+ZRaOrLzg3NhEgWr9OmPPzMZVWEyt4YNo/OgdFB5KY1GPW1DsDhSHE9FoQDIbueKrVyu0RslgQDqnapGiqNx062SKi51nXYPs7LLro4aGGBAEgclTyzf8ls4viTgdMpN+3x6wSsUXsqzyw/82M+l/I1g87y7W/Z2G1erkig5JREWay+2/cFFK0C8bg17ixMlCPnh3ELv3nGLL1uPExljo2aMOA676gcJC/0JfkgSfBmVBAKNBwmaX0enOCF49cbEhHEvPC8gIXZY3lE5y6/SXLj9Ej27J6HQit981lX0H/qlf63C4T3CFhQ5+n7qd36fuQFFUXC6FLOCzL9eza/cp3nytf7lrOZsjv852F5oPEEvtGvzZfAiOrDxcRcUIBr3PU7FoMpJ88/lJQX2xoAn8f5HiYydIm76QorQTOLJyUGWF6kN6seuNL8nfe8gji2CgKHYHit3JwLWTPa5HtW7CVbvmsv/Tn8nZuoeYK1rS8MFbPHznA2XX7lPMnL0Hl0uhT6+6dOlcC1EUWLnqiIewD5Rj6fkUFNjZtj1wg6vRpKNevWgKg/B88VcFMD2jgHV/p9GlUy16dEsOeDzAHdnscy6BOslRHDqc7SVEHU6ZGjXcro9Nm8TTtEl86b1+ferxx6w9Psds1TKB3XsyfQrv6tXDef2VfsTHhrBqdSrHT+TTskU1fv1tO6lH/ccvCAJER5u55aZWWG0u/vfLVp+ePC5ZZeu2E+zes4jk2pE8+389PIT9uZwR/mdjs7lYuvwQacfyqJkUeN2BYDx2RKOesPq1OLV8fam/fqnR90zkuMOJLsRCSN0kGo29vBOtaQL/X+LQTzPYcO/LKC6XRyBJ6u9/uv2SK6ijEA16ots183kvpGYibd55qkLjgjvFwJj7Z7Jt+z/eNDNn7yG5dhQ/fns98xfuL6N32WzcnI5BL5XrQqnXCUg6iTdf648kifTuVYffJ5d/MjAYJNq3rcGadUe97tntLvYfyKJLp+BTNA++siGTp+70yHsjigKtWlbjuad7cttdUz0EqMmk48oBDfyeHu4Z1Z5FS1IoKvJ8cSYlhfPqy30ZPvJ3n/2cTplWLdz5iYbf0Lz0+kuvLPG7doNBom+fujz5WLfS9QjA19/694ZzOGQOpGTxwsuL/bYpC71OZM/eTGomReB0yWzechyX0514zmz2XQeh1ojBpEyc4jNGxAtB5NTyv30HZ6kqUW2aEFq3JtUGdCN55BAkQ8Wqil0qaEbbfwHbqSw23Pcyss3u9WAqdkelIhEVh5OMeSvIXLO5ssv04qlnFngIe3Av9UhqDq+8vpQly3zUSi2HM6rVl15ZQnE5UaZ6vcg9ozowY3mVbrEAACAASURBVPJIOnZIAuDh+ztjNvvep7gNrQJj7m7PyiX3MHBAfZ9tjUYdSdUrFmx07z0dqJMchcWiR5IELBY90VFmXn25L/XqRvPFp0Np2iSu1D3ytpGtee7pnn7Hq54Yxu8/j2DokEbExlqoVSuCZ57qzqxpt5JUI4LoKG8vLL1OpHfPuj7Hi4n2na3TZNLx17LRvPFK/1Jhr6oqP08qv7ShqrpPRRVBUVUSq4WxZetx+l/5A08+PY9nXlhEv0Hfl6aIOJe4zm2oN/pGJIsJRBFBr0MyGenw5SsYY6M8x7fZUV3+Nw1Z67eTOmkuG+57iY0PvYqzqBhVVTm9biv7JvxE2vSFyI5/N17iv0Tzw/8XSPlmCpvGvuERDRsQbgdpt1tLOX8myWKi/1+TiG7TtOILPYujaXlcc8MvVTJWRTCZdNxxaxvuHe2dtjg/38YTz8xny5YMFAVq1Yygc6ea1KgeTp/e9aie6Da0Wm1OhlzzM3m5NpSS51ySBGKiLcyecSt6fcWyTyqKyrq/09i37zTVq4fRu2ddDIbzk8ly0+Z0Hn5sLi6XgsulYDLpiAg38utPw4mK8j41zJ67l7feXel1yrjxumY89mhXj7ZFRQ669/nmvKwbQKdzq7m++/o6Bg750Uv9ZzRKTP3tZmr4eflmb95F2h+LkUxGao8YjD0rl6X97vSO/A4SY1wUriIrquyuvqULMdP/r0n/eVGeqkLzw/+vUVXUIA2NurAQmjx1D4kDuqK4XCzpdVuZhSVkq50d4z4JKN1BICxdFpw3SqCIouDT6FotIYTsHBs6nYgsK1w7rAn3jGrnc4zwcBMTP7+mJKmY4ldwm016fvjmOl55fWnJSUWgXdvqjHuxd4WF/ZnP0KVTrQqphIKlXdsaTJl0E1Om7STtWB7t2tZg6FWN/RY8HzK4EVlZxUz8bhOgoigqQ4c05uEHO3u1NZv1mEwSNlvlvXrArTKKjDCRm2dDVVVatajGiBtb8Mes3T7bK7LKnD/3+a1FEN22GdFt/1FXOrIDS2JXHvbMf4r5KHYHriIrf40Ye1kUWNcE/nnm1F8b2fvhD6Vuk4Eg6HQM2vKHx46jxx+fs370C6UFoL1QVXK3+y5DWBGcPpJ+VRa93q1B9CXwk2tHMfW3QZw4WUBCfCghIeXrWkVRQBTLFtw1kyL45strsdqcCAgXlS/8GWpUD2fsw10CaisIAnfe3paRN7Xi5KlCYqItWCy+deWiKHD3ne357Ev/BeyDwemU6devHreNbM3EbzYwZ95+9u4/jc3m8siGWtrepZBfEHgO/ai2zdBZTF47fCnETEynVj5rLgeEopC38wDWE5kVcmq4mNB0+OeR3J37WTbwbr8pDnwhGA00fuIuD2Ev2x0c+GISjpx8t17TDxFNqy4UPj09r8rGArdwMZv0iD78o00mHQP6N8Bi0VO3TnRAwj5YzCb9RSnsK4rBIFEzKcKvsD/DqDvbct/o9qUBZ5VGhXnz9zN3/n4cDpnCQgcul+LTTGU26+heRhGbcxElie4zPkMXFoIUYkHQ6ZAsZqoP6kHfhd8T26WtX//7cpftcpE2YzFKGfaASwFNh19FOPML2T7uE1J/nQMCJN9yNUVpJzg2dYHvBGQ+kELMxHZsRa+5XyOZjKXXtz77Afs+/rHMikKSxUTfpT8R27FV6bXiYidr1x/F5VLo3LEm4eGBp8LtPeA78vIqH6QiCG4jaeeONXns0S5s3pLBW++uwumUURQVs1lHg/oxTPzimkqpWTQqh6qqJaUkRV5/azkzZvp2FS0LnSQiiASUskKnE6mZFM7H468iqUbgLptAaWJA++kc4nt1JPaKlgAosszBiZPZ8tS77uprFRBt+ogwes//hthOrYPvfIGgVbw6zyiyzPx215G35+BZPsDuWp/BFHTu+tt4ao/wDgyZGtsRR5Yf/aUgEN6oDu0mvEBi/3+McqvXpPJ/zy1AFARU3GX6nvu/nlw9pHFAa2nb8fOA1w0wckRLps/c7WUsfOj+joy8qZVH2wMpWUz/Yxc5OVZ696xLnz51L5jyfRqwdt1RnnpmQbleVGcTbNp7QXAH00mSwONju3Ljdc3L7xQgssPBkf/NJOXryeTtTsFVGFyKan1EKNceX43OXPlaAf8FmtH2PHN83koKUlI9s/yp/gs3+EP04yMs+9P/CwI3Fm5Gb/F0xcvPt/HUswu8AmrefHcFrVsnegXBHEvP5423l7Nr9ynCw4yMvKkl1RNDyTheWOZ6BQEiI0y8/EJvenSvQ9Om8Uz4bC2ZmUVEhJsYfU97brqxhVe/BvVjePrJHmWOrfHf0fGKmiQnR5JyMNtnDeAziKLb9bSgIPDMnGdQVUo8j+CDD1fTs1sy8fH+q7cFg2QwUO/uG6l3942cXr+NhZ2GB7c2WSFj7nJq3XClz/tFqenk7T1EeMNkQuvU9NnmQkUT+FVA9uZdwbtcnoskEtG8gc9b1fp1IX3Oci9jbUyHFl7CHmDZisM+VZl2u8zd986gc8da1KsXhdGgY87cvezak1naprDQwYcT1tC8WTzZ2TafOXFMJh1PPtaVPr3rlZYGBHdQ0uArG+J0ydqO/SJGFAUmfnENE7/byOy5ez1KNJ7BbHa7zf74vy2VSnUBIAoCK1Yd4cbrq26Xf4aYK1oGffxQFQVnnnfcgexwsOaWJ0mfsxzJaECxO6g2oCvdfv/IQwV7IaMZbauA0DpJ3nVfSxAk0Z2AvRyqDehGeINkn/faffgchsiw0odKNBrQhYX4zYtjs7n8fglPny5m9ty9fDRhLe+8v8pD2J9BllV278nk0Yc7UzMpojQcQK9zH8G7dK7F0CGNPYT92WjC/uLHbNbzyIOdWfTnXTz9ZHeMRneyN0FwC/ue3euwfccJnxXLgkaosK21/KEFd64pfykxfKEqKgl9vd1Yd7w0gYy5y1Fsdpx5Bcg2OycWrmbr0+9X4YrPL5rArwJq3nClu36sDwSdrnzjkSQR3jDZ7+3QujUZsm8+zV64nxpD+9DkyVEM2TOPqNZNfLbv0rny/uGKohIRbmLmtFv4c+btREdbEEsSaq1bn8ZNt06mIAiXOo2LlxE3tuDnH27k1pGtGH59cz58fzBvvNrPbzWtYFEUlZ496pB5uoinn1tA5x5f0aXn14x7bSn5+ZV3HGj/yYvoI8LcRQ3KQTKbqDvqekzxMV73Dnz1u5fjhGyzk/LtFC5UW+i5aEbbKuL0+m0s7HKTbx/5AJAsJm7I3oBkrBqXxAmfruXnSVsrXJD7zLG+TetEHnp0Nuv+PuZxatDrRYYOaczzz/SqkvVqXHxMnb6T8R+vqbDgPxOd/MSjXcgvsPPlxA0eieIEAWrVimTabzcjBnBKLgvriUy2PPUeqZNmo54bEyBJhNRMxBgbSf6+w6hOF4osE9+zA11/HY8pLpqCg0eZ3WCAb9WQIHCza/cFU0lLM9qeZ45Onc+Gh1/7R9gLAqJBV5IULcBBFBVHTl6VBH4cSMliyvSdFRb2AFGRJlq3qobTKbN+wzEvFZHTqbBgYYom8C9jhg5pwuy5+0g56K5ZfEZVbjCIJCVFkJFRgCgKuFwKtWtFkJNjxelS6dCuBvXqRhEWZqRbl9o88fR8Dh7K9hpfVSE1NZf2nb/AaJSIiw2hb5+63Hpza2JifOcM8oe5Whydf3ybnC27KNifiuJ0O1gIooghOpw27z/F2tuf9qjsdnLxWqYndqPRY3eQ8tmv+Psyx3RshavYSuqkueTu3E9Uq8bUHjEYXUhwa/w30Hb4leT4otWsGHqfdyk2UUQ06FF81IP1hSEqgusy17oLmlQCVVUZev3PpKdXLNnVGebNvp2E+FCcTpkuPb/2maI3JETPqqWjKzWPxsWN0yWzbPlhVq9JJTrawrVDm1CrViTgzkqacbyA2BgLYWH/GDUzMvJLHQucToXPvlyPK4jIbkGA665tytNP9Ag6YMyencvGh14lbdpCVFkmoV8XrvhiHGtueZLTa8tPJOeBJKIzm+j623jWj3oeV1ExriIrulALurAQrvx7KpakasGNWQVoO/zzyI6XJ/iuu6koAQt7yWKi1dtPVFrYgzvpWWZmcH7H5xIVZSahxEVOr3enGd6wKd1jl6/TifTvW79S82hc/Oh1EgP61WdAP+9nwWjUUSfZM7vlr79t45PP15VqRlwupUIunTNn7cFk1PPE2K7ldzh7TdGRdP11fEmlM7VUDVOUmhHUOODW9/dZ+hM7x03AXlLfAsBVWIzLamPjo6/TY9qnQY97PrkwlE4XMQUHvfOtl4dkNhLTsRWGqAgiWzWmy8/v02DMiCpZjztnScVPbaIInTomeVx78fneREeZS8P0LRY91RPDePQhb08GDQ1/HD2ayyefr8Nul3E43P8q6tLpcqlMnb6zwuUcBUHw0LnHdGwZ9BhykZWVw+7n+IK/vO0CskLG3BUVWtv5pEp2+IIgXAl8DEjAN6qqvn3O/TuB94D0kkufqqp6/vKyVjGKLHP4xxmkfPU7itNJ8q3DaPjASCSTkahWTTixaLXvjqIAPh5oVVXpNfcrjDFRPjpVjjrJUZhMehyO8k8XidVCycm1Ybe7UFV3OluzSc/9Y67waFc9MYxZ029l6fJDHE3LpUG9GHr0SNbcLzWCYunyQwGVXgwUl0uhqNhJZETln8OWrz7K8fl/+Q9y9IWqYs/O87u/EoKs5ftvUGmBLwiCBHwG9AeOARsEQZilquq5OVF/V1X1ocrO91+wZuTjpM9dURpclbfnEAe++o1aN1xJVOvGnFy2zjuqVgBLUjVsp7I8VD6S2USt4YMqJex96UZlWSE310Z4uJHHH+3CuNeWlTvO2Ee6EB8fyg8/bSY9vYC2rRO58442VEsI82prMukYfGXDCq9ZQ0NRVJ/ui/5KUZaHLKusXpPKVYMaVXptkc0bMnD9ZFYMvZ+iI+nldyhBtTt8+vgLBj21b7rw6udW2mgrCEJnYJyqqgNLfn4WQFXVt85qcyfQPhiBf6EYbXO27mFh15s8rPdeiCKgeu/mRQFRr0cfHoojJw/RoKfe6OG0efepoEutKYqKIMBPP2/l6283ICDgkhUG9KtHo0ZxfP3NBux22R3uHmrkdFZxmcGF/frW5d03fYeOa2icDw4fyWHk7ZOx2z03R0aDxOh72vPb5O2cPh1cxHp5RVSCRVVVMv/axL5PfyZtyvygq9EJOgnJZCS0bk36rfgZQ2TVrCuoNZxno20NIO2sn48BHX20u14QhB7AfuAxVVXTfLS54Dj116bys136u6+o7iLjDgfXnVqLPjw0aMPsjp0neevdFezbfxqdTkJRFI9j8dx5+5nzp2dtWZvN22ir0wnUrhVFYmIod93eljatqwe1Dg2NylInOYrRo9oz8buNuFwKgiAgSQIP3NeR20a25vZb2nBF1y+DGlORVf6ct49rr2mGIiuVzscjCALx3dsT160dv81YhOoMLsZAMhvpMeNzEnp3vGD88s/m3/LSmQ1MUlXVLgjCvcCPQJ9zGwmCMAYYA1Cr1oVRbsycEFPpP5zicFF48Cgx7b0TiZXFkdQc7n1wZmlgiy8DVaAbEFlW+e3n4UgXoF5R4/Jh1J3t6N2rLkuXH0IA+vWpV+rGqdOJtGiewI6dJwMez+lS+H3KTr79fjMI7mIxb77Wn0YNYyu1TkEQSOjTiRML/gqqn2xzUM1HWoYLhar49qcDZ6eMS+If4ywAqqpmqap6xor4DeCzdp2qql+rqtpeVdX2cXEXRuUZfVRE2eqcAJCtNvRhIUH3++nnrRX2QjgXVYXlKw9XyVgaGpWhTnIUd9/ZjlF3tisV9md46fnehISUXbTlXHJyrTicbq+fw0dyGH3/H1WS9qPNO08FlYMH8CjJeCFSFQJ/A9BAEIQ6giAYgJuAWWc3EAQh8awfhwLBV1f4j9j23PjKDyIIFcqmt//A6Sr1alix8kiVjaWhcT6oVzeamVNvwWgMTPUpSYLXKdfhkJm34ECl1xLVqjG1hg8KrLEgIFnMtPvoOQDyDxxh09g3WDHsfvZ98j+cBWWnGv+3qLRKR1VVlyAIDwELcLtlfqeq6i5BEF4FNqqqOgt4RBCEoYALyAburOy8/xa5O/aX36gcBL0OfXjwusWmTeLZt79qhL4oQkTExZHCVePyJjragsViwG4v34Cr+nB7djhk9h84XSVraTv+WY7PW4Uzv5zaEKJAvXtuILZTazIWrGLVdQ+hOFyoLhcnFq9h7wffc+WmaefFFTsYqkShq6rqn6qqNlRVtZ6qqm+UXHupRNijquqzqqo2U1W1laqqvVVV3VsV854PZIeDorTjyCVRsuYE76x5HogiLV59lIjmDXz63Qp6HdUHdMMQFVwZN4BePZIrnWv8DHq9jmFX+86uqaFxoWExB7YX9ff1SM/Ir5p1VE+g1dtPIJQTc6LKCilf/kbm+q2su/MZ5GIbakl9XLnYhvX4KXa/M7FK1lQZNAteCaqqsvudiUyL7cScxlcyNaYjW5/7gKbP3YdkMfvtlzigKy1efICrdszh+qy/afjI7YgmI/qIMCSzidhOrej80ztlzm2zudiwMZ1tO06UCvgFiw7w2FPzgvUK80KnEzEadTzzVHfq1yvn5aWhcYEwdEjjShVWz8qqXHqRs7FUjy9TBpxBcThZ1PVmn+VIFYeTtOkLq2xNFUXLpVPCwW+msOPVz5CL/zlG7n7ra6QQM3Hd23JyxQbUc3LmCDodrd5+svRnQ0QY7T9+nuYv3E/u9n1YalYjvGGdMuddtCSFca8tQxQFVFXFYtHTtXMtZs6u/CFIkkRG3tSS0aPaExJSNWmXNTT+DW6/tQ1r1qaxfeeJCm16IvwU56kI1fp1QZUDdJ6QFZRz0yyUoKuA40ZVc1nv8G2nstg34Se2j/uEbS985CHszyAXWclctQljVIRXAQVBJ3Fqxd9efUxx0VTr27lcYZ96NJeXXlmK1eqkqMhBcbGT06eLq0TYgzv6dsYfuzEEaADT0LhQMBp1fDfxWj56fzCdrkgiNEjPnajI8nfkgaILsdD11w+QzCZEkxEq4NosWcw0euT2KltTRbls0yOfWLyGFcMeAFVBtjmCjqg7Q1jDZK7et6BCfT/+dC2/VKJISSBYLHq+/eraSvsla2j8V6iqyuKlh3jh5UU4nYHlYBAEaNUqgTYtq7Pu72OYzXpuvK4Z/frWq3AsivVEJkenzMdVUISzoIi9479317woD0mi/j030Oz5+zm1fD36yHASB3YLOto+ULT0yOegOJ2suvFRnzv6YHEWFFW4b26u9bwKe3Dv8s/ORa6hcTFxJDWHh8bOISfHFlQZQVWFrVtPsnXrP0Fc27YfZ+78fXz0/lUVqqBlrhZHo4dvK/05JLkGG+57udx+ok7EWVDM7IYDEEQRVQXJqKfvkh//db/9y1Klc3rdtvLTJQSAoNORNKxvhft37VIbsynwd65BL/nVTQoCSOc8xJIk0LB+LNUTvZOhaWhc6Miywn0PzuL48QKsVmfp5kioYNFzWXbXY96w8Vil15a9aSebH3+r/IaAYneS+utsFJsDudiGYrXhzC1gUbeRyK6qqQscKJelwJet/7hMVRTRaMAUH02LlyuWAHTajF288dZybPby16HTiTx0f0fW/XUvyxaOolnTOCTJ84k3GnUMG9oYg0EiNNSA2aSjbp0o3n9XS5CmcXGyectxioocXtpWQYB69aKpVi00aMHvcqn8tTq10mvb9c7EKonA3/7CR5VeSzBcdiqdPR9+z7bnPgy4GpVPJJGGj9xG8+fvxxAR/O55wcIDfPDR6oCLP+t0okc2wAkfDuH5lxazaXM6kiRiseh58bne9OyezIP3d2LP3kxioy00aBCDUJGtkIbGBUB+vs1nagNFgUOHcioco1IVHjwF+49UegyAo7/9SZuzPP3ON5eVwM9YsIrtL3xcOWEPhNWvTZt3nqqwMP3qmw0BC3tw++mPe30ZDerHULduNFGRZj6fcDU5OVYKixzUqB5eqpOMijTTpdOFkXhOQ6MytGqV6NdIW5mAxNq1I8tvVA5x3dqRu3M/+HHBDBTZ4aM86nnkslLp7P3gu0obaiWLiV5zvqrUzvnkqeDzarhcMtP/8KwpExVlpmZSRIUMUBoaFzqxMRbuuK01piDsXIHw7AuLmDp9V6XGaPp/96ALsfi9H9mmiduFsyxEkepX9qjUOoLlshL41hOVz6+RfMvVhNWvXeH+TpdMUo3g0yzIskp2TuW9ijQ0LibuH9OR996+kh7datO8WbyX7aoiKIrKe+P/YtLv2ykuDsCt0gchtapz5cZpGKJ9FzjJ3boXxW5H8FP/QjToMUZH0OKVhys0f0W5rAR+9UE9EX34vooGfbm5Ms6Q0LtThef/fcoO+g74ntSj3qHX5aHTCaxZd5Q+A7/j1TeWkZ1ddaHjGhoXMl071+KjD67ip+9uoGGDWMQqsEs5nTIfTlhNvyu/Z+68fRUaI7xBMrLVj0pGVUEFVQBTYjx17ryWzj+/S/Jtw4hq14yQuknINjsLOt7Ijlc+RXFW7MUTLJeVwG/y5CgMMRGIxn+Evmg2YamV6F2T1heiQN6uiqVdXbzkIB9/upbCIgcOR/A57l0ulfx8O7m5Nub8uY9b7pyK1frvPCQaGhcKb78xgOgYMxaLHoOhchHkLpeKze7i9bdWcPhITtD9ZbsDyVyO2sYlY8/MpuUrj5DYvxui0UDOlj0U7D2Mq7AY2/FMdr8zkdU3P1HBTxEcl5XR1hQXzeDts9j30Y9kzFuFJSkBR24BWeu3BTaAoqLYKyZkv/42OEOtAPgzS7lcCvl5Nv6cv5/rr72wCy5oaFQlNZMimDvzNlavPsrJU4WEhxv56eetHDqUjUtWEITgC6K7XDIzZ+9h7MNdSDuWxxdf/c2mLRnERFu464429O9b36uPPTuXBR2H4yws/6StulzMbjgQyWxyp1k+Z4Gy1UbGn8spSEmtlLo4EC4rgQ9gio2m6TNjCElOInvTTjL+XBHY7r6EhAqUL8s8XUTaseDUOOX5IFhtLrZtP6EJfI3LDr1OolfPf/JUDRrY0O3CicDE7zYydfpOZFnF5QpM8suy+/SckZHPLXdMobjYiaKoZGYW8fKrS0lPz+fO29t69Nn23HiKU9MDrnmr2B0odv8eOaJeT+72fZrAr2oKjxxjYcfhuIqKcRUFZwQVDHr0EYEXMrHbXbz0yhKWrTgc8MMXKEaDRHJy5d3LNDQuBcLD3b71T4ztyn2jO5ByMIv/e24hmZnlpz4RBIGePerw7Q+bsFqdHi6fNpuLr7/dyIjhLTCb/kngdnTKfJQgC5yXhSLLhNY7/+7Ul6QOX3E6/ebd2HD/OOync4IW9uB+MELr1iy/YQnjP17Nyr+OVLmwB3cw1rAhWkETDQ1wJ1hbsOgA9z44k4fGzuFAShY/fnttoL1p1iSOzVuP+6wuJ0kCaUfzPK75876pCIJOR1SrxkS1alxlY/rjktrhZyxYxaaHX6Mg5Si6MAuNHr2DFi8/hFjyx1EVhROL1lQoj45kNlHzhoGYEwLLOulyKcyasxe7vWqKkIui+4UjCALJyVG8+lIfYmL8+wFraFxOvPrmchYuPIC1xE62b/9p5i84QPXEMDKOF5TZV6+XSDmYTX6e71QJTqdCbKznd63O7cPY/+kvZappAiXpuv50/Pq1So8TCJeMwD+9biurrnuoNL+FK7+IvR98hzOvkPYfP+9uJAggChCkDJZCLDR86BZavfZowH0cDrlSO3tJEqhbJ5rTp4to3jyBB+/rSM2kCJxOufT4qqGhAYcOZzN/wX6PzZXN5mLPvkzuvac9H32yrsz+UZEmnnh6Hlart4rGYJDo2rkW0dGeAr/FuIc5tXIj+XsO4grAcAtgTqqGPTPbveEUBGI7tabLL+8RkpQYUP+q4JIR+DvGfeKVzEgutnHw699p8OBIDnz2CycWrsYQFY49Kw/8VbARhH9y40siCf260PV/72GKiy53Daqqsmv3KfYfyKJmUgTVq4eTlpZXbr9z0elEunWtxfh3B3vdM5uDKwShoXGps3lLhs/rVquL48cLeeTBTkz4zL/QT0wM45QfXX/P7smMe7GP13V9aAgD10/h1PL1LL9qDLLVT7qWkih4yWTCkZ2LYncgGg2IBj3tP3mBkKRETq3cwKbH3yJv5wFM8TE0e/4+6o8ZcV7yYF0yAj9v7yGf1wVJKjXSllrUy/g9htZJoujocfdbWFY4vWIDcxoNZMC6yWVWsLLanDw8dg579mSiAqIoEBFu9Hh/BIIoCiTXjuTF53oH3klD4zImMsJcUtTEcxOn14tER1sYNrQJn36xzqe7ZlSkiZSD2T6/o0ajxOOPdvW7yRIEgYTenahz2zAO/TDDZzEUUadDF2rBkVdQmnfnjMfO2tuewlK7BhlzlpW65RWnHWfz42/jyMmn2TNjgvo9BMIlY7SNatXYZ5Js2W7HWVjk6T7lRwCLRgOyw+lOnVzydMg2O47cAjY9+kaZ83/59QZ27jqF1ebCZnNRXOwk83QxtWtFBpXCVZIE3ntrYJWWaNPQuJTp3q22z4LnkiRiMklcfe3PfnfLObk2Cgt96+FVFcIjyi8e1PrtJwmpk4Rk8Va1Kg4njuw8n0nWcrfvJ2P2Mi95JBdb2fXml+clsdolI/BbjHsYyez5C5csZvSRYeDLz/6cB0AQRXQWM9b0E95tVZWTS8vWA86eu9crgtblUjiSmhvUDt9o1JVrZNLQ0PgHo1HHV58NIyEhFItZT0iInvBwIw/e15EvvtpAcbHTp/dNWUiSQId2NTDoy/fGMURFMGjbTKoP6e32rqgCVFnBVgW5v87lkhH40W2a0mfRd8R0bIVoNGCukUDrtx4nqrUf18VzpHBk68YM3DAVQef7+CaVk/nO6awabxyHQ6Z+vZgq3GevagAAIABJREFUGUtD43KhUcNY/px5GxO/vIbPPr6aRfPuZNfuU9gdFfOVl2WVzVsyuGv09HIj5A/+OIM/avQg/Y/FwYf5loEpvurlwCWjwweI69KWgesme1wLb1KP02u2lpsWOX/vIZYNugfV5SN1gkFPjWF9sZ487dcts0f3ZBYuSgl6J3EuPbsnExcXUqkxNDQuRwRBoEnjOAoLHfw2eQdr1h0N6nR9LlabiwMpWfz6+zZG3dHOZ5uMeSvY+MC4Sle/OpcGD95S7iazIlwyO3x/JPbvSpv3/w9dqAVdmH9BKhfbKDyQ6lu/73RybMYiZtbuzbLBo3Hk5ns1GftwF6KjzEHVqPXFnn2ZQRVr1tDQ+IecXCs3jvyNL778m/z8yhU6ArDbZeb86T+b5s7XPg9e2JdXv0IUqHld/+DGDHTq8zLqBUbD+0dyfeY6+q/8BVNiXPADqOAqLEaxOzi5ZC1/DR/r1SQuNoQZU27h0Yc7V6ogSVZWMfv2V73uTkPjcuDb7zaRlVUcUK3oQJHK0MsXpfp2CZXMJqLaNkM0+FARl1OtSzQYMMacn7Qpl4XAB0AQMMZF+3SdCgbF4eTUqo0UpR33umex6Bk0sGGlBL4oin69BjQ0NMpm+UrfeasEAZ+ePOWh04l07lTT76k7pmNLn96BokFHr3lfE9/zCnc69kBd9USBiMZ1CW+QHPRaAxr+vIx6AaGqKttfnsC0mCuY3WAAjqzgi4+ci2jQYzuR6fNeaKihUikPZFmhWdP4CvfX0LicCQnxLnAE7gybISHBBy26XApTp+/iljumkOOj4lzLVx9FZzF7CHTJYqbl649hjo+lz8LvaPvRs37z5p8pvCRIEpLFRHjjuvSc/WXQ6wyUS17g73nvG/a8/x2uIiuyNQhdm1Dyx/BxnFNdLiKaeubItttdTJm2k3sfnEVcrMWnO1dSjTBMRt86flEQMJl0PPlYNy2aVkOjgtw8ooWXHU2SBFq0SGBAv/rodMGfvm02FykHs3j2xUVe9yKbN6T/mknUuKoXxrhoIls3ofNP79DooVtL27jyi1D8eAvVHjGYjj+8RXyvK4hq3YRGY+/EGBsV9BoD5ZLy0vHF7ncmBlW4XBcWgmQx0ubt/yO2a2sWdb4JR16hOxiLkrf3q494FDB2OGRGjZnB4SM5pS5cBoNEzaQICgrs5OXbUFVIzyggIT6U3DwbLpdCRISJjlfUYNeuUxQVOWnUKJbGjQJLzqahoeHNsKubsHt3JrPm7kWvF1EUleqJ4bz1+gD0OpF169NIO+btdFEeLpfKlq0Z5ORavYIio1o29rsrd+TkobhkRL2E7PIU+rpQC5LFzMYHXnGnZlBVcrbtJeWLSQxY89t58dIR/p+9sw6P4uz68D0zqzEghCRAcJfg7lagUEpbvAIUWurCW/dSd1q+UqEu1LCixa24uxMsgbgnayPfHwspYXeT3SRQCnNfV0sy88hsdvfMM+c553eu1oiQNm3aaNu2bSvVGKqi8Juhsd/tg6pXpsuMKVRs0xTh/Mo+PyGJfW98TuKy9VijK9Ho6fHE3Ny7UL/5Cw/xzvtrPcSXJEnwGqbZsH4EX342GA2NO8fOJDU1H7tdRhQETGaJF57tzsAbG5TgFevo6AAkJuVw8FAKkZWCadwosiDTdsWq47z4yvISqdhaLAZm/DqSqlW8Fy6/lIMffcfu5z9CU1WPQimi2URI7RjyTiSg2AtHE0lBVlpNfo56E0YEfI0AgiBs1zStjbdz17RLR5QkQur6V1RAslpo+/kkIto1KzD2WQeOkbHrIE1fuJ+bjy3jhnW/eBh7gNVrTnhV2vMVk3/oSCp5+U5+n7GPlOS8gqcCVdOw22XeeW9tiere6ujouImOCqVn99o0aRxVSFbB4VDO6+4EjtksER3lXwGk5LVb2f3ix6gOp4exF0xGt/ruGxO9RvEo+TbOzFpSomssjmva4AO0nvy8h+TCpYQ1rkP3eZ9TdUB3AJxZOSzrejuL2w5hwx1PMq9eXzaNew7Vh8JmeLg14Mic43EZrFodh8ObYRfgyFE9NFNHp6xp1zamxLLleXkuXnx1hV95MkemTkf1sWcoiCLVRwzEXCnce20OQcAcrodlloiqN/Wkx8IvkYJ9i5GVa1yX6D6dCn7fPP550rbsQcm348rKQbU7OPX7Xxye8pPX/kNva4rxkk3a4qKwGtSrSDkfuvaKrBEaWvb+Ox2d652IikFMGN8GSwkSJGVZZdnyY2zeEl9sW3tKus9zqsPJ0vbDWNF7jPvmcamx0DSSVm/mzBzPTeLScs0bfIConh2KrEWrXZQIIeflkzB/lUe8vpJv48j/eTf4DepH8OxTXbFYDAQHmwgKMhIaYsZXFTRBgL+WHGXUyGYeHzxRFKhevRw1quv1anV0LgfjxrbmsymDSpQvo6oaP/2yq9h2YQ1r+z6paaBpaC4Z1SkjGg0erh17Yiob7niSc0vXBXyNRXFdGPy8M+ewJ6X5PN/gkYtCqIoI3XRl5/o8N3hQI1YsvpsP3u3PZ1MGoaH5rLGiaTDtm6107FCNMXe1RJKEgpu8ySjy4P3tin5BOjo6xZJwNptHJy6gXecv6NR9Gq+/taogqbFF88oMG9IEsynw2rRnzxavZhvqZ+1rzeU6H/rtRdrdZmfPSx8HenlFcl0Y/KSVm4qsHrPrhY+wJ7tvCOaKFXzKL0R29brxXYDVaqR92xhqVC9frMKeLGtkpNsICzVjNEgFIk92h8KzLyzj4CHviV06OjpFE3cinRdfWcYtQ6ezfsNpZFnFbpdZsOgwDzwyr8AH/9jDnWjXLgazWQrIxVO3TvHV7yq0alykG/liVLsD1Yf2fc6x035flz+UicEXBKG/IAiHBUE4JgjCs17OmwVB+P38+c2CINQsi3n9xVgutMiNlrQNu1jScQSqLCMIAtZo7wbf6WOFr6oaS5Yd5aHH5vPw4wvYtOUMpmJWDk6nzNp1J/nsi80euh92u8zULzYX86p0dHQuZeeuc9w5diZ/LTmKomiFtBBdLpW4Exns2euueWGxGPjkw4HM+HUk773dj4YNIjCbi1/xr9twinETZrNrt6e8ygWienYgrEEtBFPpUp0uTfAsLaU2+IIgSMBU4EagMTBKEIRLg9/HAxmaptUFJgPvlnbeQKjSvyuioeg/vP1cMmcXrQEgffs+r21S1nrmBWiaxrMvLuW1N1excdMZNmw8zWtvrCIkpOhNV02Dt99bS77Nu7bP4cP6Cl9HJ1DefGc1drvsWxZZ04g7kVHoUEzVcnTpVINvp93GmLtaFRtw4XAo7NqdyIOPzGf3Hu9GXxAEei//Hslc8uALyWqh+ZsTS9zfG2Wxwm8HHNM0LU7TNCfwGzD4kjaDgR/O/zwT6C1cjgq9PpAsZrrMmVpkG8XuIPt8XVxfNwfRi1zCnr2JrFt/qlAcvs0uk5Tk299/gfN7N16pXNm/5A4dHR03DofMyVPFaGUJUKumd+kCi8XA/fe2ZdSIZn5JMNgdMlM+9V0JL3Xzbu8nRLHoMD5JpHyLRnSf/wWR3doWex2BUBYGvypw5qLf488f89pG0zQZyAKuaFknc7kQ8CZVegENgmvFAFB95ACPXXPRZKT6yIEe3bZsTcBRhlKs4P7g3Xdv2b7ROjrXOgaDiNHo26QZjSK1alagebPoQscVReX7n3Zw46Af6NrrK06dziQ6KhSrtXh3zNHjvoNB8k6dRfNWXlVVqdihudcauACSyUiHb98iunfHYucPlKtq01YQhAmCIGwTBGFbSkoZuzQ0DaGYMKzQ81m5rSc/T7km9dxaF1YLhpAgyjWpR+vJz3v2CTNjKqWfDtzhmEajSMWKVl58rgedO/qXIayjo+NGkkQGDWzoNfJGkgRu7Fefzz+92SOA4/W3VzPt620kJeeRl+diw8bTJJzNLjbwAigy8za8dRPfK3lVQwrxrqqr2BysG/YYWQePFzt/oJSFeFoCcHEMUsz5Y97axAuCYADKAR63Rk3TpgHTwK2lUwbXVkDFds0Q8F7QCgBJJLh6FQBM5cPov302yWu3kn3wOOUa16VS1zZeI3369anLlE83lvr6Rg2PZfy4NoSFmkulp6+jcz3zxOOdSUvLZ/3G05hMEk6nwo396vHicz28SiqkpOSxeMnRQlIm/sqLmc0S90/wHUJdsU0sEZ1bkrR8g4fhydh1kGpD+3Fq+nyvfXOPn2Zx61tp/Nx9xL70kH8X5AelFk87b8CPAL1xG/atwO2apu2/qM1DQKymafcLgjASuE3TtOFFjVsW4mmXsvO5Dzj4zldez0X2aE+fVT+WaNzNW+N55PEFJU7ZBhh8U0NeealXifvr6Oj8Q2JSDgkJ2dSsUcFnfYrUtDw++Gg9y1Yc88vIXyyGGBJi4smJnbn5pkZF9snYe5jFrW/z0NMB3Kv/YiaWrBb6bZ1J+Sb1ir/AgmF9i6eVeoWvaZosCMLDwBJAAr7VNG2/IAivAds0TZsHfAP8JAjCMSAdGFnaeUtC7MsPc/KHudgSUwr9oQ1hIbT7+vUSj9u+bQxvTOrNy5NWllj0bMmyYzz3TPdiwzl1dHSKJzoqlOioUK/n5i88xJSpm0hLy/d7PKvVwM2DGtGiWTQtm1cmIiLYryfxrP1Hvfvxwa9HCdXl4syspQEZ/KIoEx++pmmLNE2rr2laHU3T3jx/7OXzxh5N0+yapg3TNK2upmntNE2LK4t5A8VgtdB/+yyqDe2HaDYhmowIRgOK3cHCRgNY2mWU+2ZQAnr3rEPrllVKfG2qppGTU/qiyzo6Or5ZsvQob7+3NiBjD+5cm9tHNKPfDfWIjAzxy9jbU9LZMuFl/31EvijDgMaratP2SmCtHEnXPz6h35YZaKpbz0JzutBcMqnrd7C82x1+qeFdiiSJDL2tSYmvK8hqpHz5olU9dXR0SsfULzb7tRl7MRazgW5dalItplxA/eK+n11QOKmkiEYj1Yf1K9UYF3NNV7xypGVwcvp88s6co1KnVlQd1LMgxn7XMx94fTNyjp5iRlhrzJUq0OCx0TR45K4Cffyi2L4jwWsJNH8wGkUefbhDiXW6dXR0fKMoKi6XisViINGP/BhwR82ZTBKhoWaG3daEMaNbBjxv7rHT7kpWgWI0IAoigiQQ++ojlGtYJ/AxfHDNGvy0bXtZ0WsMmqyg2OwcC/mNkLo1aDPlBVRFJXnddp995dw85Nw8dj8/mezDJ2j32avFzvfJp5tK7L8XgLg4d/bfseNppKTk0bBBJSpU8E+LQ0dHxxOXrDDl003MmrMfp1OhapUwKoZbSUrOK7avqmpYLAYWzb2rxAuxiM6tODl9PnJeYO4jg9WCqUIYde4dTsP/jS3R3L64JkscaprG/Hp9yT3uKTwkGA3ed8x9IFpMDD65CmuU91qziqKyfuNpnnp2MS5XyaN0jEaRmjXKcyY+G4Mk4nQpjBoey6MPdyxS+E1HR8c7r76+kiXLjhYqZ+ir7Kg3gqxGvpl2Kw3ql6zOtGJ3sDB2EPmnzxbIrUtWM6bw8tgSkortLwVZierZnu7zvwjIBlx3JQ7zTiVgO+v9DxqIsQeQzGayDxzzei4zy87QUb/x/EvLSmXswV0O8Xicuwh6bp4Tp1Phj5n7WLLU+9w6Ojq+ycyys3jpUY/atf4aewC7w8UXX21h5eo4FCXw77dkMdN68nMYLiRYCQIVWjam44/vIfrIsi10rfk2kldvJnXDjoDn9sU1afBFg6HUG+MXcOXkkX3kpNdSZB9OXsfZhGzy870LoAWCqmqoauGLttllfv61+GILOjo6hUlKyi1SZsEfVBXWrD3Ji68sDzjPJu/MOU7PWsK6EY/jTM9yH9Q0MnYe5Pi3M6l8Q2dEYxFSL+dR7E6SvYg2lpRr0uAHxUQT1qBm2YQzqSo7n3yX1Tfd51HTdsWqOFylSLbyh+xsPVRTRydQqlYJK1Ui5MXY7TI7dp1j5erio8ltiSks7TyKBfX7sX7ERJT8wgWVFJudU78u5OzitQgGyV2/NjqC4JqXyo+5ES1mLJHF6+/7yzVp8AG6/PEJ5krhGEKDEYyl25uWc/NJWbuNhLkrCh2/3PsfRoNIty41L+scOjrXIiEhJkYMiy1R7VpvOJ0Kfy05Umy71Tfe666HbXeg+Sp5p6poDheKzQ6ahjMtk3wfPn1BEqg+7MbSXHohrlmDH1a/FrecXk2Hb9+i5ftPU+WmHojWkse5y3n5nJ6xuNCxHt1qIUmFnyIE4XzFslIiigLlylsYN7ZV6QfT0bkOGXZbE5o0jsRkFJEkgbp1wkulU5WX570q1QUy9hxyu38DjL3XXLLPvcUef32DMcy3QFugXLNhmQCS2UT1of0BqDasP3Or9Sj5YKKIIbSwJseTE7uwZ28iWdkO8vNdBFmNmM0S+TaXx2ZRoISGmJjxy0jKldOTsXR0AuXAwWQmPDAXu0Mu2Bs7cTIDo0HEUcLw6fbtYoo8b09MRTRKlO6b/w+CQaJCs/plNJqba9rgX8yWe15078JciiAgGCVEo9EdOiUKoKge+heSxUSd8cMKHatYMYg5M+5g1eo4jh1Pp1atCvTuWZvnXlzKpi3xBRl9JqOIM4AoHkGA2KZRJCbloigq4eHexZ90dHS88+Y7azyqySmKhuLLzVIMkiQwanjzIttUaNUYxeElgMMPkTRvBNeoijEkOOB+RXHdGPzktVu9n9A0Ygb1JvqGThz97BeyD8UhmE0osg1BkpCsZlRZJvbVR4ho7/mGm0wS/frW4+Lk5/fe7s/vM/Yy+88DOJ0K/frWZdny45yJz/LrWkVRYMu2BHbePweXS6Vr5xq89mpvrJbid/V1dK53MjJtHDwUuCaWwSDSvl0M4RWsLF56FEVREUUBURR46/W+BAUV/f2zRITT6Im7OfTxDyh5NsBdOOlCDH5AiCJtP3818H7FcE0mXnljVmRHHCnpXs/VfWAUyau3kH04Di4KjRQMBip1aUXn3yb7TLzyl/c/+pvfZ+zzCL28gNvvL1C+nKUgDv8CJpNE7561efO1G0p1DTo61zo2u4uRd/zOmfjsgPqZzQZuubkhEx/tjMkkceRoKus3nMZqNdCnd10ifEgsX4qmaZyZvZRDH32PMz2Tck3qkbBoDarNXnzni5FERuTuQrIEXhP3uku88ka9B2/3HqYpihz/bhbZB48XMvYAmiyTsm4H5gjvNTD9Zcu2eGb/ecCrsbdYDFSLKceShWP5e9U9REQEeUg0OJ0KK1bGFbtppKNzvbN4yVFSUwOTMhAEWLfqHp55sluBPHn9ehHcdUcLGjWKJDExx+/EK0EQqD6kH33X/8pNB/+ixqiBCCWQZhAE4bJEAV43Lp0mz99H6qadJC7fCBe/eaqKZvdtSDVZZtWN94Ki4MzIIubWG2jw6GhM5bxrbXvjrXfW+NzE1TSNTh2rERRkxGoxkpZu89pOECEn10FwsMnveXV0rjc2b43HFqAaZmio2UMvZ/PWeJ59fgmyrKLhXph9+N6NNI+N9uifunk3u579gIwdB7DGRBP7ykNUH9qfuO9mcfjT6QXunUCI6NgSQymiCn1x3azwJZOJXou/pfqQfgHH5SctW0/Syk1k7DzI/re+ZHHr23Dl+Ke6l5/vIj7B9+Olw6EwZ+5BHpu4EIBWLSp7fRAJCjJSKaJsN3B0dK41KkeHYjD4b9YMBoE7RxXem0tPz2fik4vIynaQl+8iP99FerqNhx6d7/GUnbZ1Dyt6jSZ59RZc2blkHzjGprufY3H7YWx77E0ydx0s0YZt+2/eDLiPP1w3Bh9AVRTOzF4asJ5OoTHsDmznkjn+7Sy/2ptMUrGxv06nwp59SRw6nILJJHn9fIy5q6Uun6yjUwxDbm0ckMHv0rkm48a2LnRs8dKjaN722jQ8sm13PT/ZM5s2307Gtn2eK3s/M/8je3ckrF5Nv9oGynVlQU78+KfvcmMBoOTbObtgtV9tDQaRjh2Kjt8Ft9F/7H8LWbLsqMc5QYCDh1IDvUwdneuOmKrlmPz+jURUDMJqMRRr/J1OxWNBlp5h8xqr73IpZGYWNu6Zuw76f3GahiD5LmEqGA0YQoNpO+VF/8cMkOvK4B+ZOr1sBhLAmZmF3UfUz6WMGBrrV7uU1Hxk2XNloWlw+HDJSi/q6FxvtG9XjcULxjD9x2HMn30no+9o4bPtps1nmDu/sNFu1zYGq9XT7SsZRNq0Lqx5E1zD/7KmotlElZt7IQVZMYaFYAgNxhIdQcyQflTs0Jz6D97OwL3zKde4rt9jBsp1s2kL4MoILFTLJxpk7j3C/Lo30Ofv6VRo1rDI5iEhZqxWAzZbyVxJggB161QsUV8dnesRURSoWaMCmqZRu7bvKDtV1XjnvbV061qTCuXdBYfatq5KqxZV2LHzbMEGsNVioHu3WjRqWKlQ/9hJj7Ju+GMebh2vCBDZuRVNnrkXOTcfQ0gQFdvG+lVRr6y4rlb4VQf1RDQVnTxhCA6ix7JvsVaNQgqyIphNSFaLR2iV6nDhys5l87gXip23aZMoQkoRXSMI7mSSmbP3lYkUs47O9cJrb67i7ffWFtlGMois3/BPsSRBEJj8wQCeeaobrVtVoV2bqrz0fE/emNTHo2/VgT1o++VrmItTtBRFVKfMziffZWmH4Wwa/zwIAjuf+YBN457jzOylqKWsf+sP103iFYA9OY2/Wt6CMz0Lxe5FdlgUqTakL13/+ARN08g5dgpDkJWgqlH8Ua4VcrZnaTTBIDE0fQvG0KIFjg4fSeX+h+fhcinYbK4S6fULAoRXsPLLT8P1iB0dnWI4eSqDUXf9UayuVVCQkfsntKVh/UrUrVuR8iXQr3Jm5TAror33PUJR8MjxuYBgMKDJMobgIMLbNKXXsm/90skvCj3x6jyWyIoM3LeAJi8/SGiDmu434vzjlGQxY6oQRsv3ngLcd3ljaDCIAsnrtoEvAy0ICIbiPWMN6kewZMEY3pzUhyG3NilRcQZNg7R0G1M+3RhwXx2d640NG0/7lTBls7mY+vlm/vf0X/S/6Qc++b8NASc9mcqFElK7mveTPow9UKCsKeflk7ZtLyd/WRDQvIFyXfnwAQyhwaSu34ktPtn9RkgCSCLVRwyg5ftPY6kUTvK67awb9ij2pDS3lRUEryFVgsFAlX5d/U6QMJkkunerRfdutWjaJJJ3P1iLzRZ41NCqNScC7qOjcz2QlpaP3SGjKCpTP9/sNQjiUkRRwOFQCp4E/pi5jzp1wrlpQNF7c5fSbtrrrB5wL4rd6RZqNEgQQFSgkmfj5K8LqD3m1oDmDYTraoUPcHL6fJJWb/6nkryigqKSMH8VpgphpG3fz/Jut2NPTP0nYULTCittigKGkCBC69Wg/bdvleg6br6pEUsWjCU6OsRDU19HRycwUlLyGDdhDgMG/8Swkb8xfNTvxWbcCrgTry6tc2uzy/z4c+ClRSt1bkXVm3q614aiGJCxv4Ah+PIq4153Bj/u+zleU51Vl4u0LXvYcOcTvt03BY01Wrz/NAP3L8RSqeTlx0JCzAwf0jTgfuXCzBw+osfl61w/2O0yX3+7jb4Dv6dLj6+4ffQfbNueALjlSSY8OJe9+xJxuRTsDhmnq2hjK4oCk17uicFHXHxScm7Abp3dL0wmYcEqNEX1LsVeDFKwlXr3jQi4XyBcdwbfl5CR6nSReeAYOYf8c5ckrdqEUMqaufn5Lr78eqvHCqM4EpNyufue2Xz3Q9lVs9fRuVpRFJUJD/zJ59O2kJqaT77NxaHDqdz30FwG3Pwjvft9S3x8VoDfI40O7asTHOI9ei4vz8VP03dhO5fMulET+SOkBTPKt2brQ5O8yqpoqsrRqb/4F57pgwaP3Enlvl1K3N8frjuDX2f8UKRgq8dx1eFk+2P+61dk7z8GgCMtgz0vf8LidkNZe+tDJP/tf2TR/322sUSVsTQN7A6ZqZ9vZtac/Ze9tq6Ozr/Jho2nOXw01SOyTdPci5/MLAdKERuj3tA0WL32BC8+18Or9Imqanw3bSOL2w7lzMwlyHk2XFm5HP9mJit6jSn4zil2B/HzVhD3wxzkQCWQL8IQFkKLt58scX+/57nsM1xl1BgxgIT5q4ifuwLFZivkvlHz7W7fmx+PY8F1qmFPTeev5oNxpGWiOpykb93LuaXraf3JC9S9Z1iR/Q8fSWXWnAOlei2qpvHuB2vZuz+JV1/sVaqxdHSuVnbuPocrgIpx/iCKAnaHQveuNQkNNZOV5WmsaycdwpGRXSjUUnU4yT4UR8rf2xDNJlb1H+/W3VFL5sYBEExGao4aWOLXEgjX3QpfEEU6//Ih3eZ+5j3DTVURzMZiQy3DWzfl4Aff4kjNQHX8o6Cn5NvYMfEt73H+50lKyuXBR+chy6X/EMuyxuLFRzmi+/R1rlEiI0NKVHw8LMzM0Fsbez0nSQJdO9cAoGaN8l7bROQkoeZ72e+TFTJ2HWT1gHtxZeYgZ+ci5wamwX8BQ0gQoXWq0+Kdy7+6h+vQ4F+gfJO6Po26NTKC/ltnYizvW/M+on1zzi5a47N8WdZ+TxE0cG8wPfz4Ag8RpoupVzecoCCjv+J6OF0KDz02n7/XnSw45nDInD6TpWfm6vzn6d+3XkFhkkBwOGRMJgM3DahfEAknAGazxF23t6RGdbehv//etljMhW2BxWKgZudYr+5f0WjAlpRa5KLOXzr+9B4D9s7HVD6s1GP5w3Xn0rmAtXIkIbVjyD5YWO5UNJuoMXIA1pgoqg7qzcmf/vToaywfSnSfTj4rYcl5Ngw+3sCjR9M4ey7bZ6at0Sjy2ZSbqVDByrr1J3n+5eV+Ge20dBtPP7+U11/txalTWXz7w3ZAQFFUbrm5EU9O7BKQbKyOztVC+XIWvpw6mPsenIvd4b/8gMOhMHPOfhbPH83gmxuzZOlRJEnkxn71aHZRIZP27arx2iu9+ODj9aReHjTTAAAgAElEQVSl5WM2GRg5PJa7RzVmYf0FKDZHgbtGMBpA0zjw3tclCru8GMEgETO4T6mDPwLhujX4AJ1+/oAVPUejumQUmx1DSBDWmGjMkRX5s2o3T6MsCFiiI+iz6kdESaJC8wYkr9rsObAgkHP4BGF1qnucSs+wIfkQSxIEeOTBjlQ8Xz+zdauqAUUeOBwyb727Frtdxn5RDPK8BYewWgw89kgnv8fS0bmaiG0axQP3tWPK1I0BfSdMRokz8dm0blmF1i19K1v26V2X3r3qYLPJmM1SQe2Jvht/Z8uEl0heuxUEEUtURewpGaU29gDBNateUWMP17FLByC8VRNujltO87f/R/1H76LtF5OwVq7ErqffR3W60Fz/rKxFs4mGT9zNrQl/E9agNgCC6P0xU5Akcg57D+9s3KgSLi8xwpIkMGp4M+68/Z/qO8HBJp54vBMWi//35cxMeyFjD+4Y5j9m7fO7LqeOztXEug2n6D/oByZP2RBwCLPTpRAdXbTO1QUEQSAoyFio0FBo3Rr0XvkjI+x7uS1pPY6UDDRHGdSWFgQaPDa69OMEyHVt8AHMFSvQ8LExtPnkRRypGaRu3Om1JJnqcJK4dH3BHVnTNCSrGdHsGccrmY2Uj63vdb6wMAv3jGuD9SIjbjJJREWFcP+Edu65VI1jx9M4cTKD225pTOeOPjQ6AsDpVD1uBDo6Vzubt5zhsf8tJDnZU7iwOCRJoFuXmmUiNKjYHWx54NVCARqlQTBI1Bk3tEzGCoTr2qVzKXHfzkItoqC5YJBQZZk9L3/Cwfe+QVM8V+qiyUhI7WpE9ergc5zxd7emYYMIfvltDxmZNnp2r8XI4c0ICTGxc9c5nn1hCbl5TjTNreSXl+vfh0wQ3BV/zsRneZyLiAgiKKh0Knw6Olea195cVSJlWXAvykYO96/4UHGsHjiB1E27vZ8UBQRJCqh0qjmiAoYgzw3hy41u8C+mqE+WJBLRsSUr+99D8grvapWC0UCtMbfQ8v1nii1q0LlTDTp3qlHoWHp6Pg8/Pr9QoZRAVuURFYO4Z1xr3n5vLQ6HXPByLGYDT/2vyxX3F+rolJakEqzsL6CqMH/hIVoV4bv3h4zdh0jftg/NW0TeeVXdHou/YVXfccg5ha9XNBk9IvkEo4GYWzy19a8EusG/iFpjb2PPSx97T49WVI5/9YfPMEwAY0gQ7ae9UeL5Fy0+ghpgxuDFZGTaeevdNcQ2jSI4yMShI6lUiynHhPFtPEqz6ehcjeTkOpg5az/rN54iKjIEURBQixW38k16umccfcDXdOSEz1q0QdUq02fNT4TUjGFY5jYOfvQdx7+egSCJ1HvwDsLq12TtLQ+hulxoLhnJasEUXo7YVx4u9XWVhFIZfEEQwoHfgZrASWC4pmkZXtopwN7zv57WNO3m0sx7uaj/0B0kzFtJ+vZ9XhMpijL2AEox54sjJTU/IKkFg0EslLwlyyqyDNu2n6Vn91osmnuXvqrX+c+QlWXn9tF/uIuIOxQEoeiHbn9o27b0C52wxnW9FjYRJImYW3oTUjPG/bso0vjJ8TR+cnyhdgP3zufIZ9PJOXKSyB7tqTN+KKZyvnN8Liel3bR9FlihaVo9YMX5371h0zStxfn/rkpjDyCZTfRe9SPd5kyl6i29Ec2B+bwrdW5Vqvlbt6qC1Vr0nJIkYLEY+PjDAUx6uafP5KxVa07QrffXdOw2jQcensfRY2mlujYdncvN9F93k5ZuK1j0lNbYCwLcMsh7pm0glG9Sj8hubRAt5kLHNUXh2Be/se/tL4vsH1K7Gq0+eJbu876g0f/u/teMPZTe4A8Gfjj/8w/ALaUc719HEASi+3Si5sibEE2B1aFNXruVxJUbSVy+gb9a38rvwc1Z0LA/p2cu9qt/547VqVfXt9yyJAnccnNjfp8+AqdDZtIbq4v8UuTluXA4ZDZvjefue2cTn+C5maujc7Ww5u+TOJ2BxbeLIlgskkcmrtEoMvrOloT4UMMsDlVROPXHItbc8iDrRk6k6s29MYeX82zndLHn+Y849PH3JZrnSlOqmraCIGRqmlb+/M8CkHHh90vaycAuQAbe0TTNM331Ei5HTdtAcOXmMSe6yz+FUvzFS5UbKchCm6mvUGfsbcV2dzhkhoz8lbNnczzOWSwGVi4Zh8kk0XfA96Rn+O+flCSBWwc35vlnuvvdR0fnSjLhwbkFGvf+0qtHLR5/tBNHj6Xx4eT1nEvMITjYxOg7WjBubOsSafBoqsqam+8nafVWFD+//4LRwI3bZ1M+tkHA85U1pappKwjCckEQ9nn5b/DF7TT3ncPX3aPG+Qu4HfhYEIQ6PuaaIAjCNkEQtqWkpBR3aZcVY0gw3eZ9hiEkCENoMIaQYESLmfA2sUULq3nx9Sn5drY9NImsQ8eLnddsNvDKC728anuMGBaLxWIgJSWPvPzA4oEVRWPf/qSA+ujoXEnuGNWcYoLbCiEIMPGxzsRULUfP7rVZ8OddbFx7H2uWj+eecW1KZOwBzi1dR/Ia/409gCYrHPn81xLNdyUp9s+raVofTdOaevlvLpAkCEJlgPP/JvsYI+H8v3HAaqClj3bTNE1ro2lam0qVKpXwJZUd0b06clvSBjr+8C7tpr3GLWdW03/rTOpOGB7wWEq+ncWtbuX07KXFtm3bpipvvt6HypVDEUWB4GAjo+9swSMPumP7Q0JMaAEmzQoC1KrlXftHR+dqoFOHagQH+e+CsVgMHklVJpNU4kAFOd9G3umzxM9bGbj6paZhP/fvLlL9obRhmfOAMcA75/+de2kDQRAqAPmapjkEQYgAOgPvlXLeK4YhyEq1W28odCx9x/4SjaXYHGwe9zxVb+qBVMz+QM/utenZvTZOp4LRKBb6EAcHm+jRvSZLlxf/xHABTYNt2xLo2M29wdS8WWVsNhdn4rOoUa08D9zfjnZtYnz01VAUTRdf0ylTbHYXu3adQzKI1K0TzgMPzyfHzyRDi8XAvePalEhF81JUl4ttj71J3HezEUQBVVFBEt31rv1FEqk6qGepr+VyU1qD/w7whyAI44FTwHAAQRDaAPdrmnYP0Aj4UhAEFfcTxTuappWu8se/TM7RUyXuq2kaGTsOENGhBc7MbOL/XI4zM4fovp0p37guAKosgyAgSp6bURe4fWRzlq+MCyhuPyX1n1XLlq3xBT9nZiby2P8W8d5bfenapWaha/3hp118/9MOsrMdVK0Syv8e70zP7rUDfNU6Ov+weWs8H0/ZEHBd5gthmmaTxOOPdmTYbYHXg74UTdNYM/hBzi1ZV+ICJgDGsBBq3j6o1NdzuSmVwdc0LQ3o7eX4NuCe8z9vAMomv/kqwVIpHGdaZon6qrIMaOx5+RP2vzPNHd97fuPcGhNNSK0YUjfsBEGg6qCetPtiEpbIih7jVK4cisEgBhzV4AuHQ+bDj9cXMvjTvtnGDz/tLMj2TTibwwsvLeej92+kQ/vS6/voXF9omsarr69k4V+HS2RbL8SXqJrG3+tOMXxIyc2KpmmkrN/O1gdeJWuf99oVgdBjwZdIl4RtXo3oz+gloNFT4z0KI0gWs1sruxg0WWZF77Hse/0zt/bGRVFStvhEUv7ehqYoaLJMwvxVLOsyCtWLZk+liGBat6qC0Vh2b+HpM1kFTwwuWeHHn3d5Km86ZKZ85l1aQkfHF6qqMfGpv5i/sGTG/mJcLpUtWxPIyCw+Si3vzDk23PkkMyu248/q3dn/zpcoLhdbJrzIihvuLtrYSxL+VCGKvqEzlTqVLgfnSqFLK5SA2ncPITfuDIc+/A7RZERxuqjYoTnJq7cU21dzyihO//RxNFnGlphK4tJ1VLnRM5zynTf68vTzS9i56xwul1LqRBVRhPZdvsBgEGnfNsannPLhw6kkJ+cSGemf7KzO9cHGTaf5+rvtnD2XQ93a4fTuXYeunWpQsWIQa/8+yabNZ8psLoNBICfHSYXyvgXIHOmZLG59G470TFBUnOlZ7H7uI3a/8LHbkHtZSBVCU4vM/hKMBuo9cDutPni6pC/jiqMb/BIgCALN35hI46fvJftwHEEx0cTPW+mXwQ8U1eki+8hJrwY/NNTM5/93M8nJuUyZuollK46Vqtize+WloSgKa9f53qfQNPjm++0897Qe06/jZv7CQ7z93tqCJ8KkpFzWbzyNwSBy6+BGZGbay8z9CGAyGahSueiM1WPTfkfOzfPcfPX3EaOY/bGwhrVp88kL/o11laAb/FJgDAuhYttmAITWqwGiUOyHJFBEo4HyTb1r618gMjKE557uxtFjaSSczSY/30WQ1YggurNtLwcbNv6zWtu+I4Eff95FUnIu7dtV4647WhBxvmqXzrWPoqhM/mSDV2VXWVaZM/cglSqV7vMgigKqqiEI7lyV557uVmzUWMq6He7yhJcJR6qHbNhVj27wy4ioHu0Jiokm//S5MhtTNJkIrVuDqJ7ti20bHGzilx+HsW7DaQ4dTqFK5VCio0K476F5PvtYLQYsVgPZ2fZin24vJTzc/Sg9Z+4B3nl/bcGTxfHj6SxYeIjfpo8ok8ITOlcnmqaxZ28iy1fGIbsU8m2+FxayrHLuXG6R4zWLjaJHt1p8+fVWDwFBk0li0MAGHDiYQtUqYYy+swVNm0R5HUdxOjm7aC35Z85hLBfiNfM9YAQ8U0olkeg+/72SobrBLyMEUaTflpmsG/4YKeu2+17pC4JbI/tC5RxRAA0kq4WYW/qgOp2c/WstgihS8/abaPne08Vq619AkkS6d61J9641AfcmrCQJXsvChYWaeOqJrjRtEsXQkb/iO0na7du/+ClYFAVEUWD1mjjeendNofEVVSMzy86332/nmSe7+XXdOv893n1/LfMWHi5Ud6E0vDGpDzFVy9GubQyPPbEIm81VsF/6+it96NG9VrFj5MadYWmXUci5+ahOl/t7E8gTtyAgGDwLmRjLl0N1ONxPC5qGaDJiCLbS7LVHA3mJVwWl0tK5nPzbWjqlQc63kbnvKCt6jkbJ/yeSQLCYMAYHIefZ3NWyVI3wNk3pvfonDJcppGvUXX9w5GhqoS+lwSDy3lt96XE+nn78fbPZuSuxyHGMRgFVpZBxNxpEXLJ3f2hYmJllf43FaCh9YozO1cWevYnc//C8Mi2ZeevgRrz0vDtxSVFU9h1IxuVUaBYb7Xdy1ZL2w0jbtq/Q6kQ0m9BUtdhqVFKwlbCGdTCGBZO+dS9yng3JakGQRHot/RZBEjnw/jfkHjtNZPe2NHpyPEFVvT9l/NsUpaWjG/zLSMqGHWx9cBKZew4jWS0EVa9MXtyZQrr6osVMcK0YbPGJiCYjtcfeSrPXHsMQZMWZmY1oNGAILuz/tCWlcvLnedgSU4ju1YHK/br6fApISsrlwUfnk5iYgyAKyLLKmLta8MCEf9xE5xJzGDj4J5+vQxRh8KDGLPrrMI4ANt7atanK1CmDChWF1vlvoSgqp05nEhRkJDrKvUn6yf9t4Mfpu8pkZX+BmwbU57VXSl4FypaUytwaPb3WnDWEBntUoiqEINBlxifEDO6NIEkkr95M8tptWKIjqDH8RkwVPFUyr2aKMvi6S+cyUqlTKwbsmosqy6Ru3cvyzqM8wrxUu4Ocg/9IJByZOp2kVZtRHS6yj5xAQCC6b2c6fP82lohwklZtYvWg+0FRUewOjn3xG+Gtm9Jz6Tde5RqiokKY+dtIDh5KIT3dRpMmkR6hbJUign26fgBEUeTsueyAjD3A3v3JrNtwusDFpHN1oaoaf687yaLFR5AkkUEDG9ChfbUCGY/1G0/zyqQV2OwuFEWjXt2KvP9OPwxGEVH0/XkpCaOGNytVf01WfMbMyzl5iGaTzwLkQdUqU31Iv4Lfo3p2IKqn75rU/2X0pdcVIHPvEVb2HuNXRQfV7iRjxwGy9h9Fc8moLhfnlq5jZe+xKLLMuhETUfJsKHZ39IGcm0/a1j0c/3qmzzEFQaBxo0i6dK7hNW7ZYBAZNqRJEf1hz56iXT7esNlc/L3+ZMHvdrvMps1n2L4joaBSV1JSLkeOpuJylV3I3vWMpmns3ZfEzNn72bT5jE/pDU3TePGV5Tz/8jKWrTjO4qVHefLZxbz93lry812cPp3JU88uJj3Dhs0m43QqHDyUwv0PzaN/33p+6ypdsMEmk+/2XbtUp1GjyIBf68UEVY0ipGYR1a00DcHoWVxICrL+a+UG/w30Ff4VYM9LH6PaA5MzvhjNJZMbd4aTP/5ZYOgvRsm3c+LHOdR/8PYSz/HkxK4cO5bOth1nCx2XJIERw5oxc/a+gMcURQg/f4NZvuIYr7y+ClEU0FQVBAGr1Uhmpg2TSUIURZ55sis3DWiApmn8vf4Ui/46jCAI3DSwIZ06VCuxCqI3Es5ms2VrPGGhZjp3qoHF8t/+KqSm5fP9DzuYM+8ADoeCJAkYjRIVw4P4ZtqtHmGyu3YnsmbtCWwX+eFtNpmZs/cza85+wsODcF6SIKiqGvEJ2cyavZ97x7Vh2jfbioytNxhEBt/UgIhKIZQrZ6F8OQtvvbsGl1PBJauIosDDD7Rn9J1exXN9omkaaZt3k33kJOVj6xPe0l3VqtP0D1jcZoj3hZUo0mzSIxz97Bds8YmAgCE0iNhJj1Jn3JCA5v8v89/+lP9HSN9xoPT12hCwJab6HEf0snoJBFEUmPb5LRw4kMzsuftJTs6jVYsqjBgey/cX6ekEgqrCDX3qknA2m5cmrfAIt8vPd+9l2Gzusd96dw0xVUOZNecAK1fHFRxfu+4kA29sUCbFWzRN4+MpG/h95r6CaCNJFJg6ZZDPUL+rDZdLYfnK42zbnkB0VAhdOtfg4ccXkpVlL1jRq6qGy6XicGTz6msr+PSTwsJe6zecwu7w/p5qGqSleZcHVlWN32bsw2AQuXt0KyxWA4v+OszxOM+YdFlW2b7zHLP/+Gch0rtnbfbuS8JolGjSODJgzXpnVg4rb7ib7APHQQBN1ajYLpYeC6cR3qoJoQ1qkXMozvO6XTKJS9YTUiuG6N4dKd+0PjVGDsBauXRPFv81dIN/BQiqXsV/rWxJclvKSwy7bLNz+OMfkPM89UNEs4k69wau0e+Nxo0jady48Jegfr2KJSooLUkCZ89mc/Bwil9Zlna7zGdfbGHfgeRCNxibTWbBwsMMG9KUenU9heQCYcOmM8ycvd/jeh57YiFLF4696jeY8/NdjL1nFglns7HZZExGkWnfuIMbvLlvFEVjy7YEbHYXVss/iwKjSSzVGkSWVX6cvpNPPxlEvxvqMWTELx43dHAXJtc0reDpzGiUaNWySonn3frQJDJ3HyoU+JC2aTe7X5hM68nP0/iZe9n64KuolyZcKQpJK90aUMmrt4AosvO5D2n3xSS/KtFdK1zdn+5rhPAWjXyfFATMURURJBHRaKBy746YKpZzG/6L2qCpOFLSvVpdTVa8anHLefmcmbOM0zMX48zyLJnoLzVreFSt9IsLft64uHS/jcup05k4vKw8ZUVlw8bTpKfnc+BgMjk5JcugnPPngUJujAs4HQq7S7BPcaX5+ZddnD6TVfD043SpKIpW9AaqBor8z/lFfx3m+x93lvpaHA6FGTP3UTk6hKgo77pK2TkOvvxqq99jZh04xrGvZ5CwYBWqy23U03ceYNWAe5lVqQOnfplfyNgDKHYHh6f8xPKed3H081+LDcEEQFXRHE62PfAqeWfKLlnyakdf4V8B7ClpPs+JRgM95n+BMbwCK3uN5tzSdedPCEjBViSLGTknz+NDfjGapjK3Zk+iurej+ZsTKR/bgIRFa1g//HF3YhduIbZ2X71JrTsC1+x2uVSsFmOR2ZTecDoVZszeT3JK0VmWFxBFyMl1enfBCrB85XE+n7YFo1FCdikMHdKUiY92Csgt4NONgUZ6ej6qqpW4NF6gZGTamDl7P/v2JVG7dgWGD42lcnRhfZh9+5P47IvNHDmWRrWYciQm5QasSVO5SigJZ7OZv/AQhw+nsHdfMs4y2iTPzLIjCALvvtmPO8fO8LjxKIrGT7/sYtzY1kXG02uqysYxz3Bm1lIQQJAkDEFW2n7xKhvueKpQPotXVLVEWlaapnFm5hIaThwbcN//IrrBvwKUa1yXswvXeA0LqzthBOFtYplRoQ1y1kWGUdVQ8mxUH9afE9/PKXoCVUPOziNh/ioS5q8iuEYVbImpHvNtufdFKnVuSUhN75WtfFGnTjgGowj+10wH3A8jGzae9ru9quJzr8DpUjl0OBlFocDgzZqzH1VRiTuRwbG4dGpUL88D97WjdREugxv71WPnzrMeq/z8fJkXXllO0LtrePiBDgy51XfUUlmQcDabO8b8QX6+jCyrbNx8mhkz9zPt88E0Ph+xsmv3OR58dH7B3yQ93eaPWq8HZ89mc9fdM1FVtdTSxJfSu6c7A7ZB/QjCwsxkZNg92mgapGfkF8TxeyPuhzmcmbMMxfZPfzk3n/WjnkD1EqhQVmiqiuoseUDFfw3dpXMFqHf/KMRLtPIFSaJc03q0nvIi8XOXFzb2F5G8ZiuGkMCEp/JOnfV6c9EUhVO/LgxoLACjQWLSS72wWAxIktviWCwGqlYNY8xdLTCbr0w27aV6P3a7zK9/7GXz1njS0vLZsfMsjzy+gEWLj/DZF5u594E/eevdNZw89c+GYr8b6tGsWTRWq/v9uNiAulwqWVkOPvx4PUuXH7usr+W1N1eRne0sCE+VZY18m4vX3lxFZpaNjEwbH32y3uMGWBK/u6JoyHLZG3uAXj3rFPxcp3a41zaCIBBeofBnWFNVDk35kbm1ejGjfGt2THwb5dL9KU27rMYeQDRIVL3Zo4bTNYu+wr8CBFWNovfKH9g8/gWyDsUhCAJVBnSn/ddvIAgCaZt3++zrOp80Qp6t1JE+qtOFK8c/98qldO9Wi19/Gs7M2ftJTMqhc8ca3NivHqqmsWVrAqdOZZJvcxWZwOULs1lCltUySeSx22VenrQcg0HC6VTYtfscCxYd5tWXetGkcSRVKocy9ZNBrN9wijV/n2D+wsMektJ2u8wXX22hb5+6uFwKBoPoERKqKCpbtsaTnJJH0yZRREWGYDCIfoV3qqrGtu0JXs8dOZpGr77flfwPcAUJCzMXyut4YEJ7Hnx0fqE9GIvFwJi7Wni4c7Y//hbHv5lZvKvGFxfeD3++Ez4iDqQgCw0njqVcozpeOl2b6NIKVxhnVo5bfMlqKTh2bsnfrOp/j9f2kT3a0e6LSWwc/TQZOw8CAiH1alCuSV23vzPAZZtoMlK+WQOavzmRyn27lOalFOCSFdasOcnmrWew2VysXnOyWH+/KApUqGAlOiqE8WNb8/GnGzh9OqtMrscXJpNEZKVg3nmzL40bRXLyVAa3Df/Va9uLbYTBIDL6zhY8MKEdkiRyLjGHe+7/k6wsO4qiFriYJEmkU8fqvPJizyILc+zZm8jYe2aX+esrS0wmqci9AovFwCMPdmDUiMIZsps2n+HDT9Zz4kQGFcpbuHtMK0aNaFbohmlLTGFuzV4+M1/9wg8pcsFgQLSYqDGsP+eWrkd1ughv1ZiQejUwWC3UGDGA8Nalr4t7taFr6VzlaJrGnMpdsCddUtRZELhx9zwqxLr18J0ZWSAImMqHATCnaldsZ5NLNKdktdD598nEDOpVqmu/FKdToe/A78nO9v0obrEYuOXmRjz9RNeCY8tXHOPlSSt9bqqWJUFBBn74dih3jZmB3UsooS8iKwXxzFPd+P7Hnew/kOw1DNJgEKlZozy/Tx/hNVHs9OlMxt4zi8ysy+uq8BdBcFePkmUNo1HCaJRwuRTuGNmc5JQclq+I85DUqFDewv0T2jH0tiZeX6OqKBz/egbHvvwd1emk5p030+DR0YhmE3tfnsKhyd9dVp16JBEUFcFoILx1E/qs+dmr7Mi1im7w/wM40jNZ2Xc8GTv2g6ZhqlieTtM/oEq/rl7b58cnMq/eDaXK4A2tV4NBR5aWuL8vDhxM5pGJC3E6ZBAEnE6F6KhgEpNyCQ01c+eo5oy+s6VHNMzipUf5v6kbOZfo3e1ktRoQRaFMirpcKvnsL2aTiCxrKEWsLoOsRj795CZaNK/M6TNZfDh5HZu3xmMxGxAEyCriZljWWK1G+t5Qh6VLj7mznDV3iOujD3Vg6G1N2bsvEYdToUXzaE6ezCQtLZ8mjSMJDw9CllW++X47v8/YS16ek2ax0Tw1sQv160cUOeffQx/l7F9rC9w1ktVMucZ1ierVgSNTfym5G6cESEEWWn7wLPUfGHXF5vy30Q3+fwg534bqcBar0Je+Yz8reo7GlV0ynzwAgsAo5WCZShZcQJZVdu0+h90u07JFZYKD/V9hnTiZwV13z8BulwuMstEoct89bVm5Ko4Dh/xMYvuXCLIaee6ZbnTqUJ1bh/1Cbq4T9V/4njVtEsm3027DYBCx2Vys23AKh0OhY/tqVLxMFckydh1kaeeRKPmFo3UMwUGoLvlfiYip2KEF/Tb+fsXn/bfQDf41iGyzMzuyI3Ku9xR4f7BER3DbufUFv6uyzMnp84n7fjaCKFJn/FBqjBzodwGWsiThbDbffr+dXbsTqVjRysmTmeTnu1A1rUx12EuCP1nH5ctbyM52oKlaEaVlyhajUXTnTFgNWMwGvvt6CNWrXVlp3/WjJnLqt0XeT553tZQJooi5YnnknDyE8xFwqtPldV+gUtc23LB2etnM+x9Al0e+BjFYLbR45wl2/O/dEq2apCArTV54gNy4M2TsPkRw7Rj2vPAxSas3F4THpW7eTfy8lXT5bTLgdjvlnz6HpihYY6KxRhX9aF8aqlYJ46Xne6JpGjcPmU5aen6Z6q+XBqNRQhAEnE7f1Z4yMz3j0S8nBoPA/fe2Iz/fRUxMGH371MVqLZ2+UqDE/fgnZ2Yv93pOPF/gR1XKxp1lCLLQd8NviEYDzswcwhrVZn7dvgTZAWIAABfqSURBVORfkjUrBVupO6FsZEeuBXSD/x+m/kN3ElqvJtufeIecg3HuKlpFIQqIRiOS1UzjZycQP28F2x97k0LlDS/yTSt5NhLmryJlww6OfvEbp35diCafX11LIlG9OtD1948va4GICzr+/hh7SRSoV68ihw6nFt+4FISFmvly6s3cPWFOkZvTV5JmsZW5e0yrf21+TVXZ9shrPhcfoiTS5IUH2PPq/6EVkTXubixiqhCGMz3TZ+XNXsu+I7RuDQCC3f/Qbe5nrOg1Bk2WUV0ygiQSM7g3NW8PPLv8WkV36VxDrB50H2eXrgOnd5dHdL8utJ/2OvELVnN48nfkHvMvC9YQGoxic/xj7M8jSBKVurSmz2rf1bJKy+YtZ3jq2SXk5nkaktimkURHhbL/QDIREUHcPboV3brW5IefdzL1883uaxSEguSmC4ii+7ivuP/GjSox5aObWL0mjm07z7Jm7Qns9n9W82azOwHNZnMF/NQhioJPjXpvhIWZGX1HC375bQ+ZF6lhXky7NlX5v49vwmgseQKc4nJx8P1viP9zOXKeDXtSKs70LELqVKfVB08TM9h3NSrF4WRBg/7knfKeWwDQ8cf3qHXXYBa3HUr6tr3eG4kClqgI6j0wiroP3M6cyI5efWeiycjg06u9PmHK+Tbi563EkZxGZPd2VGjesPgXf42h+/CvExSnkwPvfsWBt7/0CHuTgix0/vUjtj38Gs70LK+qmyVBtJjpOuv/iO7dEclc9qFveXlO+tz4vYegmsVi4NGHOjJyeKzXfna7zPYdCQiiQG6uk7feXYPsUpEVlfr1InhjUm/e+3AdmzefKYi4MZkk6tWtyHdf3VaowMeUTzcy/bfdHglagWI0SsQ2jeTAwWTs9qKfxkRRoEnjSH74xq3VfvZsNi+8vJwDB5NRNQ2r1UibVlW48/YWpVKfBHBmZjO3Vm9cmdlez0tBFrrMmELVAd7lqXc88TaHPvq+yDkkq4V2X71B4ooNbqkQb3bnvI9fCrJiiQwntGFtEhf/7dEstG4Nbjqy5LIEG1wL6Ab/OkOxO9j68Guc/HmeO26/QhhtprzIuSXriPthjn9qggEgBVkQJIkW7z5J5Rs6oykqwTWrltkN4I9Ze/l4ykYcDvcq22IxEFM1jB++HVJI8rcoZFnl5KkMgoNNhQTKNm46zaw5B8jLd9K/bz0G9K/vsVIeOPgnziWWXG0U4LWXezFwQANkWWX0uFmcPJVRICdsMUtUrBhEWpoNBLexL1/Owtdf3uKhP3NB875CBd+JXYGydsjDxM9eVmSbcs3q0+SZCeQcP02FZg2oMrAHosHtEZ4Z3hZnhvebxcVIQRa6z/+CNYPu94jiuRTRZKT2uCHE/7kCZ0YWqsOJYDIgGU30WPwVkV282jMddIN/3SLb7Liyc7FUCkcQRWZV6oAj1bNQRZkhnP/f+c9URJdWdPl1MkEx0aUees/eRP6YuY/09Hx69qjNoIENr1iVqkG3/kzC2eINmi/MJomNf99X8LvN7mLmrH0sXnoMq9XIsCFN6NunLsfj0tm3P5noqBDatql6xbT5f7PG+pXPYQgJQs6zIQW5s8Q1WUE0Gb26+7xhDAuh48/vk3P0FLtfmOzWl1I15DzvkWbBtWK4ccccjn8zk+S1WwlrUIt6D94esPjf9YZu8HUAmFOt+/nybr4p36oxmTsOlNmc1pgoBset8FqRy5aYwo7/vU383BUIkkTN22+ixbtPYSrnW1Xx3+Crb7by7Q87ChX48FfKRRQFevWozXtv9yu64b/I70HNLm/m63mMYSF0mfEJlft2wZGWQdLqLWiywobRT3vdyC3frAEDds+77Nd1rVGUwdfVMq8j6t47HMlq9npOkCRqjh6MuZJ3xcOSYotP4veg5syJ6cbBD79117MF8hNTWNDwRk79tggl346ck0fcd3NY0eMurrZFyOg7W9K4USRWqwGDQSQoyEj58lY+eKc/rVtVwWyWqFQpmOFDmxZSFDUZRUKCTTz6cId/9fqdmdkc/fI39k76lMTlGzz+vlVv8b0hGxDF+dRFkcge7QAwV6xA9SH9qDFiABFtYxGkwm40KchK/YfvLJvr0ilAD8u8jmj87L2kbd5F0uot7g0vQcBSuRJt/u8lIto1w1ShHNsee4OkZRt86w5IkqdOcTFosoItIYk9L08h7/Q5Gv1vLAtjByHn5BVqpzqd5Bw7xYH3v+bU9PlkHTyOtXIksa88TLVb+3Ds6xkkLl0PokB0747UHjcES0TZ3qC8YTYb+PqLW9ix8yz7DyQTFRVCj261MJsN9OxRu1DbkcNjmf7Lbk6cyqB5bGVGjoilUkRwQPPZk9OwnUshtG51DMGly4hN27qHFX3GoskqSr4NQ0gQ4W1j6bn46wJ9GWtUJbc7rpT3WXNkOI4k78V+RJOR7vM+96pp0/mPj1nZeyz58YkgCKgumRojB1Bn/NDSXZCOB7pL5zokY/chMnYeILhWDJHd2haKdsg+epK/WtziqXciCgiC6F4dlkJYXbSYie7dkbOLVns1MBeyJi/eWJas7k1hxeEodFw0m2j35WvkHD1J/J/LMYWXo8FjY6h2W9//ZASHnG9j45hnSJi/CtFkRFMUmr70EE2enVCi8ZI37GBV33EeOvNSkIUWbz9Bg0dHo6kqM8Ja+/SjB0KN2wcRf0kRE3C/p/23zqRCc9+lPjVNI3XjTmwJSYS3jdX99P/f3plHR1Xlefzze6/2JJBASAIJIUjYEkGCCDTYGgUVRUFobHFmVE4rSB+n1W7nIMLYttoto45KNy6NMCo2I66oOIgLsquIzRpCJGyyJQQIm5AQUlV3/qgiJKQqVSGkEqj7OadO3nLrvd+7efV99/3u7/5uA9A+fE292LfoO1b+ZhIVJaUor5ek3L5kT7qPJTfd1+DEV5a4mKBD4IHw8hacVV6sliofsBnjpOsDd9Lr6YcbZGdjc3hdAWsnPEfpqg04khPJnjye4i9XsOfDL/FUm/TDjHHSb+ZfaJXTHeXx0qJ7JzzlJ9n94Rf8vG03rXK614iYOU3Bi2+wftILQTtj4y/rxk3rPsFdVs77cb2rXG3njAjDdy1h89RZbHn1bV+fgAim3UbWo+Po8dj9DTu+Jmy04GvqjVKK8qL9WGKc2OJbUFZUwqeZ19dqvZ3GEhtD+q+HsP3NuSHzlNdb1OuJ4bBx684lOJJah/2d4q++YeuM9/CUldNh9FA6jB5aS0Tr4vhPe6g4eJj4S7tgOgL3k5zmyMZCvuj/6xotb8PpQJ2qDDha2rBZEYsFBKxxMXgrTuGtdOM+XoYl1oUrvR3XfzOnKm12RelhPkq7qs7Im4Re3blx7cds+NM0Nj75UsC3rdPROKFCKAH6vTGFTmNGAnBw1QZ2vjsfwzTpcMfNtMrJCvl9zflD59LR1BsRwZWaXLVuT0xALIFHcjpTk7lh5Xu40lIoXZXH0Y2FdR88iNgbdlvDJsXwY9pslP6QR+rQ3LDKr3v0v9k8bXaVAJcsWcWOWR+R+/n/YJh1j149ub+UZSPu5/DaTYjVCl4vvadOIvOe286UOXiIwmmzKVn8PbGZ6ZzYVVRLRL1BHqTgSwqG/w3mbPeM+3gZx7fuZMNjU+kz7Y8A7F++GsNmCyr4pstBp3tHcWzzdgqemRFY7B12cj+bwZG8zRROm83xbbtQARKfGXYbNxcsILbjGRdMYt+eJPbtWauspunRgq8JC9NmI+uRseRPmV5DdEyng4FvP48rLYXyfQf4ectP4R1QwLDZMKwWlNuDp+JUULEXq8UX5x3mS4HyenGm+Ibde91uSldtABFa+6NBDq/J58TOIhJ6ZyEi/Dj1rRpzp3pOlHNw5XqK5i8h9ZZrKf1+PWV7S4jv2ZXyvSWgFIkDe2PabCy9ZTyH1m7y9S34QxtXP/AXnG2TcKYkYtisfD1oDJXHjuM9WcHBb9f43Cfn8QXHe6qSne98ViX41hYxQV00Ypq0+WUfMsfdzo9TZ+EN1AEvwiVjbyP56r4kX92XFl06snzUA7U62cVqIWvi2Bpir2neaMHXhE32pPFYW8SS//R0Tu4vpWX3S+j9wqMkXXUFAKcOH8OwWsJrpSvI/s/fYmsZx9oJz9bp4kkckMOBpT+EZaOYJq70tiT0zqZk8UqW3/Yg3ko3KIVYTKyxLk6WlCKmrwO6Ve9s33R5Z+E+XsaWv89h3cTnKdtdjPJ6fa1y08C02zGsFnq/MJEjeYW1Ri57yspZest4rLEuKk+U+Vxc/usL1Eo+H7jLT7Lw2rsQhJ+37sQTJG228no5tHYTG6dMx7RYEMOo9ewxbFZiO6RWrScP+gX2VvF4yspr2G/abGSOu70xLkfTSDTIhy8itwF/AroDfZVSAZ3uIjIE+CtgAjOVUv8V6tjah3/h4XW7mZs0wDcVYxgM276QvfOXsm7Cc0H7BsRmRQyjRgu8BoaBNc7XolVuNy2yMvnl3JewuBzMyxgUMvpErBYQCZzBMUSoomG3YdistVq+TYFYTJQ7/HBZsVqxtW5J5ZFjtVw/psPOzT8uIKaa6J/YVcSK2x/i8NoCxBAcKW0YMPs52gxougydmsA0pg9/IzASmF7HyU3gZeA6YA/wg4jMU0qdv+GcmmaBYbHQ55XH+f6eSb4oDaWCdtDGZqYT27E9lUeO4anjjUCdqqzT+2G6nIzc/y1bp79L3pMvc3h1PvM6XBO0v6HW8SvdvvSZAXfW/V1vkE7WcBCLiVitdfruzxQ+yxZDMF1OPGXlvha6x1svsQdQlZVUHj5G8qD+lCz6vmqSG+X1cvm0x2qIPUBMejtu+O49yksO4j1ZgSu93QUZ+hrtNEjwlVIFQKh/fF9gq1Jqu7/sO8BwQAv+RUjG6KHEdkzjxxfe4MTOIuJ7dmHnnPl4Tlb4RMkQrHGxDFrsS6mcMngA+VNeCxzuGcbEs616Z1G6agNrJzxbo6VaHwG0tojxTRVZj7TFvpOocwpnFKuFlMEDuPyvk1mQc2utjtja56m5atrtxHZqz7FN23zXeY5v6d6KU5TtKmb4T4vYO28RKEXqsGtxprQJ+p3GnPRG0/hEwoefCuyutr4H6BeB82qaiMR+l3Hlu1Or1ns+9RDbZr7P0YJtJPa7jEvuHoG1RSwArftdRuqwayj6dPGZlM0Wk7jOGZzYtgvvqeCCarocdP3dv5H3xEsNmsy9zZWXs2/hd8HdRnVR34cEoDwe+r3+NK6UNgxe/BbLRz1A2a7i0F/04yk/ydH1m+t93kA42rTCmZxI5lg9K1Q0EFLwRWQhECjd4WSl1Cfn0xgRGQeMA0hPTz+fh9Y0Ic7kRC6d/NuA+0SEgf/7PLvnfsn2Nz9CROg4ZgT21vEsu/V+X0hiAAy7nZRBA0gbcR1r/hCySyg4hkHO8xNZ0COCsyJ5FaUr1+O6dTAxGWn1dsfUG9ME5a31cDJjnHT9/ZjGPbemWRFS8JVSDc2stBdoX209zb8t0LleA14DX6dtA8+ruUAQwyB91BDSRw2p2nb8pz1Bo32cqcn0f/1pUgYPQAyDhJzuteYyPXNwoWV2JmaLWI7lFdboYBWbhdxPp9OyS0faDc2laP6SoA+YWoc1TZTXc87hlT9v2QlA/pTpjZqyuv2vrqfPS39k+6yPKZw2m4rSQ5h2G96KSrInjSftlmsb7dya5kckXDo/AJ1FpCM+oR8N/EsEzqu5gInNSCPp6isoWbKqhvCbLge5/zedhF5n8rL0fOIBir9cEditoxTHd+wBpWqkLBCLSXx2F5Jy+7Lr/QVYW8bhbJdEefEBxDDwnKzAcNpRFbU7Zg2blcz7RlP48uxz9p+3u+FKAPbO+zrsh8wZ4wN3hFv8o3ANhw1V6aHbH8bQ86mHEBGyHxlL9iNjObppKydLDpKQk1U1MlcTPTQoPbKIjBCRPcAvgPki8oV/ezsR+QxAKeUG/h34AigA3lNK5TfMbE00cOUHf6P9iOt84Y92G670tvzyw2k1xB58aQIGL5lNfI8u/klYauI5Ue6Loa/m0lBuD8cKdzC/x82s/M0kdrw5l/LiA2AIPZ74HSP3fUNsRlrgVAd2Gy0v7YzFdW6zTsV160h8z64AWOsjuqZBXOcOdJ9wb1Xag6pdLge5819jRPEKrl8xh5H7v+WyP/++VkBFy6xMkq/pr8U+StG5dDTNHveJMiqPl+FIah0yFHDLq2+z5uFngsb1V+d0fpqzB045khMZUbSchdfcyYFlte9B02FnaMFnfHPHwxxZV1D15mDYbZhOu6/zWUHLrE4kDerP1lfmoNy+6RnbDOxN7oIZWP1pj3fM/oRV4x+vEakjFgvxOd1J6NWNnzfvILF/L7IeGYu9VXxVmZKlq8h7fBrHCncQ36MrPZ96UKcz0AA6l47mAscS4wo7L7zpclbFlIdCeT0Bo2zcJ8o4mr+Fbg+N4dDq/LPE2CQhJ4vYjDQGLZrFpmdmsGOWb1LujDuHkz1xHGKaeE9VVkUi5Uz5D45v340juXUN0QbI+NdhHFqziS2vvO3zrXs8xGV2IPfTv9cZApl8dV+Sl/wjrOvUaE6jW/iai4pTR47xUepVIdM4i9XiE+YAoZimy8GNaz8mrnMGeU9MY9MzM3xi7PbQonMGuQtm1Bmrfi6U7zvAodX5ONslkdCrux7UpDlndHpkTVRR9PkyVox6EEwDlMJb6abH4/dT/PlyDqxYDWKQess1JF19BesnvVjz4SBCXJcMbi5YUCW6FaWHObRmE86UROJ7dG2iq9JowkMLvibqcJ8oo+jz5Xgr3bS9fmCVK8VbWQkiGBYLyuvl27smsGfuVyAgpgWL086gpf+gZbdOTXwFGs25oQVfo6mDI/lbOPjNGhwpibS78SoMq7WpTdJozhndaavR1EF8dmfiszs3tRkaTaPToDh8jUaj0Vw4aMHXaDSaKEELvkaj0UQJWvA1Go0mStCCr9FoNFFCsw3LFJEDwM5GPEUicLARj38xoOsoNLqO6kbXT2jOdx11UEoFHArebAW/sRGRfwaLVdX40HUUGl1HdaPrJzSRrCPt0tFoNJooQQu+RqPRRAnRLPivNbUBFwC6jkKj66hudP2EJmJ1FLU+fI1Go4k2ormFr9FoNFGFFnyNRqOJEqJG8EXkNhHJFxGviAQNgRKRISKyWUS2isjESNrY1IhIKxH5SkS2+P8mBCnnEZF1/s+8SNsZaULdEyJiF5F3/fu/F5GMyFvZtIRRR2NE5EC1++beprCzqRCR10Vkv4hsDLJfRORv/vrbICK9G8OOqBF8YCMwElgWrICImMDLwI1AFnCHiGRFxrxmwUTga6VUZ+Br/3ogypVSvfyfYZEzL/KEeU/cAxxWSmUCLwLPRNbKpqUev5t3q903MyNqZNPzJjCkjv03Ap39n3HAq41hRNQIvlKqQCm1OUSxvsBWpdR2pdQp4B1geONb12wYDszyL88Cbm1CW5oL4dwT1evtA2CQRNektNH+uwmJUmoZcKiOIsOBt5SPlUC8iLQ933ZEjeCHSSqwu9r6Hv+2aCFZKVXsX94HJAcp5xCRf4rIShG52B8K4dwTVWWUUm7gKNA6ItY1D8L93fzK7674QETaR8a0C4aIaM9FNeOViCwEUgLsmqyU+iTS9jRH6qqj6itKKSUiwWJ2Oyil9orIJcAiEclTSm0737ZqLio+BeYopSpE5D58b0TXNrFNUcdFJfhKqcENPMReoHrLI82/7aKhrjoSkRIRaauUKva/Tu4Pcoy9/r/bRWQJkANcrIIfzj1xusweEbEALYHSyJjXLAhZR0qp6vUxE3g2AnZdSEREe7RLpyY/AJ1FpKOI2IDRwEUfhVKNecDd/uW7gVpvRSKSICJ2/3IiMBDYFDELI08490T1ehsFLFLRNaIxZB2d5Y8eBhRE0L4LgXnAXf5onf7A0Wru1fOHUioqPsAIfH6xCqAE+MK/vR3wWbVyNwGF+Fqsk5va7gjXUWt80TlbgIVAK//2PsBM//IAIA9Y7/97T1PbHYF6qXVPAE8Cw/zLDuB9YCuwCrikqW1uhnU0Bcj33zeLgW5NbXOE62cOUAxU+nXoHmA8MN6/X/BFOm3z/676NIYdOrWCRqPRRAnapaPRaDRRghZ8jUajiRK04Gs0Gk2UoAVfo9FoogQt+BqNRhMlaMHXaDSaKEELvkaj0UQJ/w+kksVCFGug4wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EmuUVtenj-tC"
      },
      "source": [
        "And let's see how our model is making predictions on it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_vFgOI88itVD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "59c5e43c-e8e2-4624-cfc0-c2f1b73a19e1"
      },
      "source": [
        "# Check the deicison boundary (blue is blue class, yellow is the crossover, red is red class)\n",
        "plot_decision_boundary(model_4, X, y)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "doing binary classifcation...\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XgNyVx3XkG4K"
      },
      "source": [
        "Well, it looks like we're getting a straight (linear) line prediction again. \n",
        "\n",
        "But our data is non-linear (not a straight line)...\n",
        "\n",
        "What we're going to have to do is add some non-linearity to our model.\n",
        "\n",
        "To do so, we'll use the `activation` parameter in on of our layers."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "utJIUKmHkbyV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fc8a7f4b-7510-4fea-ad7f-0be877dcc790"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model with a non-linear activation\n",
        "model_5 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1, activation=tf.keras.activations.relu), # can also do activation='relu'\n",
        "  tf.keras.layers.Dense(1) # output layer \n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_5.compile(loss=tf.keras.losses.binary_crossentropy,\n",
        "              optimizer=tf.keras.optimizers.Adam(),\n",
        "              metrics=[\"accuracy\"])\n",
        "\n",
        "# Fit the model\n",
        "history = model_5.fit(X, y, epochs=100)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.8377 - accuracy: 0.5000\n",
            "Epoch 2/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 1.4449 - accuracy: 0.5000\n",
            "Epoch 3/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.3410 - accuracy: 0.5000\n",
            "Epoch 4/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.2678 - accuracy: 0.4770\n",
            "Epoch 5/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 1.2116 - accuracy: 0.4390\n",
            "Epoch 6/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 1.1664 - accuracy: 0.4180\n",
            "Epoch 7/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.1294 - accuracy: 0.4250\n",
            "Epoch 8/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.0970 - accuracy: 0.4420\n",
            "Epoch 9/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 1.0670 - accuracy: 0.4540\n",
            "Epoch 10/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.0407 - accuracy: 0.4550\n",
            "Epoch 11/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 1.0147 - accuracy: 0.4600\n",
            "Epoch 12/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9872 - accuracy: 0.4630\n",
            "Epoch 13/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.9579 - accuracy: 0.4620\n",
            "Epoch 14/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.9201 - accuracy: 0.4660\n",
            "Epoch 15/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.8514 - accuracy: 0.4660\n",
            "Epoch 16/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7888 - accuracy: 0.4720\n",
            "Epoch 17/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7580 - accuracy: 0.4740\n",
            "Epoch 18/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7392 - accuracy: 0.4760\n",
            "Epoch 19/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7273 - accuracy: 0.4850\n",
            "Epoch 20/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7180 - accuracy: 0.4870\n",
            "Epoch 21/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7121 - accuracy: 0.4880\n",
            "Epoch 22/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7070 - accuracy: 0.4880\n",
            "Epoch 23/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.7036 - accuracy: 0.4870\n",
            "Epoch 24/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.7011 - accuracy: 0.4900\n",
            "Epoch 25/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6993 - accuracy: 0.4860\n",
            "Epoch 26/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6977 - accuracy: 0.4910\n",
            "Epoch 27/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6970 - accuracy: 0.4950\n",
            "Epoch 28/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6959 - accuracy: 0.4970\n",
            "Epoch 29/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6955 - accuracy: 0.4950\n",
            "Epoch 30/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6949 - accuracy: 0.4970\n",
            "Epoch 31/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6946 - accuracy: 0.4990\n",
            "Epoch 32/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6943 - accuracy: 0.4910\n",
            "Epoch 33/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6940 - accuracy: 0.5000\n",
            "Epoch 34/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6939 - accuracy: 0.4910\n",
            "Epoch 35/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6937 - accuracy: 0.4940\n",
            "Epoch 36/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6935 - accuracy: 0.4930\n",
            "Epoch 37/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4950\n",
            "Epoch 38/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6935 - accuracy: 0.4900\n",
            "Epoch 39/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4840\n",
            "Epoch 40/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.5000\n",
            "Epoch 41/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6936 - accuracy: 0.5060\n",
            "Epoch 42/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4800\n",
            "Epoch 43/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5050\n",
            "Epoch 44/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6936 - accuracy: 0.4810\n",
            "Epoch 45/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.4550\n",
            "Epoch 46/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6932 - accuracy: 0.4920\n",
            "Epoch 47/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4870\n",
            "Epoch 48/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.5100\n",
            "Epoch 49/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4770\n",
            "Epoch 50/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.5000\n",
            "Epoch 51/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6933 - accuracy: 0.4760\n",
            "Epoch 52/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.5010\n",
            "Epoch 53/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4880\n",
            "Epoch 54/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6933 - accuracy: 0.5530\n",
            "Epoch 55/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.5060\n",
            "Epoch 56/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6935 - accuracy: 0.5200\n",
            "Epoch 57/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6933 - accuracy: 0.4910\n",
            "Epoch 58/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4990\n",
            "Epoch 59/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6938 - accuracy: 0.5000\n",
            "Epoch 60/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.5000\n",
            "Epoch 61/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4900\n",
            "Epoch 62/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4820\n",
            "Epoch 63/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6933 - accuracy: 0.4700\n",
            "Epoch 64/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4820\n",
            "Epoch 65/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4620\n",
            "Epoch 66/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4760\n",
            "Epoch 67/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4830\n",
            "Epoch 68/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.4680\n",
            "Epoch 69/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5010\n",
            "Epoch 70/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4970\n",
            "Epoch 71/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6933 - accuracy: 0.4680\n",
            "Epoch 72/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.5070\n",
            "Epoch 73/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.5320\n",
            "Epoch 74/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5290\n",
            "Epoch 75/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6935 - accuracy: 0.5000\n",
            "Epoch 76/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4730\n",
            "Epoch 77/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4870\n",
            "Epoch 78/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4830\n",
            "Epoch 79/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6935 - accuracy: 0.4640\n",
            "Epoch 80/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5040\n",
            "Epoch 81/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6936 - accuracy: 0.5000\n",
            "Epoch 82/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.5020\n",
            "Epoch 83/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6936 - accuracy: 0.4840\n",
            "Epoch 84/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6932 - accuracy: 0.5070\n",
            "Epoch 85/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5000\n",
            "Epoch 86/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.5000\n",
            "Epoch 87/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.5000\n",
            "Epoch 88/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6933 - accuracy: 0.4680\n",
            "Epoch 89/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4590\n",
            "Epoch 90/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6937 - accuracy: 0.4980\n",
            "Epoch 91/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6933 - accuracy: 0.4910\n",
            "Epoch 92/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4850\n",
            "Epoch 93/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6938 - accuracy: 0.4970\n",
            "Epoch 94/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4710\n",
            "Epoch 95/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4720\n",
            "Epoch 96/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 0.6934 - accuracy: 0.4880\n",
            "Epoch 97/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4510\n",
            "Epoch 98/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6934 - accuracy: 0.4640\n",
            "Epoch 99/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6935 - accuracy: 0.4940\n",
            "Epoch 100/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 0.6936 - accuracy: 0.5180\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eW3l-KicgLW8"
      },
      "source": [
        "Hmm... still not learning...\n",
        "\n",
        "What we if increased the number of neurons and layers?\n",
        "\n",
        "Say, 2 hidden layers, with [ReLU](https://www.tensorflow.org/api_docs/python/tf/keras/activations/relu), pronounced \"rel-u\", (short for [rectified linear unit](https://machinelearningmastery.com/rectified-linear-activation-function-for-deep-learning-neural-networks/)), activation on the first one, and 4 neurons each?\n",
        "\n",
        "To see this network in action, check out the [TensorFlow Playground demo](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.001&regularizationRate=0&noise=0&networkShape=4,4&seed=0.93799&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&regularizationRate_hide=true&batchSize_hide=true&dataset_hide=true).\n",
        "\n",
        "![multi-layer neural net created with TensorFlow playground](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-tensorflow-playground-two-layer-net-relu-activation.png)\n",
        "*The neural network we're going to recreate with TensorFlow code. See it live at [TensorFlow Playground](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.001&regularizationRate=0&noise=0&networkShape=4,4&seed=0.93799&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&regularizationRate_hide=true&batchSize_hide=true&dataset_hide=true).*\n",
        "\n",
        "Let's try."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yXxtQFHwlc9w",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "02276bba-ee38-4c50-c289-b99ada09b752"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model\n",
        "model_6 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(4, activation=tf.keras.activations.relu), # hidden layer 1, 4 neurons, ReLU activation\n",
        "  tf.keras.layers.Dense(4, activation=tf.keras.activations.relu), # hidden layer 2, 4 neurons, ReLU activation\n",
        "  tf.keras.layers.Dense(1) # ouput layer\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_6.compile(loss=tf.keras.losses.binary_crossentropy,\n",
        "                optimizer=tf.keras.optimizers.Adam(lr=0.001), # Adam's default learning rate is 0.001\n",
        "                metrics=['accuracy'])\n",
        "\n",
        "# Fit the model\n",
        "history = model_6.fit(X, y, epochs=100)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n",
            "  super(Adam, self).__init__(name, **kwargs)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32/32 [==============================] - 1s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 2/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 3/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 4/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 5/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 6/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 7/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 8/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 9/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 10/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 11/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 12/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 13/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 14/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 15/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 16/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 17/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 18/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 19/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 20/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 21/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 22/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 23/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 24/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 25/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 26/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 27/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 28/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 29/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 30/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 31/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 32/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 33/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 34/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 35/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 36/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 37/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 38/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 39/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 40/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 41/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 42/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 43/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 44/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 45/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 46/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 47/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 48/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 49/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 50/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 51/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 52/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 53/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 54/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 55/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 56/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 57/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 58/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 59/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 60/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 61/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 62/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 63/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 64/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 65/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 66/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 67/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 68/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 69/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 70/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 71/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 72/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 73/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 74/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 75/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 76/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 77/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 78/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 79/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 80/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 81/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 82/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 83/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 84/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 85/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 86/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 87/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 88/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 89/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 90/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 91/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 92/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 93/100\n",
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 94/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 95/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 96/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 97/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 98/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 99/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n",
            "Epoch 100/100\n",
            "32/32 [==============================] - 0s 2ms/step - loss: 7.7125 - accuracy: 0.5000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bJqimQ0UsiO5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0ede99be-3fcc-42ca-800f-a525ca51718e"
      },
      "source": [
        "# Evaluate the model\n",
        "model_6.evaluate(X, y)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32/32 [==============================] - 0s 1ms/step - loss: 7.7125 - accuracy: 0.5000\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[7.712474346160889, 0.5]"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dh6l8egoc-Wr"
      },
      "source": [
        "We're still hitting 50% accuracy, our model is still practically as good as guessing.\n",
        "\n",
        "How do the predictions look?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OtmmuzJkcclw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "c68385b4-f8fe-4f26-c1e2-e9e5c56aa5d3"
      },
      "source": [
        "# Check out the predictions using 2 hidden layers\n",
        "plot_decision_boundary(model_6, X, y)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "doing binary classifcation...\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q-hj-lAodLYU"
      },
      "source": [
        "What gives? \n",
        "\n",
        "It seems like our model is the same as the one in the [TensorFlow Playground](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.03&regularizationRate=0&noise=0&networkShape=4,4&seed=0.93799&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&regularizationRate_hide=true&batchSize_hide=true) but model it's still drawing straight lines... \n",
        "\n",
        "Ideally, the yellow lines go on the inside of the red circle and the blue circle.\n",
        "\n",
        "Okay, okay, let's model this circle once and for all. \n",
        "\n",
        "One more model (I promise... actually, I'm going to have to break that promise... we'll be building plenty more models). \n",
        "\n",
        "This time we'll change the activation function on our output layer too. Remember the architecture of a classification model? For binary classification, the output layer activation is usually the [Sigmoid activation function](https://www.tensorflow.org/api_docs/python/tf/math/sigmoid)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zgyJ67E3corL"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model\n",
        "model_7 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(4, activation=tf.keras.activations.relu), # hidden layer 1, ReLU activation\n",
        "  tf.keras.layers.Dense(4, activation=tf.keras.activations.relu), # hidden layer 2, ReLU activation\n",
        "  tf.keras.layers.Dense(1, activation=tf.keras.activations.sigmoid) # ouput layer, sigmoid activation\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_7.compile(loss=tf.keras.losses.binary_crossentropy,\n",
        "                optimizer=tf.keras.optimizers.Adam(),\n",
        "                metrics=['accuracy'])\n",
        "\n",
        "# Fit the model\n",
        "history = model_7.fit(X, y, epochs=100, verbose=0)"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e5wpRgBVtSRK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "666556a3-bc92-4896-93c6-0d1367144d5d"
      },
      "source": [
        "# Evaluate our model\n",
        "model_7.evaluate(X, y)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32/32 [==============================] - 0s 1ms/step - loss: 0.2948 - accuracy: 0.9910\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.2948004901409149, 0.9909999966621399]"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XsB0aZ42eIS2"
      },
      "source": [
        "Woah! It looks like our model is getting some incredible results, let's check them out."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zSoLyVMmczP4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "53695ba5-50bd-4f3c-b0d3-93a01e3d3b07"
      },
      "source": [
        "# View the predictions of the model with relu and sigmoid activations\n",
        "plot_decision_boundary(model_7, X, y)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "doing binary classifcation...\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zKR2JO4PeTie"
      },
      "source": [
        "Nice! It looks like our model is almost perfectly (apart from a few examples) separating the two circles.\n",
        "\n",
        "> 🤔 **Question:** What's wrong with the predictions we've made? Are we really evaluating our model correctly here? Hint: what data did the model learn on and what did we predict on?\n",
        "\n",
        "Before we answer that, it's important to recognize what we've just covered.\n",
        "\n",
        "> 🔑 **Note:** The combination of **linear (straight lines) and non-linear (non-straight lines) functions** is one of the key fundamentals of neural networks.\n",
        "\n",
        "Think of it like this:\n",
        "\n",
        "If I gave you an unlimited amount of straight lines and non-straight lines, what kind of patterns could you draw?\n",
        "\n",
        "That's essentially what neural networks do to find patterns in data.\n",
        "\n",
        "Now you might be thinking, \"but I haven't seen a linear function or a non-linear function before...\"\n",
        "\n",
        "Oh but you have.\n",
        "\n",
        "We've been using them the whole time.\n",
        "\n",
        "They're what power the layers in the models we just built.\n",
        "\n",
        "To get some intuition about the activation functions we've just used, let's create them and then try them on some toy data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qm-b9aoemQ8A",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "76acda75-d194-4f92-a336-566df2884ae6"
      },
      "source": [
        "# Create a toy tensor (similar to the data we pass into our model)\n",
        "A = tf.cast(tf.range(-10, 10), tf.float32)\n",
        "A"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(20,), dtype=float32, numpy=\n",
              "array([-10.,  -9.,  -8.,  -7.,  -6.,  -5.,  -4.,  -3.,  -2.,  -1.,   0.,\n",
              "         1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.],\n",
              "      dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ti67IeWI9vnP"
      },
      "source": [
        "How does this look?\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mYWO_14e-Pf8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "3007d4e8-dd34-474f-b04a-4900f5401dfc"
      },
      "source": [
        "# Visualize our toy tensor\n",
        "plt.plot(A);"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5f9qOgTb-O7L"
      },
      "source": [
        "A straight (linear) line!\n",
        "\n",
        "Nice, now let's recreate the [sigmoid function](https://en.wikipedia.org/wiki/Sigmoid_function) and see what it does to our data. You can also find a pre-built sigmoid function at [`tf.keras.activations.sigmoid`](https://www.tensorflow.org/api_docs/python/tf/keras/activations/sigmoid)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "corG975yiwAP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8f85c710-8d43-41bc-f0e2-3e1865dbb1ac"
      },
      "source": [
        "# Sigmoid - https://www.tensorflow.org/api_docs/python/tf/keras/activations/sigmoid\n",
        "def sigmoid(x):\n",
        "  return 1 / (1 + tf.exp(-x))\n",
        "\n",
        "# Use the sigmoid function on our tensor\n",
        "sigmoid(A)"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(20,), dtype=float32, numpy=\n",
              "array([4.5397872e-05, 1.2339458e-04, 3.3535014e-04, 9.1105117e-04,\n",
              "       2.4726233e-03, 6.6928510e-03, 1.7986210e-02, 4.7425874e-02,\n",
              "       1.1920292e-01, 2.6894143e-01, 5.0000000e-01, 7.3105860e-01,\n",
              "       8.8079703e-01, 9.5257413e-01, 9.8201376e-01, 9.9330717e-01,\n",
              "       9.9752742e-01, 9.9908900e-01, 9.9966466e-01, 9.9987662e-01],\n",
              "      dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3EpZb0F6-cn7"
      },
      "source": [
        "And how does it look?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vz4Pr2Mk-eko",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "51453a9f-d6f8-4f89-938f-edc9fcd445aa"
      },
      "source": [
        "# Plot sigmoid modified tensor\n",
        "plt.plot(sigmoid(A));"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EGT2qtUV-k5f"
      },
      "source": [
        "A non-straight (non-linear) line!\n",
        "\n",
        "Okay, how about the [ReLU function](https://machinelearningmastery.com/rectified-linear-activation-function-for-deep-learning-neural-networks/#:~:text=The%20rectified%20linear%20activation%20function,otherwise%2C%20it%20will%20output%20zero.) (ReLU turns all negatives to 0 and positive numbers stay the same)?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_PUMn--Hiwyz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6503150e-3a9d-41ca-832f-76b63877c308"
      },
      "source": [
        "# ReLU - https://www.tensorflow.org/api_docs/python/tf/keras/activations/relu\n",
        "def relu(x):\n",
        "  return tf.maximum(0, x)\n",
        "\n",
        "# Pass toy tensor through ReLU function\n",
        "relu(A)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(20,), dtype=float32, numpy=\n",
              "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 2., 3., 4., 5., 6.,\n",
              "       7., 8., 9.], dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xAkmlNeZ-90e"
      },
      "source": [
        "How does the ReLU-modified tensor look?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iXWCO2R4mlk7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "2f4cb04c-d623-4b0b-f4a8-06a286b8d83d"
      },
      "source": [
        "# Plot ReLU-modified tensor\n",
        "plt.plot(relu(A));"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-NLdoxJr_Grk"
      },
      "source": [
        "Another non-straight line!\n",
        "\n",
        "Well, how about TensorFlow's [linear activation function](https://www.tensorflow.org/api_docs/python/tf/keras/activations/linear)? "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cg_kBQLVoXRB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "71524721-a1cf-4478-b60d-e18eacc4b3bf"
      },
      "source": [
        "# Linear - https://www.tensorflow.org/api_docs/python/tf/keras/activations/linear (returns input non-modified...)\n",
        "tf.keras.activations.linear(A)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(20,), dtype=float32, numpy=\n",
              "array([-10.,  -9.,  -8.,  -7.,  -6.,  -5.,  -4.,  -3.,  -2.,  -1.,   0.,\n",
              "         1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.],\n",
              "      dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d0NnpC_N_uWT"
      },
      "source": [
        "Hmm, it looks like our inputs are unmodified..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iwlgKpco_7V2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cef498e8-8dc7-4fd4-ccfc-002811a58d35"
      },
      "source": [
        "# Does the linear activation change anything?\n",
        "A == tf.keras.activations.linear(A)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(20,), dtype=bool, numpy=\n",
              "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True])>"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KcCT_ipvADpR"
      },
      "source": [
        "Okay, so it makes sense now the model doesn't really learn anything when using only linear activation functions, because the linear activation function doesn't change our input data in anyway.\n",
        "\n",
        "Where as, with our non-linear functions, our data gets manipulated. A neural network uses these kind of transformations at a large scale to figure draw patterns between its inputs and outputs.\n",
        "\n",
        "Now rather than dive into the guts of neural networks, we're going to keep coding applying what we've learned to different problems but if you want a more in-depth look at what's going on behind the scenes, check out the Extra Curriculum section below. \n",
        "\n",
        "> 📖  **Resource:** For more on activation functions, check out the [machine learning cheatsheet page](https://ml-cheatsheet.readthedocs.io/en/latest/activation_functions.html#) on them."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BPCpA90uQBjk"
      },
      "source": [
        "## Evaluating and improving our classification model\n",
        "\n",
        "If you answered the question above, you might've picked up what we've been doing wrong.\n",
        "\n",
        "We've been evaluating our model on the same data it was trained on.\n",
        "\n",
        "A better approach would be to split our data into training, validation (optional) and test sets.\n",
        "\n",
        "Once we've done that, we'll train our model on the training set (let it find patterns in the data) and then see how well it learned the patterns by using it to predict values on the test set.\n",
        "\n",
        "Let's do it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NjOviFscgl4S",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "152f5aa9-eb89-4a3e-b8de-edbd18aa57ad"
      },
      "source": [
        "# How many examples are in the whole dataset?\n",
        "len(X)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1000"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qNvKa8QrkSWR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9d99eacd-c6bb-42b0-ff1c-d6553554bfd0"
      },
      "source": [
        "# Split data into train and test sets\n",
        "X_train, y_train = X[:800], y[:800] # 80% of the data for the training set\n",
        "X_test, y_test = X[800:], y[800:] # 20% of the data for the test set\n",
        "\n",
        "# Check the shapes of the data\n",
        "X_train.shape, X_test.shape # 800 examples in the training set, 200 examples in the test set "
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((800, 2), (200, 2))"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YtNge18ahgqa"
      },
      "source": [
        "Great, now we've got training and test sets, let's model the training data and evaluate what our model has learned on the test set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0RUOBhA1g8Kx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "59b681ac-a3f5-4edb-ee3c-483e1649fd42"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model (same as model_7)\n",
        "model_8 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"), # hidden layer 1, using \"relu\" for activation (same as tf.keras.activations.relu)\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(1, activation=\"sigmoid\") # output layer, using 'sigmoid' for the output\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_8.compile(loss=tf.keras.losses.binary_crossentropy,\n",
        "                optimizer=tf.keras.optimizers.Adam(lr=0.01), # increase learning rate from 0.001 to 0.01 for faster learning\n",
        "                metrics=['accuracy'])\n",
        "\n",
        "# Fit the model\n",
        "history = model_8.fit(X_train, y_train, epochs=25)"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n",
            "  super(Adam, self).__init__(name, **kwargs)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6847 - accuracy: 0.5425\n",
            "Epoch 2/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6777 - accuracy: 0.5525\n",
            "Epoch 3/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6736 - accuracy: 0.5512\n",
            "Epoch 4/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6681 - accuracy: 0.5775\n",
            "Epoch 5/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6633 - accuracy: 0.5850\n",
            "Epoch 6/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6546 - accuracy: 0.5838\n",
            "Epoch 7/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6413 - accuracy: 0.6750\n",
            "Epoch 8/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6264 - accuracy: 0.7013\n",
            "Epoch 9/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6038 - accuracy: 0.7487\n",
            "Epoch 10/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.5714 - accuracy: 0.7738\n",
            "Epoch 11/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5404 - accuracy: 0.7650\n",
            "Epoch 12/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5015 - accuracy: 0.7837\n",
            "Epoch 13/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4683 - accuracy: 0.7975\n",
            "Epoch 14/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4113 - accuracy: 0.8450\n",
            "Epoch 15/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.3625 - accuracy: 0.9125\n",
            "Epoch 16/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.3209 - accuracy: 0.9312\n",
            "Epoch 17/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2847 - accuracy: 0.9488\n",
            "Epoch 18/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2597 - accuracy: 0.9525\n",
            "Epoch 19/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2375 - accuracy: 0.9563\n",
            "Epoch 20/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2135 - accuracy: 0.9663\n",
            "Epoch 21/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1938 - accuracy: 0.9775\n",
            "Epoch 22/25\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1752 - accuracy: 0.9737\n",
            "Epoch 23/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1619 - accuracy: 0.9787\n",
            "Epoch 24/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1550 - accuracy: 0.9775\n",
            "Epoch 25/25\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1490 - accuracy: 0.9762\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aAnKqoDxloAA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c765556f-140f-48e3-814d-7b64ca439f70"
      },
      "source": [
        "# Evaluate our model on the test set\n",
        "loss, accuracy = model_8.evaluate(X_test, y_test)\n",
        "print(f\"Model loss on the test set: {loss}\")\n",
        "print(f\"Model accuracy on the test set: {100*accuracy:.2f}%\")"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7/7 [==============================] - 0s 2ms/step - loss: 0.1247 - accuracy: 1.0000\n",
            "Model loss on the test set: 0.1246885135769844\n",
            "Model accuracy on the test set: 100.00%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c1lWpsNwjD5C"
      },
      "source": [
        "100% accuracy? Nice!\n",
        "\n",
        "Now, when we started to create `model_8` we said it was going to be the same as `model_7` but you might've found that to be a little lie.\n",
        "\n",
        "That's because we changed a few things: \n",
        "* **The `activation` parameter** - We used strings (`\"relu\"` & `\"sigmoid\"`) instead of using library paths (`tf.keras.activations.relu`), in TensorFlow, they both offer the same functionality.\n",
        "* **The `learning_rate` (also `lr`) parameter** - We increased the **learning rate** parameter in the [Adam optimizer](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adam) to `0.01` instead of `0.001` (an increase of 10x).\n",
        "  * You can think of the learning rate as how quickly a model learns. The higher the learning rate, the faster the model's capacity to learn, however, there's such a thing as a *too high* learning rate, where a model tries to learn too fast and doesn't learn anything. We'll see a trick to find the ideal learning rate soon.\n",
        "* **The number of epochs** - We lowered the number of epochs (using the `epochs` parameter) from 100 to 25 but our model still got an incredible result on both the training and test sets.\n",
        "  * One of the reasons our model performed well in even less epochs (remember a single epoch is the model trying to learn patterns in the data by looking at it once, so 25 epochs means the model gets 25 chances) than before is because we increased the learning rate.\n",
        "\n",
        "We know our model is performing well based on the evaluation metrics but let's see how it performs visually.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LRvAIBfAmtdc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 425
        },
        "outputId": "74f420fc-1f84-4261-b5bc-1a89b3ea5bba"
      },
      "source": [
        "# Plot the decision boundaries for the training and test sets\n",
        "plt.figure(figsize=(12, 6))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.title(\"Train\")\n",
        "plot_decision_boundary(model_8, X=X_train, y=y_train)\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.title(\"Test\")\n",
        "plot_decision_boundary(model_8, X=X_test, y=y_test)\n",
        "plt.show()"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "doing binary classifcation...\n",
            "doing binary classifcation...\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "42KDFaHonmGN"
      },
      "source": [
        "Check that out! How cool. With a few tweaks, our model is now predicting the blue and red circles almost perfectly."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EqaFRxFaiklC"
      },
      "source": [
        "### Plot the loss curves\n",
        "\n",
        "Looking at the plots above, we can see the outputs of our model are very good.\n",
        "\n",
        "But how did our model go whilst it was learning?\n",
        "\n",
        "As in, how did the performance change everytime the model had a chance to look at the data (once every epoch)?\n",
        "\n",
        "To figure this out, we can check the **loss curves** (also referred to as the **learning curves**).\n",
        "\n",
        "You might've seen we've been using the variable `history` when calling the `fit()` function on a model ([`fit()` returns a `History` object](https://www.tensorflow.org/api_docs/python/tf/keras/Model#fit)).\n",
        "\n",
        "This is where we'll get the information for how our model is performing as it learns.\n",
        "\n",
        "Let's see how we might use it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sBHuMm9mpoOz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 833
        },
        "outputId": "b9023bfb-6073-4aec-ab61-a026977cfdd5"
      },
      "source": [
        "# You can access the information in the history variable using the .history attribute\n",
        "pd.DataFrame(history.history)"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>loss</th>\n",
              "      <th>accuracy</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.684651</td>\n",
              "      <td>0.54250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.677721</td>\n",
              "      <td>0.55250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.673595</td>\n",
              "      <td>0.55125</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.668149</td>\n",
              "      <td>0.57750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.663269</td>\n",
              "      <td>0.58500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>0.654567</td>\n",
              "      <td>0.58375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0.641258</td>\n",
              "      <td>0.67500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0.626428</td>\n",
              "      <td>0.70125</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>0.603831</td>\n",
              "      <td>0.74875</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>0.571404</td>\n",
              "      <td>0.77375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>0.540443</td>\n",
              "      <td>0.76500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>0.501504</td>\n",
              "      <td>0.78375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>0.468332</td>\n",
              "      <td>0.79750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>0.411302</td>\n",
              "      <td>0.84500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>0.362506</td>\n",
              "      <td>0.91250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>0.320904</td>\n",
              "      <td>0.93125</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>0.284708</td>\n",
              "      <td>0.94875</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>0.259720</td>\n",
              "      <td>0.95250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>0.237469</td>\n",
              "      <td>0.95625</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>0.213520</td>\n",
              "      <td>0.96625</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>0.193820</td>\n",
              "      <td>0.97750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>0.175244</td>\n",
              "      <td>0.97375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>0.161893</td>\n",
              "      <td>0.97875</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>0.154989</td>\n",
              "      <td>0.97750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>0.148973</td>\n",
              "      <td>0.97625</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        loss  accuracy\n",
              "0   0.684651   0.54250\n",
              "1   0.677721   0.55250\n",
              "2   0.673595   0.55125\n",
              "3   0.668149   0.57750\n",
              "4   0.663269   0.58500\n",
              "5   0.654567   0.58375\n",
              "6   0.641258   0.67500\n",
              "7   0.626428   0.70125\n",
              "8   0.603831   0.74875\n",
              "9   0.571404   0.77375\n",
              "10  0.540443   0.76500\n",
              "11  0.501504   0.78375\n",
              "12  0.468332   0.79750\n",
              "13  0.411302   0.84500\n",
              "14  0.362506   0.91250\n",
              "15  0.320904   0.93125\n",
              "16  0.284708   0.94875\n",
              "17  0.259720   0.95250\n",
              "18  0.237469   0.95625\n",
              "19  0.213520   0.96625\n",
              "20  0.193820   0.97750\n",
              "21  0.175244   0.97375\n",
              "22  0.161893   0.97875\n",
              "23  0.154989   0.97750\n",
              "24  0.148973   0.97625"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mblFGnDap48J"
      },
      "source": [
        "Inspecting the outputs, we can see the loss values going down and the accuracy going up. \n",
        "\n",
        "How's it look (visualize, visualize, visualize)?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mqlwnZGJpYNF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "7c09e619-dcfb-40f7-ad3f-f453612720a3"
      },
      "source": [
        "# Plot the loss curves\n",
        "pd.DataFrame(history.history).plot()\n",
        "plt.title(\"Model_8 training curves\")"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Model_8 training curves')"
            ]
          },
          "metadata": {},
          "execution_count": 49
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mofXV4znqmNh"
      },
      "source": [
        "Beautiful. This is the ideal plot we'd be looking for when dealing with a classification problem, loss going down, accuracy going up.\n",
        "\n",
        "> 🔑 **Note:** For many problems, the loss function going down means the model is improving (the predictions it's making are getting closer to the ground truth labels)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QyZA0CYLir5-"
      },
      "source": [
        "### Finding the best learning rate\n",
        "\n",
        "Aside from the architecture itself (the layers, number of neurons, activations, etc), the most important hyperparameter you can tune for your neural network models is the **learning rate**.\n",
        "\n",
        "In `model_8` you saw we lowered the Adam optimizer's learning rate from the default of `0.001` (default) to `0.01`.\n",
        "\n",
        "And you might be wondering why we did this.\n",
        "\n",
        "Put it this way, it was a lucky guess.\n",
        "\n",
        "I just decided to try a lower learning rate and see how the model went.\n",
        "\n",
        "Now you might be thinking, \"Seriously? You can do that?\"\n",
        "\n",
        "And the answer is yes. You can change any of the hyperparamaters of your neural networks.\n",
        "\n",
        "With practice, you'll start to see what kind of hyperparameters work and what don't.\n",
        "\n",
        "That's an important thing to understand about machine learning and deep learning in general. It's very experimental. You build a model and evaluate it, build a model and evaluate it.\n",
        "\n",
        "That being said, I want to introduce you a trick which will help you find the optimal learning rate (at least to begin training with) for your models going forward.\n",
        "\n",
        "To do so, we're going to use the following:\n",
        "* A [learning rate **callback**](https://www.tensorflow.org/api_docs/python/tf/keras/callbacks/LearningRateScheduler).\n",
        "   * You can think of a callback as an extra piece of functionality you can add to your model *while* its training.\n",
        "* Another model (we could use the same ones as above, we we're practicing building models here).\n",
        "* A modified loss curves plot.\n",
        "\n",
        "We'll go through each with code, then explain what's going on.\n",
        "\n",
        "> 🔑 **Note:** The default hyperparameters of many neural network building blocks in TensorFlow are setup in a way which usually work right out of the box (e.g. the [Adam optimizer's](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adam) default settings can usually get good results on many datasets). So it's a good idea to try the defaults first, then adjust as needed."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3g05waDawhsZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d691c949-bdb6-488b-d549-656159933772"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create a model (same as model_8)\n",
        "model_9 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(1, activation=\"sigmoid\")\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_9.compile(loss=\"binary_crossentropy\", # we can use strings here too\n",
        "              optimizer=\"Adam\", # same as tf.keras.optimizers.Adam() with default settings\n",
        "              metrics=[\"accuracy\"]) \n",
        "\n",
        "# Create a learning rate scheduler callback\n",
        "lr_scheduler = tf.keras.callbacks.LearningRateScheduler(lambda epoch: 1e-4 * 10**(epoch/20)) # traverse a set of learning rate values starting from 1e-4, increasing by 10**(epoch/20) every epoch\n",
        "\n",
        "# Fit the model (passing the lr_scheduler callback)\n",
        "history = model_9.fit(X_train, \n",
        "                      y_train, \n",
        "                      epochs=100,\n",
        "                      callbacks=[lr_scheduler])"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6945 - accuracy: 0.4988 - lr: 1.0000e-04\n",
            "Epoch 2/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6938 - accuracy: 0.4975 - lr: 1.1220e-04\n",
            "Epoch 3/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6930 - accuracy: 0.4963 - lr: 1.2589e-04\n",
            "Epoch 4/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6922 - accuracy: 0.4975 - lr: 1.4125e-04\n",
            "Epoch 5/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6914 - accuracy: 0.5063 - lr: 1.5849e-04\n",
            "Epoch 6/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6906 - accuracy: 0.5013 - lr: 1.7783e-04\n",
            "Epoch 7/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6898 - accuracy: 0.4950 - lr: 1.9953e-04\n",
            "Epoch 8/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6889 - accuracy: 0.5038 - lr: 2.2387e-04\n",
            "Epoch 9/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6880 - accuracy: 0.5013 - lr: 2.5119e-04\n",
            "Epoch 10/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6871 - accuracy: 0.5050 - lr: 2.8184e-04\n",
            "Epoch 11/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6863 - accuracy: 0.5200 - lr: 3.1623e-04\n",
            "Epoch 12/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6856 - accuracy: 0.5163 - lr: 3.5481e-04\n",
            "Epoch 13/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6847 - accuracy: 0.5175 - lr: 3.9811e-04\n",
            "Epoch 14/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6842 - accuracy: 0.5200 - lr: 4.4668e-04\n",
            "Epoch 15/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6835 - accuracy: 0.5213 - lr: 5.0119e-04\n",
            "Epoch 16/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6829 - accuracy: 0.5213 - lr: 5.6234e-04\n",
            "Epoch 17/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6826 - accuracy: 0.5225 - lr: 6.3096e-04\n",
            "Epoch 18/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6819 - accuracy: 0.5300 - lr: 7.0795e-04\n",
            "Epoch 19/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6816 - accuracy: 0.5312 - lr: 7.9433e-04\n",
            "Epoch 20/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6811 - accuracy: 0.5387 - lr: 8.9125e-04\n",
            "Epoch 21/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6806 - accuracy: 0.5400 - lr: 0.0010\n",
            "Epoch 22/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6801 - accuracy: 0.5412 - lr: 0.0011\n",
            "Epoch 23/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6796 - accuracy: 0.5400 - lr: 0.0013\n",
            "Epoch 24/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6790 - accuracy: 0.5425 - lr: 0.0014\n",
            "Epoch 25/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6784 - accuracy: 0.5450 - lr: 0.0016\n",
            "Epoch 26/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6778 - accuracy: 0.5387 - lr: 0.0018\n",
            "Epoch 27/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6770 - accuracy: 0.5425 - lr: 0.0020\n",
            "Epoch 28/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6760 - accuracy: 0.5537 - lr: 0.0022\n",
            "Epoch 29/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6754 - accuracy: 0.5512 - lr: 0.0025\n",
            "Epoch 30/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6739 - accuracy: 0.5575 - lr: 0.0028\n",
            "Epoch 31/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6726 - accuracy: 0.5500 - lr: 0.0032\n",
            "Epoch 32/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6711 - accuracy: 0.5512 - lr: 0.0035\n",
            "Epoch 33/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6688 - accuracy: 0.5562 - lr: 0.0040\n",
            "Epoch 34/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6672 - accuracy: 0.5612 - lr: 0.0045\n",
            "Epoch 35/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6660 - accuracy: 0.5888 - lr: 0.0050\n",
            "Epoch 36/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6625 - accuracy: 0.5625 - lr: 0.0056\n",
            "Epoch 37/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6560 - accuracy: 0.5813 - lr: 0.0063\n",
            "Epoch 38/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6521 - accuracy: 0.6025 - lr: 0.0071\n",
            "Epoch 39/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6415 - accuracy: 0.7088 - lr: 0.0079\n",
            "Epoch 40/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6210 - accuracy: 0.7113 - lr: 0.0089\n",
            "Epoch 41/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5904 - accuracy: 0.7487 - lr: 0.0100\n",
            "Epoch 42/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5688 - accuracy: 0.7312 - lr: 0.0112\n",
            "Epoch 43/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5346 - accuracy: 0.7563 - lr: 0.0126\n",
            "Epoch 44/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4533 - accuracy: 0.8150 - lr: 0.0141\n",
            "Epoch 45/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.3455 - accuracy: 0.9112 - lr: 0.0158\n",
            "Epoch 46/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2570 - accuracy: 0.9463 - lr: 0.0178\n",
            "Epoch 47/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1968 - accuracy: 0.9575 - lr: 0.0200\n",
            "Epoch 48/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1336 - accuracy: 0.9700 - lr: 0.0224\n",
            "Epoch 49/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1310 - accuracy: 0.9613 - lr: 0.0251\n",
            "Epoch 50/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1002 - accuracy: 0.9700 - lr: 0.0282\n",
            "Epoch 51/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1166 - accuracy: 0.9638 - lr: 0.0316\n",
            "Epoch 52/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1368 - accuracy: 0.9513 - lr: 0.0355\n",
            "Epoch 53/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0879 - accuracy: 0.9787 - lr: 0.0398\n",
            "Epoch 54/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1187 - accuracy: 0.9588 - lr: 0.0447\n",
            "Epoch 55/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0733 - accuracy: 0.9712 - lr: 0.0501\n",
            "Epoch 56/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1132 - accuracy: 0.9550 - lr: 0.0562\n",
            "Epoch 57/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1057 - accuracy: 0.9613 - lr: 0.0631\n",
            "Epoch 58/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0664 - accuracy: 0.9750 - lr: 0.0708\n",
            "Epoch 59/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1898 - accuracy: 0.9275 - lr: 0.0794\n",
            "Epoch 60/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1895 - accuracy: 0.9312 - lr: 0.0891\n",
            "Epoch 61/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.4131 - accuracy: 0.8612 - lr: 0.1000\n",
            "Epoch 62/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1707 - accuracy: 0.9725 - lr: 0.1122\n",
            "Epoch 63/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0569 - accuracy: 0.9937 - lr: 0.1259\n",
            "Epoch 64/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1007 - accuracy: 0.9638 - lr: 0.1413\n",
            "Epoch 65/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1323 - accuracy: 0.9488 - lr: 0.1585\n",
            "Epoch 66/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1819 - accuracy: 0.9375 - lr: 0.1778\n",
            "Epoch 67/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6672 - accuracy: 0.7613 - lr: 0.1995\n",
            "Epoch 68/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5301 - accuracy: 0.6687 - lr: 0.2239\n",
            "Epoch 69/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4140 - accuracy: 0.7925 - lr: 0.2512\n",
            "Epoch 70/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4574 - accuracy: 0.7412 - lr: 0.2818\n",
            "Epoch 71/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4759 - accuracy: 0.7262 - lr: 0.3162\n",
            "Epoch 72/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.3748 - accuracy: 0.8112 - lr: 0.3548\n",
            "Epoch 73/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4710 - accuracy: 0.8150 - lr: 0.3981\n",
            "Epoch 74/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.4143 - accuracy: 0.8087 - lr: 0.4467\n",
            "Epoch 75/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5961 - accuracy: 0.7412 - lr: 0.5012\n",
            "Epoch 76/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4787 - accuracy: 0.7713 - lr: 0.5623\n",
            "Epoch 77/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4720 - accuracy: 0.7113 - lr: 0.6310\n",
            "Epoch 78/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2565 - accuracy: 0.8675 - lr: 0.7079\n",
            "Epoch 79/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 1.1824 - accuracy: 0.6275 - lr: 0.7943\n",
            "Epoch 80/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6873 - accuracy: 0.5425 - lr: 0.8913\n",
            "Epoch 81/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7068 - accuracy: 0.5575 - lr: 1.0000\n",
            "Epoch 82/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6879 - accuracy: 0.5838 - lr: 1.1220\n",
            "Epoch 83/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6996 - accuracy: 0.5700 - lr: 1.2589\n",
            "Epoch 84/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6471 - accuracy: 0.5863 - lr: 1.4125\n",
            "Epoch 85/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7457 - accuracy: 0.5312 - lr: 1.5849\n",
            "Epoch 86/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7546 - accuracy: 0.5038 - lr: 1.7783\n",
            "Epoch 87/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7681 - accuracy: 0.5063 - lr: 1.9953\n",
            "Epoch 88/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7596 - accuracy: 0.4963 - lr: 2.2387\n",
            "Epoch 89/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7778 - accuracy: 0.5063 - lr: 2.5119\n",
            "Epoch 90/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7741 - accuracy: 0.4787 - lr: 2.8184\n",
            "Epoch 91/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7851 - accuracy: 0.5163 - lr: 3.1623\n",
            "Epoch 92/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7441 - accuracy: 0.4888 - lr: 3.5481\n",
            "Epoch 93/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7354 - accuracy: 0.5163 - lr: 3.9811\n",
            "Epoch 94/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.7548 - accuracy: 0.4938 - lr: 4.4668\n",
            "Epoch 95/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.8087 - accuracy: 0.4863 - lr: 5.0119\n",
            "Epoch 96/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.7714 - accuracy: 0.4638 - lr: 5.6234\n",
            "Epoch 97/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.8001 - accuracy: 0.5013 - lr: 6.3096\n",
            "Epoch 98/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.9554 - accuracy: 0.4963 - lr: 7.0795\n",
            "Epoch 99/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.9268 - accuracy: 0.4913 - lr: 7.9433\n",
            "Epoch 100/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.8563 - accuracy: 0.4663 - lr: 8.9125\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KKln6dnbNPVR"
      },
      "source": [
        "Now our model has finished training, let's have a look at the training history."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wCd12upnyO4y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "outputId": "f5a153b4-53e9-4de2-f589-1b13450b2f40"
      },
      "source": [
        "# Checkout the history\n",
        "pd.DataFrame(history.history).plot(figsize=(10,7), xlabel=\"epochs\");"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9OkUFgZSx6hP"
      },
      "source": [
        "As you you see the learning rate exponentially increases as the number of epochs increases.\n",
        "\n",
        "And you can see the model's accuracy goes up (and loss goes down) at a specific point when the learning rate slowly increases.\n",
        "\n",
        "To figure out where this infliction point is, we can plot the loss versus the log-scale learning rate."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8fnEklbYyGBG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 462
        },
        "outputId": "db506f6e-9b50-4b1d-9290-7678fc197eba"
      },
      "source": [
        "# Plot the learning rate versus the loss\n",
        "lrs = 1e-4 * (10 ** (np.arange(100)/20))\n",
        "plt.figure(figsize=(10, 7))\n",
        "plt.semilogx(lrs, history.history[\"loss\"]) # we want the x-axis (learning rate) to be log scale\n",
        "plt.xlabel(\"Learning Rate\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.title(\"Learning rate vs. loss\");"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w0kMFKLvOF8s"
      },
      "source": [
        "To figure out the ideal value of the learning rate (at least the ideal value to *begin* training our model), the rule of thumb is to take the learning rate value where the loss is still decreasing but not quite flattened out (usually about 10x smaller than the bottom of the curve).\n",
        "\n",
        "In this case, our ideal learning rate ends up between `0.01` ($10^{-2}$) and `0.02`.\n",
        "\n",
        "![finding the ideal learning rate by plotting learning rate vs. loss](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-learning-rate-vs-loss.png)\n",
        "\n",
        "*The ideal learning rate at the start of model training is somewhere just before the loss curve bottoms out (a value where the loss is still decreasing).*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vJo-nDw4zFfx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fd873c10-831a-4196-8f85-f930c5704086"
      },
      "source": [
        "# Example of other typical learning rate values\n",
        "10**0, 10**-1, 10**-2, 10**-3, 1e-4"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 0.1, 0.01, 0.001, 0.0001)"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iALar-WvPlEc"
      },
      "source": [
        "Now we've estimated the ideal learning rate (we'll use `0.02`) for our model, let's refit it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EJ9wbXblzPPL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7a6242ea-e789-477c-c7f8-338049e329a6"
      },
      "source": [
        "# Set the random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model\n",
        "model_10 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(1, activation=\"sigmoid\")\n",
        "])\n",
        "\n",
        "# Compile the model with the ideal learning rate\n",
        "model_10.compile(loss=\"binary_crossentropy\",\n",
        "                optimizer=tf.keras.optimizers.Adam(lr=0.02), # to adjust the learning rate, you need to use tf.keras.optimizers.Adam (not \"adam\")\n",
        "                metrics=[\"accuracy\"])\n",
        "\n",
        "# Fit the model for 20 epochs (5 less than before)\n",
        "history = model_10.fit(X_train, y_train, epochs=20)"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n",
            "  super(Adam, self).__init__(name, **kwargs)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6837 - accuracy: 0.5600\n",
            "Epoch 2/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6744 - accuracy: 0.5750\n",
            "Epoch 3/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.6626 - accuracy: 0.5875\n",
            "Epoch 4/20\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6332 - accuracy: 0.6388\n",
            "Epoch 5/20\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.5830 - accuracy: 0.7563\n",
            "Epoch 6/20\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.4907 - accuracy: 0.8313\n",
            "Epoch 7/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.4251 - accuracy: 0.8450\n",
            "Epoch 8/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.3596 - accuracy: 0.8875\n",
            "Epoch 9/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.3152 - accuracy: 0.9100\n",
            "Epoch 10/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2512 - accuracy: 0.9500\n",
            "Epoch 11/20\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2152 - accuracy: 0.9500\n",
            "Epoch 12/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1721 - accuracy: 0.9750\n",
            "Epoch 13/20\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1443 - accuracy: 0.9837\n",
            "Epoch 14/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1232 - accuracy: 0.9862\n",
            "Epoch 15/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1085 - accuracy: 0.9850\n",
            "Epoch 16/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0940 - accuracy: 0.9937\n",
            "Epoch 17/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0827 - accuracy: 0.9962\n",
            "Epoch 18/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0798 - accuracy: 0.9937\n",
            "Epoch 19/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0845 - accuracy: 0.9875\n",
            "Epoch 20/20\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0790 - accuracy: 0.9887\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qb9xwISc0pnF"
      },
      "source": [
        "Nice! With a little higher learning rate (`0.02` instead of `0.01`) we reach a higher accuracy than `model_8` in less epochs (`20` instead of `25`).\n",
        "\n",
        "> 🛠 **Practice:** Now you've seen an example of what can happen when you change the learning rate, try changing the learning rate value in the [TensorFlow Playground](https://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.03&regularizationRate=0&noise=0&networkShape=4,2&seed=0.03154&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&regularizationRate_hide=true&problem_hide=true) and see what happens. What happens if you increase it? What happens if you decrease it?\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3ZCYAqitKUk2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "db781d1b-dea2-448f-c20e-63f5caed393e"
      },
      "source": [
        "# Evaluate model on the test dataset\n",
        "model_10.evaluate(X_test, y_test)"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7/7 [==============================] - 0s 2ms/step - loss: 0.0574 - accuracy: 0.9900\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.05740184709429741, 0.9900000095367432]"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YWqQShzZKT7R"
      },
      "source": [
        "\n",
        "\n",
        "Let's see how the predictions look."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rJbzQ5kQ2HSh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 425
        },
        "outputId": "c71fd1bd-66b1-4dc6-85b1-97a8ccbfc7bb"
      },
      "source": [
        "# Plot the decision boundaries for the training and test sets\n",
        "plt.figure(figsize=(12, 6))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.title(\"Train\")\n",
        "plot_decision_boundary(model_10, X=X_train, y=y_train)\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.title(\"Test\")\n",
        "plot_decision_boundary(model_10, X=X_test, y=y_test)\n",
        "plt.show()"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "doing binary classifcation...\n",
            "doing binary classifcation...\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ppVLzAao2Hkl"
      },
      "source": [
        "And as we can see, almost perfect again.\n",
        "\n",
        "These are the kind of experiments you'll be running often when building your own models.\n",
        "\n",
        "Start with default settings and see how they perform on your data.\n",
        "\n",
        "And if they don't perform as well as you'd like, improve them.\n",
        "\n",
        "Let's look at a few more ways to evaluate our classification models."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0bNdy1EbftYp"
      },
      "source": [
        "### More classification evaluation methods\n",
        "\n",
        "Alongside the visualizations we've been making, there are a number of different evaluation metrics we can use to evaluate our classification models.\n",
        "\n",
        "| **Metric name/Evaluation method** | **Defintion** | **Code** |\n",
        "| --- | --- | --- |\n",
        "| Accuracy | Out of 100 predictions, how many does your model get correct? E.g. 95% accuracy means it gets 95/100 predictions correct. | [`sklearn.metrics.accuracy_score()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html) or [`tf.keras.metrics.Accuracy()`](tensorflow.org/api_docs/python/tf/keras/metrics/Accuracy) |\n",
        "| Precision | Proportion of true positives over total number of samples. Higher precision leads to less false positives (model predicts 1 when it should've been 0). | [`sklearn.metrics.precision_score()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_score.html) or [`tf.keras.metrics.Precision()`](tensorflow.org/api_docs/python/tf/keras/metrics/Precision) |\n",
        "| Recall | Proportion of true positives over total number of true positives and false negatives (model predicts 0 when it should've been 1). Higher recall leads to less false negatives. | [`sklearn.metrics.recall_score()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.recall_score.html) or [`tf.keras.metrics.Recall()`](tensorflow.org/api_docs/python/tf/keras/metrics/Recall) |\n",
        "| F1-score | Combines precision and recall into one metric. 1 is best, 0 is worst. | [`sklearn.metrics.f1_score()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html) |\n",
        "| [Confusion matrix](https://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/)  | Compares the predicted values with the true values in a tabular way, if 100% correct, all values in the matrix will be top left to bottom right (diagnol line). | Custom function or [`sklearn.metrics.plot_confusion_matrix()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.plot_confusion_matrix.html) |\n",
        "| Classification report | Collection of some of the main classification metrics such as precision, recall and f1-score. | [`sklearn.metrics.classification_report()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html) |\n",
        "\n",
        "> 🔑 **Note:** Every classification problem will require different kinds of evaluation methods. But you should be familiar with at least the ones above.\n",
        "\n",
        "Let's start with accuracy.\n",
        "\n",
        "Because we passed `[\"accuracy\"]` to the `metrics` parameter when we compiled our model, calling `evaluate()` on it will return the loss as well as accuracy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LUvEwzqp4zVW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "09e702cc-fa25-4fda-9bad-030198b750dd"
      },
      "source": [
        "# Check the accuracy of our model\n",
        "loss, accuracy = model_10.evaluate(X_test, y_test)\n",
        "print(f\"Model loss on test set: {loss}\")\n",
        "print(f\"Model accuracy on test set: {(accuracy*100):.2f}%\")"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7/7 [==============================] - 0s 2ms/step - loss: 0.0574 - accuracy: 0.9900\n",
            "Model loss on test set: 0.05740184709429741\n",
            "Model accuracy on test set: 99.00%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a5fXPTGi5aRX"
      },
      "source": [
        "How about a confusion matrix?\n",
        "\n",
        "![anatomy of a confusion matrix](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-anatomy-of-a-confusion-matrix.png)\n",
        "*Anatomy of a confusion matrix (what we're going to be creating). Correct predictions appear down the diagonal (from top left to bottom right).*\n",
        "\n",
        "We can make a confusion matrix using [Scikit-Learn's `confusion_matrix`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html) method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g_Zee4lI5vi2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 364
        },
        "outputId": "7b31fb4a-b49a-43c4-f286-bee10f3e2fdc"
      },
      "source": [
        "# Create a confusion matrix\n",
        "from sklearn.metrics import confusion_matrix\n",
        "\n",
        "# Make predictions\n",
        "y_preds = model_10.predict(X_test)\n",
        "\n",
        "# Create confusion matrix\n",
        "confusion_matrix(y_test, y_preds)"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-58-f9843efd97f5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;31m# Create confusion matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mconfusion_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_preds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sklearn/metrics/_classification.py\u001b[0m in \u001b[0;36mconfusion_matrix\u001b[0;34m(y_true, y_pred, labels, sample_weight, normalize)\u001b[0m\n\u001b[1;32m    300\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    301\u001b[0m     \"\"\"\n\u001b[0;32m--> 302\u001b[0;31m     \u001b[0my_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_check_targets\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    303\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0my_type\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m\"binary\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"multiclass\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    304\u001b[0m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"%s is not supported\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0my_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sklearn/metrics/_classification.py\u001b[0m in \u001b[0;36m_check_targets\u001b[0;34m(y_true, y_pred)\u001b[0m\n\u001b[1;32m     93\u001b[0m         raise ValueError(\n\u001b[1;32m     94\u001b[0m             \"Classification metrics can't handle a mix of {0} and {1} targets\".format(\n\u001b[0;32m---> 95\u001b[0;31m                 \u001b[0mtype_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtype_pred\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     96\u001b[0m             )\n\u001b[1;32m     97\u001b[0m         )\n",
            "\u001b[0;31mValueError\u001b[0m: Classification metrics can't handle a mix of binary and continuous targets"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4GLOPxx9fx__"
      },
      "source": [
        "Ahh, it seems our predictions aren't in the format they need to be.\n",
        "\n",
        "Let's check them out."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aLBs249Gfu-W",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "850adda8-3c09-42e5-d4c4-5c685c4b26b6"
      },
      "source": [
        "# View the first 10 predictions\n",
        "y_preds[:10]"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[9.8526537e-01],\n",
              "       [9.9923790e-01],\n",
              "       [9.9032348e-01],\n",
              "       [9.9706942e-01],\n",
              "       [3.9622977e-01],\n",
              "       [1.8126935e-02],\n",
              "       [9.6829069e-01],\n",
              "       [1.9746721e-02],\n",
              "       [9.9967170e-01],\n",
              "       [5.6460500e-04]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zacw9BNegVkY"
      },
      "source": [
        "What about our test labels?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3BH8XHAegYMd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c97c7695-ad6b-41f5-a242-66697bfd3392"
      },
      "source": [
        "# View the first 10 test labels\n",
        "y_test[:10]"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1, 0, 0, 1, 0, 1, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4vd8EA95ggks"
      },
      "source": [
        "It looks like we need to get our predictions into the binary format (0 or 1).\n",
        "\n",
        "But you might be wondering, what format are they currently in?\n",
        "\n",
        "In their current format (`9.8526537e-01`), they're in a form called **prediction probabilities**.\n",
        "\n",
        "You'll see this often with the outputs of neural networks. Often they won't be exact values but more a probability of how *likely* they are to be one value or another.\n",
        "\n",
        "So one of the steps you'll often see after making predicitons with a neural network is converting the prediction probabilities into labels.\n",
        "\n",
        "In our case, since our ground truth labels (`y_test`) are binary (0 or 1), we can convert the prediction probabilities using to their binary form using [`tf.round()`](https://www.tensorflow.org/api_docs/python/tf/math/round)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YaS_yvGA6KV3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2663f394-b2ef-4a4b-bc71-8230a71dc884"
      },
      "source": [
        "# Convert prediction probabilities to binary format and view the first 10\n",
        "tf.round(y_preds)[:10]"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(10, 1), dtype=float32, numpy=\n",
              "array([[1.],\n",
              "       [1.],\n",
              "       [1.],\n",
              "       [1.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [1.],\n",
              "       [0.],\n",
              "       [1.],\n",
              "       [0.]], dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mLvWYgFIh_A9"
      },
      "source": [
        "Wonderful! Now we can use the `confusion_matrix` function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GEZx1WHCiC8n",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d3ea773e-13f0-46d8-b3d7-dd11f59edae3"
      },
      "source": [
        "# Create a confusion matrix\n",
        "confusion_matrix(y_test, tf.round(y_preds))"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[99,  2],\n",
              "       [ 0, 99]])"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VY1LmNeTiKHl"
      },
      "source": [
        "Alright, we can see the highest numbers are down the diagonal (from top left to bottom right) so this a good sign, but the rest of the matrix doesn't really tell us much.\n",
        "\n",
        "How about we make a function to make our confusion matrix a little more visual?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IIPSs9ERi78w",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 799
        },
        "outputId": "70e606c9-d6a3-4cbb-d129-73d488c79087"
      },
      "source": [
        "# Note: The following confusion matrix code is a remix of Scikit-Learn's \n",
        "# plot_confusion_matrix function - https://scikit-learn.org/stable/modules/generated/sklearn.metrics.plot_confusion_matrix.html\n",
        "# and Made with ML's introductory notebook - https://github.com/GokuMohandas/MadeWithML/blob/main/notebooks/08_Neural_Networks.ipynb \n",
        "\n",
        "figsize = (10, 10)\n",
        "\n",
        "# Create the confusion matrix\n",
        "cm = confusion_matrix(y_test, tf.round(y_preds))\n",
        "cm_norm = cm.astype(\"float\") / cm.sum(axis=1)[:, np.newaxis] # normalize it\n",
        "n_classes = cm.shape[0]\n",
        "\n",
        "# Let's prettify it\n",
        "fig, ax = plt.subplots(figsize=figsize)\n",
        "# Create a matrix plot\n",
        "cax = ax.matshow(cm, cmap=plt.cm.Blues) # https://matplotlib.org/3.2.0/api/_as_gen/matplotlib.axes.Axes.matshow.html\n",
        "fig.colorbar(cax)\n",
        "\n",
        "# Create classes\n",
        "classes = False\n",
        "\n",
        "if classes:\n",
        "  labels = classes\n",
        "else:\n",
        "  labels = np.arange(cm.shape[0])\n",
        "\n",
        "# Label the axes\n",
        "ax.set(title=\"Confusion Matrix\",\n",
        "       xlabel=\"Predicted label\",\n",
        "       ylabel=\"True label\",\n",
        "       xticks=np.arange(n_classes),\n",
        "       yticks=np.arange(n_classes),\n",
        "       xticklabels=labels,\n",
        "       yticklabels=labels)\n",
        "\n",
        "# Set x-axis labels to bottom\n",
        "ax.xaxis.set_label_position(\"bottom\")\n",
        "ax.xaxis.tick_bottom()\n",
        "\n",
        "# Adjust label size\n",
        "ax.xaxis.label.set_size(20)\n",
        "ax.yaxis.label.set_size(20)\n",
        "ax.title.set_size(20)\n",
        "\n",
        "# Set threshold for different colors\n",
        "threshold = (cm.max() + cm.min()) / 2.\n",
        "\n",
        "# Plot the text on each cell\n",
        "for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n",
        "  plt.text(j, i, f\"{cm[i, j]} ({cm_norm[i, j]*100:.1f}%)\",\n",
        "           horizontalalignment=\"center\",\n",
        "           color=\"white\" if cm[i, j] > threshold else \"black\",\n",
        "           size=15)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-63-5fac90fd5c5b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     46\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     47\u001b[0m \u001b[0;31m# Plot the text on each cell\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 48\u001b[0;31m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mitertools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproduct\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     49\u001b[0m   plt.text(j, i, f\"{cm[i, j]} ({cm_norm[i, j]*100:.1f}%)\",\n\u001b[1;32m     50\u001b[0m            \u001b[0mhorizontalalignment\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"center\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'itertools' is not defined"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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UaXZjSZKkPg5QliRJmiAmO5IkqY+TCg5Zkn2TXJLk0iSHjbs9kiSpW8aa7CTZBHg/8DTgGuDsJCdV1UXjbJckSRstJxUcuj2BS6vqsqq6Hfg48Lwxt0mSJHXIuMfs7ABc3fP5GuAxszdK8krglQBsdveRNEySpI1RcMzOWFTV0VW1vqrWZ9Otxt0cSZI0Qcad7FwL3L/n847tMkmSNBYx2Rmys4Fdk+ySZHNgf+CkMbdJkiR1yFiTnaq6M8mrgVOATYBjqurCcbZJkqSNXceCnbF3Y1FVJwMnj7sdkiSpm8Ze7EiSpLXFMTuSJEkTxGRHkiTNcAZlSZKkyWKxI0mSOs1uLEmSNM3HRUiSJE0Ykx1JktSnY8GOyY4kSeo2kx1JktTHMTuSJEkTxGRHkiT16ViwY7IjSZK6zWRHkiTNiGN2JEmSJorJjiRJmtbMoDzuVgyXyY4kSeo0kx1JktQjjtmRJEmaJCY7kiSpT8eCHZMdSZLUbRY7kiSp0+zGkiRJfRygLEmSNEFMdiRJ0ow4QFmSJGmimOxIkqRpzeMiuhXtmOxIkqROM9mRJEl9THYkSZImiMmOJEnq07Fgx2RHkiR1m8mOJEnq45gdSZKkCWKyI0mSZjiDsiRJ0mQx2ZEkSdNCHLMjSZI0SSx2JElSp9mNJUmS+nSsF8tkR5IkdZvJjiRJ6rOuY9GOyY4kSeo0kx1JktSnY8GOyY4kSeo2ix1JkjQtaR4EOorX0tqTbZKckOTbSS5O8rgk90ryxSTfbd+3XegYFjuSJGktezfw+ap6CPBI4GLgMODUqtoVOLX9PC/H7EiSpD7r1siYnSRbA08CDgSoqtuB25M8D9ir3ezDwOnAofMdx2RHkiSNy3ZJzul5vXLW+l2AG4EPJflGkg8kuRuwfVX9oN3mOmD7hU5isiNJkvqM8EGgG6pq/QLrNwV2B/6gqs5K8m5mdVlVVSWphU5isiNJktaqa4Brquqs9vMJNMXP9UnuB9C+37DQQSx2JElSn+aOrNV/LaaqrgOuTrJbu2gf4CLgJOCAdtkBwIkLHcduLEmStJb9AfDRJJsDlwEvpQlrjk9yEHAlsN9CB7DYkSRJ0wKENXI7FlBV5wNzjevZZ6nHsBtLkiR1msWOJEnqNLuxJElSn7UyqeCwmOxIkqROM9mRJEkzBnhI56Qw2ZEkSZ1msiNJkvp0LNiZv9hJctkyj1lV9cBl7itJkjRUCyU764AFH6w1j47Vg5IkbTwCrOtYtDNvsVNVO4+wHZIkSavCMTuSJKlPx4Kd5d+NlWTbJPcfZmMkSZKGbaBiJ8ndk/xNkuuADcDlPesek+TkJLsPu5GSJGl00s61s9qvUVlysZNka+CrwGuB7wMX0z8Y+b+AXwVeNMwGSpIkrcQgyc6fAg8HDqyq3YFP9q6sqv8D/oMBHrkuSZLWlmR0r1EZpNj5DeCUqvqnBba5EthhZU2SJEkankHuxtoR+NQi2/wPsPXymyNJksata/PsDJLs/Ai47yLb7EIzcFmSJGlNGKTYORt4TpJ7zLUyyf2AZwFfHkbDJEmShmGQYufdwL2Bk5M8tHdF+/mTwJbAe4bXPEmSNGoZ0WtUljxmp6pOSfIm4AjgAuAOgCQbgG1p2n1oVZ25Gg2VJElajoEmFayqN9HcWn4ScBPwU5qHhZ4MPLWq3jH0FkqSpJHq2qSCAz8bq6pOA05bhbZIkiQNnQ8ClSRJ0wKs69ad54MXO0l2Bn4HeDTNnDq3AN8A/rmqLp9/T0mSpNEbqNhJcgjwNmAz+gdSPx94Q5LDq+qdQ2yfJEkapRGPpxmFJRc7SV4EvINmYPJ7gNOB64CfB/YGXgO8I8m1VfWJ4TdVkiRpcIMkO4fQFDq7V9WVPcsvAf4jyYeBc4E/Aix2JEmaUB0Ldga69fxhwPGzCp1p7XidT9I8GV2SJGlNGCTZ+RFw8yLb3ATcuvzmSJKkcevamJ1Bkp0vAM+Yb2Wab+bp7XaSJElrwiDFzp8A2yb5WJIH9K5IshNwHLBNu50kSZpAU/PsjOI1KvN2YyX50hyLbwb2A34zyVXA9cD2wE7AJsC3gI/SPFJCkiRp7BYas7PXIvv9Yvvq9UiaZ2VJkqQJ1bUxO/MWO1U10ENCJUmS1iILGkmS1Gk+CFSSJPXpVifWMoudJDsCOwBbzLW+qs5YSaMkSZKGZdAHgT4deBfwkEU23WTZLZIkSWOTwLqODVBe8pidJI8FPkMzl877aFKuM4B/BL7dfv408ObhN1OSJGl5BhmgfDhwG7BHVR3cLjutqn4PeATwVuCpwAnDbaIkSRqlZDSvURmk2HkccFJVfX/2/tX4M+Bi4E1DbJ8kSdKKDDJmZ2vgqp7PtwN3m7XNV4AXr7RRkiRpfLo2qeAgyc4NwLazPj9w1jabAVuttFGSJEnDMkiy8x36i5uvAc9M8uCq+k6Snwd+E/juMBsoSZJGq2PBzkDJzueBJye5V/v53TQpzjeSnE1zR9Z9gKOG20RJkqTlG6TY+QfgScAdAFX1FeCFwOU0d2P9AHhVVf3TsBspSZJGI4R1Gc1rVJbcjVVVtwJnzVr2r8C/DrtRkiRJw+KzsSRJ0owRz4EzCj71XJIkddq8yU6Sy5Z5zKqq2bekS5KkCdG1eXYW6sZaB9Qyjrmq39CjH7oTXznrfat5Cklz2HaPV4+7CdJG6SeXXLX4RlrQvMVOVe08wnZIkqQ1omtjXLp2PZIkSX0sdiRJUqd567kkSZoWujdA2WRHkiR1msmOJEnqs65bwY7JjiRJ6jaTHUmS1MdkR5IkaYIMnOwk+WXgxcBDgbtV1VPb5TsDewJfrKqbhthGSZI0Ikn37sYaqNhJ8mbg9cwkQr2Pk1gHfAz4Q+C9Q2mdJEnSCi25GyvJ/sAbgC8CjwLe3ru+qi4DzgGeO8wGSpKk0VqX0bxGdj0DbPsa4FLgeVX1LeD2Oba5GNh1GA2TJEkahkG6sX4JOLaq5ipypnwf2H5lTZIkSePUsSE7AyU7AX62yDbbA7ctvzmSJEnDNUiy813g8fOtTLIOeCJw4UobJUmSxiPAuo5FO4MkO8cDuyc5ZJ71rwceBBy34lZJkiQNySDJzlHAC4G/SrIf7W3nSf4a+FVgPfA14OhhN1KSJI1O12YcXnKxU1U/TrI38G7gJcAm7arX0Yzl+Wfg1VV159BbKUmStEwDTSpYVbcAByZ5HbAHcG/gFuDrVXXjKrRPkiRpRZb1INCq+iFwypDbIkmS1oCOjU/uXLecJElSnyUnO0mOWeKmVVUHLbM9kiRpjJJ07tbzQbqxDlxkfdHcnl+AxY4kSVoTBil2dpln+TY0g5XfCJwJHLbSRkmSpPHpWLAz0K3nV86z6krgm0lOAb4F/DvwwSG0TZIkacWGNkC5qq4GPg0cPKxjSpKk0VuX0bxGdj1DPt71wK5DPqYkSdKyLWuenbkk2QR4Cs0kg5IkaQJ18UGgg9x6/qQFjnF/4KXAo4APDKFdkiRJQzFIsnM67cM/5xHgDOCPV9IgSZI0Xh0LdgYqdt7M3MXOz4CbaJ6P9fWhtEqSJGlIBrn1/MhVbIckSVoLRnyn1Cgs+W6sJMckee1qNkaSJGnYBrn1/MXAfVerIZIkaW3IiP4blUGKnSuw2JEkSRNmkGLnOOCZSbZdrcZIkiQN2yDFztuBc4DTkjwnyfar1CZJkjQmzaSC3XpcxIJ3YyX5XeD8qvoWcNvUYuDEdv1cu1VVDW1mZkmSpJVYrCg5FjiC5mnm/8nCkwpKkqQO6Nqt50tJYAJQVXutblMkSZKGz+4mSZLUZ55hKhNrkAHKkiRJE2cpyc42SXYa5KBVddUy2yNJksZo6m6sLllKsXNw+1qqWuJxJUmSVt1SipJbgZtXuyGSJGkNCHRsyM6Sip13VdWbV70lkiRJq8DuJkmS1Gddx6Id78aSJEmdZrEjSZKmrbVnYyXZJMk3knym/bxLkrOSXJrkE0k2X+wYFjuSJGktOxi4uOfzX9KMJ34QcBNw0GIHWLDYqap1Dk6WJGnjkozmtXg7siPwbOAD7ecATwFOaDf5MPD8xY5jsiNJksZluyTn9LxeOWv9UcCfAD9rP98buLmq7mw/XwPssNhJvBtLkiSNy4aqWj/XiiTPAW6oqnOT7LWSk1jsSJKkHmEda+LW8ycAz03yLGBL4J7Au2keY7Vpm+7sCFy72IHsxpIkSWtOVR1eVTtW1c7A/sCXquolwGnAC9rNDgBOXOxYFjuSJGlaWDsDlOdxKPC6JJfSjOH54GI72I0lSZLWtKo6HTi9/fNlwJ6D7G+xI0mSZgww4d+ksBtLkiR1msmOJEnq44NAJUmSJojJjiRJmjZ1N1aXmOxIkqROM9mRJEl9HLMjSZI0QUx2JElSn44FOyY7kiSp20x2JEnStNC9JKRr1yNJktTHYkeSJHWa3ViSJGlGIB0boWyyI0mSOs1kR5Ik9elWrmOyI0mSOs5kR5IkTQs+LkKSJGmimOxIkqQ+3cp1THYkSVLHmexIkqQ+HRuyY7IjSZK6zWRHkiT1iDMoS5IkTRKTHUmSNC10Lwnp2vVIkiT1MdmRJEl9HLMjSZI0QSx2JElSp9mNJUmS+nSrE8tkR5IkdZzJjiRJmhEHKEuSJE0Ukx1JkjTNSQUlSZImjMmOJEnq45gdSZKkCWKyI0mS+nQr1zHZkSRJHWeyI0mS+nRsyI7JjiRJ6jaTHUmSNK2ZZ6db0Y7JjiRJ6jSTHUmS1McxO5IkSRPEYkeSJHWa3ViSJKlHiAOUJUmSJofJjiRJ6uMAZUmSpAky1mQnyTHAc4AbquoR42yLJElyUsHVcCyw75jbIEmSOmysyU5VnZFk53G2QZIk9YhjdsYiySuTnJPknBs33Dju5kiSpAkyEcVOVR1dVeurav19trvPuJsjSVKnJaN5jcpEFDuSJEnL5Tw7kiSpjzMoD1GSjwFfBXZLck2Sg8bZHkmS1D3jvhvrReM8vyRJ6hdgXbeCHcfsSJKkbnPMjiRJ6uOYHUmSpAlisSNJkjrNbixJktTHx0VIkiRNEJMdSZLUxwHKkiRJE8RkR5IkTXNSQUmSpAljsiNJknrEMTuSJEmTxGRHkiTNiPPsSJIkTRSTHUmS1KdjwY7JjiRJ6jaTHUmSNK2ZZ6db2Y7JjiRJ6jSTHUmS1KdbuY7JjiRJ6jiLHUmS1Gl2Y0mSpH4d68cy2ZEkSZ1msiNJkvr4IFBJkqQJYrIjSZL6dGxOQZMdSZLUbSY7kiSpT8eCHZMdSZLUbSY7kiSpX8eiHZMdSZLUaSY7kiRpWnCeHUmSpIlisiNJkmbEeXYkSZImismOJEnq07Fgx2RHkiR1m8WOJEnqNLuxJElSv471Y5nsSJKkTjPZkSRJPeKkgpIkSaOQ5P5JTktyUZILkxzcLr9Xki8m+W77vu1Cx7HYkSRJfZLRvJbgTuCQqnoY8Fjg95M8DDgMOLWqdgVObT/Py2JHkiStSVX1g6o6r/3zj4CLgR2A5wEfbjf7MPD8hY7jmB1JkjQtjPRmrO2SnNPz+eiqOnquDZPsDDwaOAvYvqp+0K66Dth+oZNY7EiSpHHZUFXrF9soyd2BTwF/WFW3pqcPrKoqSS20v91YkiSpX0b0WkpTks1oCp2PVtW/tIuvT3K/dv39gBsWOobFjiRJWpPSRDgfBC6uqnf2rDoJOKD98wHAiQsdx24sSZLUZw3Ns/ME4HeA/0pyfrvs9cBfAMcnOQi4EthvoYNY7EiSpDWpqr7M/B1e+yz1OBY7kiSpzxLnwJkYjtmRJEmdZrIjSZL6dCzYMdmRJEndZrIjSZJmjHgK5VEw2ZEkSZ1msSNJkjrNbixJktRnDU0qOBQmO5IkqdNMdiRJ0rTgpIKSJEkTxWRHkiT16ViwY7IjSZK6zWRHkiT161i0Y7IjSZI6zWRHkiT1cZ4dSZKkCWKyI0mS+jjPjiRJ0gQx2ZEkSX06FuyY7EiSpG4z2ZEkSf06Fu2Y7EiSpE6z2JEkSZ1mN5YkSZoWnFRQkiRpopjsSJKkGXFSQUmSpIlisiNJkvp0LNgx2ZEkSd1msiNJkvp1LNox2ZEkSZ1msiNJknrEeXYkSZImicmOJEnq4zw7kiRJE8RkR5IkTQuduxnLZISMrrYAAAqkSURBVEeSJHWbyY4kSerXsWjHZEeSJHWaxY4kSeo0u7EkSVIfJxWUJEmaICY7kiSpj5MKSpIkTRCTHUmS1KdjwY7JjiRJ6jaTHUmSNCOO2ZEkSZooJjuSJGmWbkU7JjuSJKnTTHYkSdK04JgdSZKkiWKyI0mS+nQs2DHZkSRJ3TZxyc555527YavNcuW426Fl2Q7YMO5GSBshf/Ym2wNGfcKujdmZuGKnqu4z7jZoeZKcU1Xrx90OaWPjz542dnZjSZKkTpu4ZEeSJK2udGyIssmORunocTdA2kj5s6eNmsmORqaq/AdXGgN/9jSwbgU7JjuSJKnbTHYkSVKfjgU7JjsajST7JrkkyaVJDht3e6SNQZJjktyQ5IJxt0UaJ4sdrbokmwDvB54JPAx4UZKHjbdV0kbhWGDfcTdCkyUZ3WtULHY0CnsCl1bVZVV1O/Bx4HljbpPUeVV1BvDDcbdDGjfH7GgUdgCu7vl8DfCYMbVFkrQI59mRJEmaICY7GoVrgfv3fN6xXSZJWou6FeyY7GgkzgZ2TbJLks2B/YGTxtwmSdJGwmJHq66q7gReDZwCXAwcX1UXjrdVUvcl+RjwVWC3JNckOWjcbdJkyIheo2I3lkaiqk4GTh53O6SNSVW9aNxtkNYCix1JktRnlHPgjILdWJIkqdMsdiRJUqfZjSVJknrESQUlSZImicWOtMYlqSSnz1p2ZLt8r/G0ajCDtjfJse32O6/wvKcnqZUcYwnnGEpbpbUi+CBQqZPaX1a9r58m2ZDkS0lePO72rYa5iihJ6iLH7Ej93tS+bwY8hObp7HsnWV9Vrxtfs+7ifTRPj79q3A2RpLXOYkfqUVVH9n5Osg/wReAPk7ynqq4YR7tmq6oNwIZxt0OSJoHdWNICqupU4Ns03dh7QP/4kyQvTnJWkv9JcsXUfkl+LsnhSc5P8r/t+q8mmXNG2ySbJ3ljku8l+UmSy5O8NckW82w/7xiYJA9JckySK9pj3ZDkP5O8ql1/YM84lifP6r47ctaxHpPkhCTXJbk9ydVJ/iHJL8zTrl9J8vkkP0pya5J/T/K4Rb7mJWvb/qkklyX5cXuOryT57UX226L9Pi9vv5PvJTmifVbbXNs/pB2Lc3V73dcnOS7JbsO6Fmkt69qYHZMdaXFTP5KzB7oeAjwN+DRwGrA1QJJtgC8BjwbOA46h+R+LZwDHJXl4Vb1h+uBJgONpusy+R9NFtTnwMuCXBmpo8mzgk8AWwOeBjwHbAI8E/gT4O+B8mu66I4ArgWN7DnF6z7FeBhwN/ITmwa1XA7sCLwd+Lcljq+qqnu0fD/x72/Z/AS4FHtUe80uDXMcC/g64EDgD+AFwb+BZwEeS7FZVb5xnv+NpitUTgDtovusjgfVJnltV03+3SfZt278Zzd/tpcCOwG8Az06yd1WdN6TrkTQCFjvSApI8FdiNptA5e9bqpwCPq6pvzFp+FE2hc2hV/VXPsbYE/g14fZITqur8dtWLaH75fg3Yu6pua7c/Yo5zLtTW7YDjaH6un1JV/zFr/Y4A7XnPb49/xeyuu3bbBwN/D1wBPLmqru1Ztw/wBeDdwK+3y0JT1G0FPL+qTuzZ/uD2OxmGR1TV92a1dXPgc8BhSf6+t609Hgo8vKpuavf5U5oC9TnAbwMfaZdvS1Mg/h/wpKq6qOc8j6D5O/oAsPuQrkdak5xnR+qwtnvoyCRvS3ICTToS4KiqunLW5kfPLnSS3Jvml+c5vYUOQFvEHNoer/cOr5e276+fKnTa7X8IvGWA5h8A3BP4u9mFTnu8awY41qtoko2DZxcPbdfeSTTpzj3axY+nKQrP6C10Wu+jSaxWbHah0y67HXg/TZG3zzy7vmWq0Gn3uQ04vP34sp7tfpcmCTuit9Bp97kA+Efg0UketuyLkDRyJjtSvyPa9wJuBv4T+GBV/fMc2359jmV7AJsAdxn/0tqsfX9oz7LdgZ8BX55j+9MXb/K0x7bvnxtgn/lMjbN5cpI95lh/X5rrfDBwLjNJx1xF1k+TfBl44EoblWQnmoJxH2AnmiSp1w7z7HqXdtF83z+lSeGmTF33I+f5+3tw+/5Q4KI51kuTb8TjaUbBYkfqUVWD/IhfN8eye7fve7Sv+dy9589bAz+sqjuWeI75bNO+z9WNM6ip6/jjRbabuo6t2/fr59lukOuYU5JfpCkwt6UpQr8A3EJTsOxMk2zNOaB7rnZV1Z1JNtAUblOmrvsVizTn7ousl7SGWOxIyzfXzLy3tO/vGmBenluAeyXZbI6C5+cHaM/N7fsOwH8NsN98bQLYuqpuHWD77edZP8h1zOd1NMXIS6vq2N4V7V1uByyw7/bMmpMoyabAdkDv9U1dxyOr6lsrbbA0iQIdG7HjmB1p2L5O0yX1qwPscx7Nz+IT51i31wDH+Vr7/swlbv8zmq6ohY611OuYujvpybNXJNmEua9tUA9q3z81x7q7nHcJ659Ic/29464GvW5JE8BiRxqiqroB+CjNLc1vbH/R90nywCS79Cz6UPv+tvaOrant7gW8gaX7ME1K8aokT5rjvDvOWvTfwP3nOdb7aG7Rfld7Z9bsY22epLcgOBO4BHhSkufN2vzVDGG8Ds2dYTCrAEzyDJrb4RfyxvZOq6l9tgTe3n78UM92H6JJyI5IsufsgyRZN9fcRlLnZESvEbEbSxq+V9PMR/Nm4HfawbnXA79AM7B1D5rbzS9vt/8Y8FvAc4ELkpxIM5D5BTS3ni+pUKiqDWme43UCcFqSzwHforlD65dpCpveIutUYP8kn6ZJZu6guZvqjKr6djvPzjHAhUk+D3ynbddONMnHjTSP1KCqKslBNLNNfypJ7zw7+9Dc1bbv0r6+ef0tzZ1rn2zvlPs+8Ij2uMfTfIfzubi9jt55dh4IfJb2tvP2Ov47yQuAfwW+luRUmnl9iub7exxNV9qWSJoYFjvSkFXVrUmeDLyS5hbz36T55Xg98F3gtTRFwdT2leSFwGHAgTTF0g9oUoY3A7exRFX12STrmblj6enATTSzQL991uYH0/wS34dmYr51NJMNntEe65+TfJNm8sS922P9L02RcQLwiVnn/kqb9ryNma60s2iSmGewwmKnqr6VZG/grcCzaf79+ibNZH83s3Cxsx/wRuAlNEXntTSTCv5F74SC7XlOTfLLwB+17f5V4Haa6/4Sc3ejSVrDMuvnXJIkbcR2/5X1dcaZS57PdEXuseW6c6tq/WqfxzE7kiSp0+zGkiRJfbo2qaDJjiRJ6jSTHUmS1KdjwY7JjiRJ6jaTHUmS1K9j0Y7JjiRJ6jSTHUmS1Ccdi3ZMdiRJ0pqVZN8klyS5NMlhyzmGyY4kSZoW1s48O+3DlN8PPA24Bjg7yUlVddEgxzHZkSRJa9WewKVVdVlV3Q58nOZBvgMx2ZEkSdPOO+/cU7baLNuN6HRbJjmn5/PRVXV0z+cdgKt7Pl8DPGbQk1jsSJKkaVW177jbMGx2Y0mSpLXqWuD+PZ93bJcNxGJHkiStVWcDuybZJcnmwP7ASYMexG4sSZK0JlXVnUleDZwCbAIcU1UXDnqcVNXQGydJkrRW2I0lSZI6zWJHkiR1msWOJEnqNIsdSZLUaRY7kiSp0yx2JElSp1nsSJKkTvv/HwyKszijnZIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x720 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0EaKOeeNnWbq"
      },
      "source": [
        "That looks much better. It seems our model has made almost perfect predictions on the test set except for two false positives (top right corner)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZvNQjM-rk7uE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b6befc2f-2c20-46a1-c763-9edf928407e9"
      },
      "source": [
        "# What does itertools.product do? Combines two things into each combination\n",
        "import itertools\n",
        "for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n",
        "  print(i, j)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 0\n",
            "0 1\n",
            "1 0\n",
            "1 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2WLKnUi6fI6B"
      },
      "source": [
        "## Working with a larger example (multiclass classification)\n",
        "\n",
        "We've seen a binary classification example (predicting if a data point is part of a red circle or blue circle) but what if you had multiple different classes of things?\n",
        "\n",
        "For example, say you were a fashion company and you wanted to build a neural network to predict whether a piece of clothing was a shoe, a shirt or a jacket (3 different options).\n",
        "\n",
        "When you have more than two classes as an option, this is known as **multiclass classification**.\n",
        "\n",
        "The good news is, the things we've learned so far (with a few tweaks) can be applied to multiclass classification problems as well.\n",
        "\n",
        "Let's see it in action.\n",
        "\n",
        "To start, we'll need some data. The good thing for us is TensorFlow has a multiclass classication dataset known as [Fashion MNIST built-in](https://github.com/zalandoresearch/fashion-mnist). Meaning we can get started straight away.\n",
        "\n",
        "We can import it using the [`tf.keras.datasets`](https://www.tensorflow.org/api_docs/python/tf/keras/datasets) module.\n",
        "\n",
        "> 📖 **Resource:** The following multiclass classification problem has been adapted from the [TensorFlow classification guide](https://www.tensorflow.org/tutorials/keras/classification). A good exercise would be to once you've gone through the following example, replicate the TensorFlow guide."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zl50sxPTqpw4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5a2c2a6f-c657-4eb8-de07-58edec5810c4"
      },
      "source": [
        "import tensorflow as tf\n",
        "from tensorflow.keras.datasets import fashion_mnist\n",
        "\n",
        "# The data has already been sorted into training and test sets for us\n",
        "(train_data, train_labels), (test_data, test_labels) = fashion_mnist.load_data()"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-labels-idx1-ubyte.gz\n",
            "32768/29515 [=================================] - 0s 0us/step\n",
            "40960/29515 [=========================================] - 0s 0us/step\n",
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-images-idx3-ubyte.gz\n",
            "26427392/26421880 [==============================] - 0s 0us/step\n",
            "26435584/26421880 [==============================] - 0s 0us/step\n",
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-labels-idx1-ubyte.gz\n",
            "16384/5148 [===============================================================================================] - 0s 0us/step\n",
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-images-idx3-ubyte.gz\n",
            "4423680/4422102 [==============================] - 0s 0us/step\n",
            "4431872/4422102 [==============================] - 0s 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D6qJforMrCZy"
      },
      "source": [
        "Now let's check out an example."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8PWdrQsyrBcy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "132c0e16-360a-4cdd-c826-db314dd68a50"
      },
      "source": [
        "# Show the first training example\n",
        "print(f\"Training sample:\\n{train_data[0]}\\n\") \n",
        "print(f\"Training label: {train_labels[0]}\")"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training sample:\n",
            "[[  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   1   0   0  13  73   0\n",
            "    0   1   4   0   0   0   0   1   1   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   3   0  36 136 127  62\n",
            "   54   0   0   0   1   3   4   0   0   3]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   6   0 102 204 176 134\n",
            "  144 123  23   0   0   0   0  12  10   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 155 236 207 178\n",
            "  107 156 161 109  64  23  77 130  72  15]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   1   0  69 207 223 218 216\n",
            "  216 163 127 121 122 146 141  88 172  66]\n",
            " [  0   0   0   0   0   0   0   0   0   1   1   1   0 200 232 232 233 229\n",
            "  223 223 215 213 164 127 123 196 229   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 183 225 216 223 228\n",
            "  235 227 224 222 224 221 223 245 173   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 193 228 218 213 198\n",
            "  180 212 210 211 213 223 220 243 202   0]\n",
            " [  0   0   0   0   0   0   0   0   0   1   3   0  12 219 220 212 218 192\n",
            "  169 227 208 218 224 212 226 197 209  52]\n",
            " [  0   0   0   0   0   0   0   0   0   0   6   0  99 244 222 220 218 203\n",
            "  198 221 215 213 222 220 245 119 167  56]\n",
            " [  0   0   0   0   0   0   0   0   0   4   0   0  55 236 228 230 228 240\n",
            "  232 213 218 223 234 217 217 209  92   0]\n",
            " [  0   0   1   4   6   7   2   0   0   0   0   0 237 226 217 223 222 219\n",
            "  222 221 216 223 229 215 218 255  77   0]\n",
            " [  0   3   0   0   0   0   0   0   0  62 145 204 228 207 213 221 218 208\n",
            "  211 218 224 223 219 215 224 244 159   0]\n",
            " [  0   0   0   0  18  44  82 107 189 228 220 222 217 226 200 205 211 230\n",
            "  224 234 176 188 250 248 233 238 215   0]\n",
            " [  0  57 187 208 224 221 224 208 204 214 208 209 200 159 245 193 206 223\n",
            "  255 255 221 234 221 211 220 232 246   0]\n",
            " [  3 202 228 224 221 211 211 214 205 205 205 220 240  80 150 255 229 221\n",
            "  188 154 191 210 204 209 222 228 225   0]\n",
            " [ 98 233 198 210 222 229 229 234 249 220 194 215 217 241  65  73 106 117\n",
            "  168 219 221 215 217 223 223 224 229  29]\n",
            " [ 75 204 212 204 193 205 211 225 216 185 197 206 198 213 240 195 227 245\n",
            "  239 223 218 212 209 222 220 221 230  67]\n",
            " [ 48 203 183 194 213 197 185 190 194 192 202 214 219 221 220 236 225 216\n",
            "  199 206 186 181 177 172 181 205 206 115]\n",
            " [  0 122 219 193 179 171 183 196 204 210 213 207 211 210 200 196 194 191\n",
            "  195 191 198 192 176 156 167 177 210  92]\n",
            " [  0   0  74 189 212 191 175 172 175 181 185 188 189 188 193 198 204 209\n",
            "  210 210 211 188 188 194 192 216 170   0]\n",
            " [  2   0   0   0  66 200 222 237 239 242 246 243 244 221 220 193 191 179\n",
            "  182 182 181 176 166 168  99  58   0   0]\n",
            " [  0   0   0   0   0   0   0  40  61  44  72  41  35   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]]\n",
            "\n",
            "Training label: 9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MMqbRp8jrdtv"
      },
      "source": [
        "Woah, we get a large list of numbers, followed (the data) by a single number (the class label).\n",
        "\n",
        "What about the shapes?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gN5-jr6arj19",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "08535f9c-c714-445c-8f12-df6ef87f6749"
      },
      "source": [
        "# Check the shape of our data\n",
        "train_data.shape, train_labels.shape, test_data.shape, test_labels.shape"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((60000, 28, 28), (60000,), (10000, 28, 28), (10000,))"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wNfIOUUEsJRt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7ac5b07-10dd-47eb-c238-1eca2d39f195"
      },
      "source": [
        "# Check shape of a single example\n",
        "train_data[0].shape, train_labels[0].shape"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((28, 28), ())"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r2wW0cEfsAve"
      },
      "source": [
        "Okay, 60,000 training examples each with shape (28, 28) and a label each as well as 10,000 test examples of shape (28, 28).\n",
        "\n",
        "But these are just numbers, let's visualize."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RmC2VsWOscKP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "3bd60d20-a1be-4e1f-f7ad-8215f9560388"
      },
      "source": [
        "# Plot a single example\n",
        "import matplotlib.pyplot as plt\n",
        "plt.imshow(train_data[7]);"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sOqirdtfstdQ"
      },
      "source": [
        "Hmm, but what about its label?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hzTDEpaYsxga",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "09aea58e-213d-471c-f66c-5551681df271"
      },
      "source": [
        "# Check our samples label\n",
        "train_labels[7]"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZHdVBrCUs10A"
      },
      "source": [
        "It looks like our labels are in numerical form. And while this is fine for a neural network, you might want to have them in human readable form.\n",
        "\n",
        "Let's create a small list of the class names (we can find them on [the dataset's GitHub page](https://github.com/zalandoresearch/fashion-mnist#labels)).\n",
        "\n",
        "> 🔑 **Note:** Whilst this dataset has been prepared for us and ready to go, it's important to remember many datasets won't be ready to go like this one. Often you'll have to do a few preprocessing steps to have it ready to use with a neural network (we'll see more of this when we work with our own data later)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uGOi32T8s1ai",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "16af056f-4f87-404f-94b8-8f870bb00122"
      },
      "source": [
        "class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat', \n",
        "               'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']\n",
        "\n",
        "# How many classes are there (this'll be our output shape)?\n",
        "len(class_names)"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zOiwINQQtzys"
      },
      "source": [
        "Now we have these, let's plot another example.\n",
        "\n",
        "> 🤔 **Question:** Pay particular attention to what the data we're working with *looks* like. Is it only straight lines? Or does it have non-straight lines as well? Do you think if we wanted to find patterns in the photos of clothes (which are actually collections of pixels), will our model need non-linearities (non-straight lines) or not?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_qD40id2tytn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "2ed57ab3-f2bd-4abd-8f02-ada925040679"
      },
      "source": [
        "# Plot an example image and its label\n",
        "plt.imshow(train_data[17], cmap=plt.cm.binary) # change the colours to black & white\n",
        "plt.title(class_names[train_labels[17]]);"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rtz9__w3s4JF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 427
        },
        "outputId": "aa74bce5-ad81-469e-8be1-ee79b3269105"
      },
      "source": [
        "# Plot multiple random images of fashion MNIST\n",
        "import random\n",
        "plt.figure(figsize=(7, 7))\n",
        "for i in range(4):\n",
        "  ax = plt.subplot(2, 2, i + 1)\n",
        "  rand_index = random.choice(range(len(train_data)))\n",
        "  plt.imshow(train_data[rand_index], cmap=plt.cm.binary)\n",
        "  plt.title(class_names[train_labels[rand_index]])\n",
        "  plt.axis(False)"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 4 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TLqZif3Rv0Aq"
      },
      "source": [
        "Alright, let's build a model to figure out the relationship between the pixel values and their labels.\n",
        "\n",
        "Since this is a multiclass classification problem, we'll need to make a few changes to our architecture (inline with Table 1 above):\n",
        "\n",
        "* The **input shape** will have to deal with 28x28 tensors (the height and width of our images).\n",
        "  * We're actually going to squash the input into a tensor (vector) of shape `(784)`.\n",
        "* The **output shape** will have to be 10 because we need our model to predict for 10 different classes.\n",
        "  * We'll also change the `activation` parameter of our output layer to be [`\"softmax\"`](https://www.tensorflow.org/api_docs/python/tf/keras/activations/softmax) instead of `'sigmoid'`. As we'll see the `\"softmax\"` activation function outputs a series of values between 0 & 1 (the same shape as **output shape**, which together add up to ~1. The index with the highest value is predicted by the model to be the most *likely* class.\n",
        "* We'll need to change our loss function from a binary loss function to a multiclass loss function. \n",
        "  * More specifically, since our labels are in integer form, we'll use [`tf.keras.losses.SparseCategoricalCrossentropy()`](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/keras/losses/SparseCategoricalCrossentropy), if our labels were one-hot encoded (e.g. they looked something like `[0, 0, 1, 0, 0...]`), we'd use [`tf.keras.losses.CategoricalCrossentropy()`](https://www.tensorflow.org/api_docs/python/tf/keras/losses/CategoricalCrossentropy).\n",
        "* We'll also use the `validation_data` parameter when calling the `fit()` function. This will give us an idea of how the model performs on the test set during training.\n",
        "\n",
        "You ready? Let's go."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qUFHuzIpv30K",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "76dce169-a31e-4994-b490-aa3987f8a813"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model\n",
        "model_11 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Flatten(input_shape=(28, 28)), # input layer (we had to reshape 28x28 to 784, the Flatten layer does this for us)\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(10, activation=\"softmax\") # output shape is 10, activation is softmax\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_11.compile(loss=tf.keras.losses.SparseCategoricalCrossentropy(), # different loss function for multiclass classifcation\n",
        "                 optimizer=tf.keras.optimizers.Adam(),\n",
        "                 metrics=[\"accuracy\"])\n",
        "\n",
        "# Fit the model\n",
        "non_norm_history = model_11.fit(train_data,\n",
        "                                train_labels,\n",
        "                                epochs=10,\n",
        "                                validation_data=(test_data, test_labels)) # see how the model performs on the test set during training"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "1875/1875 [==============================] - 5s 2ms/step - loss: 2.1671 - accuracy: 0.1606 - val_loss: 1.7959 - val_accuracy: 0.2046\n",
            "Epoch 2/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.7066 - accuracy: 0.2509 - val_loss: 1.6567 - val_accuracy: 0.2805\n",
            "Epoch 3/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.6321 - accuracy: 0.2806 - val_loss: 1.6094 - val_accuracy: 0.2857\n",
            "Epoch 4/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.6052 - accuracy: 0.2833 - val_loss: 1.6041 - val_accuracy: 0.2859\n",
            "Epoch 5/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.5975 - accuracy: 0.2862 - val_loss: 1.6064 - val_accuracy: 0.2756\n",
            "Epoch 6/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.5950 - accuracy: 0.2920 - val_loss: 1.5747 - val_accuracy: 0.2994\n",
            "Epoch 7/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.5775 - accuracy: 0.3040 - val_loss: 1.6030 - val_accuracy: 0.3000\n",
            "Epoch 8/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.5708 - accuracy: 0.3175 - val_loss: 1.5635 - val_accuracy: 0.3315\n",
            "Epoch 9/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.5638 - accuracy: 0.3280 - val_loss: 1.5534 - val_accuracy: 0.3334\n",
            "Epoch 10/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.5432 - accuracy: 0.3346 - val_loss: 1.5390 - val_accuracy: 0.3549\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3hzYWEgoVJ_p",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "061bd3d1-095f-4518-80a3-a0373c6b67b9"
      },
      "source": [
        "# Check the shapes of our model\n",
        "# Note: the \"None\" in (None, 784) is for batch_size, we'll cover this in a later module\n",
        "model_11.summary()"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_11\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " flatten (Flatten)           (None, 784)               0         \n",
            "                                                                 \n",
            " dense_28 (Dense)            (None, 4)                 3140      \n",
            "                                                                 \n",
            " dense_29 (Dense)            (None, 4)                 20        \n",
            "                                                                 \n",
            " dense_30 (Dense)            (None, 10)                50        \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 3,210\n",
            "Trainable params: 3,210\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XRfkre59zSto"
      },
      "source": [
        "Alright, our model gets to about ~35% accuracy after 10 epochs using a similar style model to what we used on our binary classification problem.\n",
        "\n",
        "Which is better than guessing (guessing with 10 classes would result in about 10% accuracy) but we can do better.\n",
        "\n",
        "Do you remember when we talked about neural networks preferring numbers between 0 and 1? (if not, treat this as a reminder)\n",
        "\n",
        "Well, right now, the data we have isn't between 0 and 1, in other words, it's not normalized (hence why we used the `non_norm_history` variable when calling `fit()`). It's pixel values are between 0 and 255.\n",
        "\n",
        "Let's see."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tGiweanwz82_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d5fb22da-af82-4c94-b591-4bbc659561d4"
      },
      "source": [
        "# Check the min and max values of the training data\n",
        "train_data.min(), train_data.max()"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0, 255)"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "syB7LOk30H0_"
      },
      "source": [
        "We can get these values between 0 and 1 by dividing the entire array by the maximum: `255.0` (dividing by a float also converts to a float).\n",
        "\n",
        "\n",
        "Doing so will result in all of our data being between 0 and 1 (known as **scaling** or **normalization**)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ABRKp5U8voV_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f7d34406-6cfb-4719-8da2-172bf606227c"
      },
      "source": [
        "# Divide train and test images by the maximum value (normalize it)\n",
        "train_data = train_data / 255.0\n",
        "test_data = test_data / 255.0\n",
        "\n",
        "# Check the min and max values of the training data\n",
        "train_data.min(), train_data.max()"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 1.0)"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LeYQEXOf06oo"
      },
      "source": [
        "Beautiful! Now our data is between 0 and 1. Let's see what happens when we model it.\n",
        "\n",
        "We'll use the same model as before (`model_11`) except this time the data will be normalized."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z1QRy7y_K_87",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c4f951ec-cc48-45d7-88e6-140625c96e0d"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model\n",
        "model_12 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Flatten(input_shape=(28, 28)), # input layer (we had to reshape 28x28 to 784)\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(10, activation=\"softmax\") # output shape is 10, activation is softmax\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_12.compile(loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "                 optimizer=tf.keras.optimizers.Adam(),\n",
        "                 metrics=[\"accuracy\"])\n",
        "\n",
        "# Fit the model (to the normalized data)\n",
        "norm_history = model_12.fit(train_data,\n",
        "                            train_labels,\n",
        "                            epochs=10,\n",
        "                            validation_data=(test_data, test_labels))"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "1875/1875 [==============================] - 5s 2ms/step - loss: 1.0348 - accuracy: 0.6474 - val_loss: 0.6937 - val_accuracy: 0.7617\n",
            "Epoch 2/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6376 - accuracy: 0.7757 - val_loss: 0.6400 - val_accuracy: 0.7820\n",
            "Epoch 3/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5942 - accuracy: 0.7914 - val_loss: 0.6247 - val_accuracy: 0.7783\n",
            "Epoch 4/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5750 - accuracy: 0.7979 - val_loss: 0.6078 - val_accuracy: 0.7881\n",
            "Epoch 5/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5641 - accuracy: 0.8006 - val_loss: 0.6169 - val_accuracy: 0.7881\n",
            "Epoch 6/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5544 - accuracy: 0.8043 - val_loss: 0.5855 - val_accuracy: 0.7951\n",
            "Epoch 7/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5488 - accuracy: 0.8063 - val_loss: 0.6097 - val_accuracy: 0.7836\n",
            "Epoch 8/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5428 - accuracy: 0.8077 - val_loss: 0.5787 - val_accuracy: 0.7971\n",
            "Epoch 9/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5373 - accuracy: 0.8097 - val_loss: 0.5698 - val_accuracy: 0.7977\n",
            "Epoch 10/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5360 - accuracy: 0.8124 - val_loss: 0.5658 - val_accuracy: 0.8014\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C_I2KNJiMWZ8"
      },
      "source": [
        "Woah, we used the exact same model as before but we with normalized data we're now seeing a much higher accuracy value!\n",
        "\n",
        "Let's plot each model's history (their loss curves)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zmRcYU7xN1wQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "outputId": "ee47337a-22cc-4c99-e50a-dc6fec09b82c"
      },
      "source": [
        "import pandas as pd\n",
        "# Plot non-normalized data loss curves\n",
        "pd.DataFrame(non_norm_history.history).plot(title=\"Non-normalized Data\")\n",
        "# Plot normalized data loss curves\n",
        "pd.DataFrame(norm_history.history).plot(title=\"Normalized data\");"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VKm8MsACOm4j"
      },
      "source": [
        "Wow. From these two plots, we can see how much quicker our model with the normalized data (`model_12`) improved than the model with the non-normalized data (`model_11`).\n",
        "\n",
        "> 🔑 **Note:** The same model with even *slightly* different data can produce *dramatically* different results. So when you're comparing models, it's important to make sure you're comparing them on the same criteria (e.g. same architecture but different data or same data but different architecture).\n",
        "\n",
        "How about we find the ideal learning rate and see what happens?\n",
        "\n",
        "We'll use the same architecture we've been using."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LcR_wb4nPSb2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fcc6abb6-a501-4746-a275-0d317e866aae"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model\n",
        "model_13 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Flatten(input_shape=(28, 28)), # input layer (we had to reshape 28x28 to 784)\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(10, activation=\"softmax\") # output shape is 10, activation is softmax\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_13.compile(loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "                 optimizer=tf.keras.optimizers.Adam(),\n",
        "                 metrics=[\"accuracy\"])\n",
        "\n",
        "# Create the learning rate callback\n",
        "lr_scheduler = tf.keras.callbacks.LearningRateScheduler(lambda epoch: 1e-3 * 10**(epoch/20))\n",
        "\n",
        "# Fit the model\n",
        "find_lr_history = model_13.fit(train_data,\n",
        "                               train_labels,\n",
        "                               epochs=40, # model already doing pretty good with current LR, probably don't need 100 epochs\n",
        "                               validation_data=(test_data, test_labels),\n",
        "                               callbacks=[lr_scheduler])"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.0348 - accuracy: 0.6474 - val_loss: 0.6937 - val_accuracy: 0.7617 - lr: 0.0010\n",
            "Epoch 2/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6366 - accuracy: 0.7759 - val_loss: 0.6400 - val_accuracy: 0.7808 - lr: 0.0011\n",
            "Epoch 3/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5934 - accuracy: 0.7911 - val_loss: 0.6278 - val_accuracy: 0.7770 - lr: 0.0013\n",
            "Epoch 4/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5749 - accuracy: 0.7969 - val_loss: 0.6122 - val_accuracy: 0.7871 - lr: 0.0014\n",
            "Epoch 5/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5655 - accuracy: 0.7987 - val_loss: 0.6061 - val_accuracy: 0.7913 - lr: 0.0016\n",
            "Epoch 6/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5569 - accuracy: 0.8022 - val_loss: 0.5917 - val_accuracy: 0.7940 - lr: 0.0018\n",
            "Epoch 7/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5542 - accuracy: 0.8036 - val_loss: 0.5898 - val_accuracy: 0.7896 - lr: 0.0020\n",
            "Epoch 8/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5509 - accuracy: 0.8039 - val_loss: 0.5829 - val_accuracy: 0.7949 - lr: 0.0022\n",
            "Epoch 9/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5468 - accuracy: 0.8047 - val_loss: 0.6036 - val_accuracy: 0.7833 - lr: 0.0025\n",
            "Epoch 10/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5478 - accuracy: 0.8058 - val_loss: 0.5736 - val_accuracy: 0.7974 - lr: 0.0028\n",
            "Epoch 11/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5446 - accuracy: 0.8059 - val_loss: 0.5672 - val_accuracy: 0.8016 - lr: 0.0032\n",
            "Epoch 12/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5432 - accuracy: 0.8067 - val_loss: 0.5773 - val_accuracy: 0.7950 - lr: 0.0035\n",
            "Epoch 13/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5425 - accuracy: 0.8056 - val_loss: 0.5775 - val_accuracy: 0.7992 - lr: 0.0040\n",
            "Epoch 14/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5407 - accuracy: 0.8078 - val_loss: 0.5616 - val_accuracy: 0.8075 - lr: 0.0045\n",
            "Epoch 15/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5408 - accuracy: 0.8052 - val_loss: 0.5773 - val_accuracy: 0.8039 - lr: 0.0050\n",
            "Epoch 16/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5437 - accuracy: 0.8058 - val_loss: 0.5682 - val_accuracy: 0.8015 - lr: 0.0056\n",
            "Epoch 17/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5419 - accuracy: 0.8075 - val_loss: 0.5995 - val_accuracy: 0.7964 - lr: 0.0063\n",
            "Epoch 18/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5488 - accuracy: 0.8058 - val_loss: 0.5544 - val_accuracy: 0.8087 - lr: 0.0071\n",
            "Epoch 19/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5506 - accuracy: 0.8042 - val_loss: 0.6068 - val_accuracy: 0.7864 - lr: 0.0079\n",
            "Epoch 20/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5537 - accuracy: 0.8030 - val_loss: 0.5597 - val_accuracy: 0.8076 - lr: 0.0089\n",
            "Epoch 21/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5572 - accuracy: 0.8036 - val_loss: 0.5998 - val_accuracy: 0.7934 - lr: 0.0100\n",
            "Epoch 22/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5615 - accuracy: 0.8013 - val_loss: 0.5756 - val_accuracy: 0.8034 - lr: 0.0112\n",
            "Epoch 23/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5655 - accuracy: 0.8017 - val_loss: 0.6386 - val_accuracy: 0.7668 - lr: 0.0126\n",
            "Epoch 24/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5819 - accuracy: 0.7963 - val_loss: 0.6356 - val_accuracy: 0.7869 - lr: 0.0141\n",
            "Epoch 25/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5810 - accuracy: 0.7977 - val_loss: 0.6481 - val_accuracy: 0.7865 - lr: 0.0158\n",
            "Epoch 26/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5960 - accuracy: 0.7901 - val_loss: 0.6997 - val_accuracy: 0.7802 - lr: 0.0178\n",
            "Epoch 27/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6101 - accuracy: 0.7870 - val_loss: 0.6124 - val_accuracy: 0.7917 - lr: 0.0200\n",
            "Epoch 28/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6178 - accuracy: 0.7846 - val_loss: 0.6137 - val_accuracy: 0.7962 - lr: 0.0224\n",
            "Epoch 29/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6357 - accuracy: 0.7771 - val_loss: 0.6655 - val_accuracy: 0.7621 - lr: 0.0251\n",
            "Epoch 30/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6671 - accuracy: 0.7678 - val_loss: 0.7597 - val_accuracy: 0.7194 - lr: 0.0282\n",
            "Epoch 31/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6836 - accuracy: 0.7585 - val_loss: 0.6958 - val_accuracy: 0.7342 - lr: 0.0316\n",
            "Epoch 32/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.7062 - accuracy: 0.7553 - val_loss: 0.7015 - val_accuracy: 0.7732 - lr: 0.0355\n",
            "Epoch 33/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.7383 - accuracy: 0.7500 - val_loss: 0.7146 - val_accuracy: 0.7706 - lr: 0.0398\n",
            "Epoch 34/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.8033 - accuracy: 0.7300 - val_loss: 0.8987 - val_accuracy: 0.6848 - lr: 0.0447\n",
            "Epoch 35/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.8429 - accuracy: 0.7110 - val_loss: 0.8750 - val_accuracy: 0.7053 - lr: 0.0501\n",
            "Epoch 36/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.8651 - accuracy: 0.7033 - val_loss: 0.8176 - val_accuracy: 0.6989 - lr: 0.0562\n",
            "Epoch 37/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.9203 - accuracy: 0.6837 - val_loss: 0.7876 - val_accuracy: 0.7333 - lr: 0.0631\n",
            "Epoch 38/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.2374 - accuracy: 0.5191 - val_loss: 1.3699 - val_accuracy: 0.4902 - lr: 0.0708\n",
            "Epoch 39/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.1828 - accuracy: 0.5311 - val_loss: 1.1010 - val_accuracy: 0.5819 - lr: 0.0794\n",
            "Epoch 40/40\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.6640 - accuracy: 0.3303 - val_loss: 1.8528 - val_accuracy: 0.2779 - lr: 0.0891\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hi2YODTwQ1ie",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "outputId": "b3431c04-4439-441d-f2c7-eaa30301f63c"
      },
      "source": [
        "# Plot the learning rate decay curve\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "lrs = 1e-3 * (10**(np.arange(40)/20))\n",
        "plt.semilogx(lrs, find_lr_history.history[\"loss\"]) # want the x-axis to be log-scale\n",
        "plt.xlabel(\"Learning rate\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.title(\"Finding the ideal learning rate\");"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GqtOjggqWcfS"
      },
      "source": [
        "In this case, it looks like somewhere close to the default learning rate of the [Adam optimizer](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/Adam) (`0.001`) is the ideal learning rate.\n",
        "\n",
        "Let's refit a model using the ideal learning rate."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i9KFhAwKXjWd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "db6da8d8-d690-499d-fe72-0f0fe80e66f3"
      },
      "source": [
        "# Set random seed\n",
        "tf.random.set_seed(42)\n",
        "\n",
        "# Create the model\n",
        "model_14 = tf.keras.Sequential([\n",
        "  tf.keras.layers.Flatten(input_shape=(28, 28)), # input layer (we had to reshape 28x28 to 784)\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(10, activation=\"softmax\") # output shape is 10, activation is softmax\n",
        "])\n",
        "\n",
        "# Compile the model\n",
        "model_14.compile(loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "                 optimizer=tf.keras.optimizers.Adam(lr=0.001), # ideal learning rate (same as default)\n",
        "                 metrics=[\"accuracy\"])\n",
        "\n",
        "# Fit the model\n",
        "history = model_14.fit(train_data,\n",
        "                       train_labels,\n",
        "                       epochs=20,\n",
        "                       validation_data=(test_data, test_labels))"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n",
            "  super(Adam, self).__init__(name, **kwargs)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 1.0348 - accuracy: 0.6474 - val_loss: 0.6937 - val_accuracy: 0.7617\n",
            "Epoch 2/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.6376 - accuracy: 0.7757 - val_loss: 0.6400 - val_accuracy: 0.7820\n",
            "Epoch 3/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5942 - accuracy: 0.7914 - val_loss: 0.6247 - val_accuracy: 0.7783\n",
            "Epoch 4/20\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.5750 - accuracy: 0.7979 - val_loss: 0.6078 - val_accuracy: 0.7881\n",
            "Epoch 5/20\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.5641 - accuracy: 0.8006 - val_loss: 0.6169 - val_accuracy: 0.7881\n",
            "Epoch 6/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5544 - accuracy: 0.8043 - val_loss: 0.5855 - val_accuracy: 0.7951\n",
            "Epoch 7/20\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.5488 - accuracy: 0.8063 - val_loss: 0.6097 - val_accuracy: 0.7836\n",
            "Epoch 8/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5428 - accuracy: 0.8077 - val_loss: 0.5787 - val_accuracy: 0.7971\n",
            "Epoch 9/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5373 - accuracy: 0.8097 - val_loss: 0.5698 - val_accuracy: 0.7977\n",
            "Epoch 10/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5360 - accuracy: 0.8124 - val_loss: 0.5658 - val_accuracy: 0.8014\n",
            "Epoch 11/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5311 - accuracy: 0.8130 - val_loss: 0.5714 - val_accuracy: 0.8002\n",
            "Epoch 12/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5284 - accuracy: 0.8132 - val_loss: 0.5626 - val_accuracy: 0.8027\n",
            "Epoch 13/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5271 - accuracy: 0.8138 - val_loss: 0.5619 - val_accuracy: 0.8041\n",
            "Epoch 14/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5249 - accuracy: 0.8143 - val_loss: 0.5718 - val_accuracy: 0.7991\n",
            "Epoch 15/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5231 - accuracy: 0.8148 - val_loss: 0.5706 - val_accuracy: 0.8024\n",
            "Epoch 16/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5203 - accuracy: 0.8162 - val_loss: 0.5731 - val_accuracy: 0.8023\n",
            "Epoch 17/20\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.5191 - accuracy: 0.8176 - val_loss: 0.5594 - val_accuracy: 0.8030\n",
            "Epoch 18/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5176 - accuracy: 0.8157 - val_loss: 0.5582 - val_accuracy: 0.8053\n",
            "Epoch 19/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5156 - accuracy: 0.8169 - val_loss: 0.5644 - val_accuracy: 0.8007\n",
            "Epoch 20/20\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.5146 - accuracy: 0.8177 - val_loss: 0.5660 - val_accuracy: 0.8075\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ODWXAlnWqri"
      },
      "source": [
        "Now we've got a model trained with a close-to-ideal learning rate and performing pretty well, we've got a couple of options.\n",
        "\n",
        "We could:\n",
        "* Evaluate its performance using other classification metrics (such as a [confusion matrix](https://scikit-learn.org/stable/auto_examples/model_selection/plot_confusion_matrix.html#sphx-glr-auto-examples-model-selection-plot-confusion-matrix-py) or [classification report](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.classification_report.html)).\n",
        "* Assess some of its predictions (through visualizations).\n",
        "* Improve its accuracy (by training it for longer or changing the architecture).\n",
        "* Save and export it for use in an application.\n",
        "\n",
        "Let's go through the first two options.\n",
        "\n",
        "First we'll create a classification matrix to visualize its predictions across the different classes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jK4zA47sYVp5"
      },
      "source": [
        "# Note: The following confusion matrix code is a remix of Scikit-Learn's \n",
        "# plot_confusion_matrix function - https://scikit-learn.org/stable/modules/generated/sklearn.metrics.plot_confusion_matrix.html\n",
        "# and Made with ML's introductory notebook - https://github.com/GokuMohandas/MadeWithML/blob/main/notebooks/08_Neural_Networks.ipynb\n",
        "import itertools\n",
        "from sklearn.metrics import confusion_matrix\n",
        "\n",
        "# Our function needs a different name to sklearn's plot_confusion_matrix\n",
        "def make_confusion_matrix(y_true, y_pred, classes=None, figsize=(10, 10), text_size=15): \n",
        "  \"\"\"Makes a labelled confusion matrix comparing predictions and ground truth labels.\n",
        "\n",
        "  If classes is passed, confusion matrix will be labelled, if not, integer class values\n",
        "  will be used.\n",
        "\n",
        "  Args:\n",
        "    y_true: Array of truth labels (must be same shape as y_pred).\n",
        "    y_pred: Array of predicted labels (must be same shape as y_true).\n",
        "    classes: Array of class labels (e.g. string form). If `None`, integer labels are used.\n",
        "    figsize: Size of output figure (default=(10, 10)).\n",
        "    text_size: Size of output figure text (default=15).\n",
        "  \n",
        "  Returns:\n",
        "    A labelled confusion matrix plot comparing y_true and y_pred.\n",
        "\n",
        "  Example usage:\n",
        "    make_confusion_matrix(y_true=test_labels, # ground truth test labels\n",
        "                          y_pred=y_preds, # predicted labels\n",
        "                          classes=class_names, # array of class label names\n",
        "                          figsize=(15, 15),\n",
        "                          text_size=10)\n",
        "  \"\"\"  \n",
        "  # Create the confustion matrix\n",
        "  cm = confusion_matrix(y_true, y_pred)\n",
        "  cm_norm = cm.astype(\"float\") / cm.sum(axis=1)[:, np.newaxis] # normalize it\n",
        "  n_classes = cm.shape[0] # find the number of classes we're dealing with\n",
        "\n",
        "  # Plot the figure and make it pretty\n",
        "  fig, ax = plt.subplots(figsize=figsize)\n",
        "  cax = ax.matshow(cm, cmap=plt.cm.Blues) # colors will represent how 'correct' a class is, darker == better\n",
        "  fig.colorbar(cax)\n",
        "\n",
        "  # Are there a list of classes?\n",
        "  if classes:\n",
        "    labels = classes\n",
        "  else:\n",
        "    labels = np.arange(cm.shape[0])\n",
        "  \n",
        "  # Label the axes\n",
        "  ax.set(title=\"Confusion Matrix\",\n",
        "         xlabel=\"Predicted label\",\n",
        "         ylabel=\"True label\",\n",
        "         xticks=np.arange(n_classes), # create enough axis slots for each class\n",
        "         yticks=np.arange(n_classes), \n",
        "         xticklabels=labels, # axes will labeled with class names (if they exist) or ints\n",
        "         yticklabels=labels)\n",
        "  \n",
        "  # Make x-axis labels appear on bottom\n",
        "  ax.xaxis.set_label_position(\"bottom\")\n",
        "  ax.xaxis.tick_bottom()\n",
        "\n",
        "  # Set the threshold for different colors\n",
        "  threshold = (cm.max() + cm.min()) / 2.\n",
        "\n",
        "  # Plot the text on each cell\n",
        "  for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n",
        "    plt.text(j, i, f\"{cm[i, j]} ({cm_norm[i, j]*100:.1f}%)\",\n",
        "             horizontalalignment=\"center\",\n",
        "             color=\"white\" if cm[i, j] > threshold else \"black\",\n",
        "             size=text_size)"
      ],
      "execution_count": 83,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mi5kNRyZdyXA"
      },
      "source": [
        "Since a confusion matrix compares the truth labels (`test_labels`) to the predicted labels, we have to make some predictions with our model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HhxrXhrjbjja",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bf6e5522-351b-49d0-df78-8bece79e453d"
      },
      "source": [
        "# Make predictions with the most recent model\n",
        "y_probs = model_14.predict(test_data) # \"probs\" is short for probabilities\n",
        "\n",
        "# View the first 5 predictions\n",
        "y_probs[:5]"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[8.56299753e-11, 3.53615629e-13, 2.66337556e-05, 4.63562024e-08,\n",
              "        5.09498605e-05, 9.61192474e-02, 8.17780403e-08, 9.18688551e-02,\n",
              "        4.06052778e-03, 8.07873666e-01],\n",
              "       [3.42785552e-06, 1.28992649e-16, 9.59891498e-01, 2.05162564e-07,\n",
              "        1.53292371e-02, 2.45320095e-13, 2.41428725e-02, 1.13834485e-28,\n",
              "        6.32718089e-04, 4.47896404e-08],\n",
              "       [6.10630595e-05, 9.96576726e-01, 4.38669758e-08, 3.34058981e-03,\n",
              "        1.32494861e-05, 1.43831603e-21, 8.27906115e-06, 7.32374630e-18,\n",
              "        5.48116041e-08, 4.92251402e-14],\n",
              "       [7.50314357e-05, 9.90536869e-01, 4.25285322e-07, 9.22318175e-03,\n",
              "        1.36231421e-04, 1.82760903e-18, 2.68082422e-05, 4.81248308e-14,\n",
              "        1.45215904e-06, 2.22114601e-11],\n",
              "       [7.21899569e-02, 1.54957536e-06, 2.55668938e-01, 1.03631355e-02,\n",
              "        4.35413495e-02, 1.10693023e-13, 6.16930187e-01, 6.75438989e-23,\n",
              "        1.30491622e-03, 1.21404065e-09]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eP5zslXbf5ZY"
      },
      "source": [
        "Our model outputs a list of **prediction probabilities**, meaning, it outputs a number for how likely it thinks a particular class is to be the label.\n",
        "\n",
        "The higher the number in the prediction probabilities list, the more likely the model believes that is the right class.\n",
        "\n",
        "To find the highest value we can use the [`argmax()`](https://numpy.org/doc/stable/reference/generated/numpy.argmax.html) method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hQvrJbbWf4Es",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b4c5bfb4-9dab-4e19-b1a8-9c7382d8d2d4"
      },
      "source": [
        "# See the predicted class number and label for the first example\n",
        "y_probs[0].argmax(), class_names[y_probs[0].argmax()]"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(9, 'Ankle boot')"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BFPgnBCghrTz"
      },
      "source": [
        "Now let's do the same for all of the predictions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ozUpeZU6g2An",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "706d3acf-c884-4992-cc7c-fdd19c208813"
      },
      "source": [
        "# Convert all of the predictions from probabilities to labels\n",
        "y_preds = y_probs.argmax(axis=1)\n",
        "\n",
        "# View the first 10 prediction labels\n",
        "y_preds[:10]"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([9, 2, 1, 1, 6, 1, 4, 6, 5, 7])"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "47g1wNk6iYTd"
      },
      "source": [
        "Wonderful, now we've got our model's predictions in label form, let's create a confusion matrix to view them against the truth labels."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FBMSVSRqcU_m",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ffd1c055-795c-434a-90be-f4bddf50cbd2"
      },
      "source": [
        "# Check out the non-prettified confusion matrix\n",
        "from sklearn.metrics import confusion_matrix\n",
        "confusion_matrix(y_true=test_labels, \n",
        "                 y_pred=y_preds)"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[696,   8,  25,  87,   9,   5, 160,   0,  10,   0],\n",
              "       [  2, 939,   2,  35,   9,   0,  13,   0,   0,   0],\n",
              "       [ 19,   2, 656,  10, 188,   0, 110,   0,  15,   0],\n",
              "       [ 39,  10,  10, 819,  55,   0,  47,   1,  19,   0],\n",
              "       [  0,   0,  95,  23, 800,   0,  73,   0,   7,   2],\n",
              "       [  0,   0,   1,   0,   0, 894,   0,  60,   7,  38],\n",
              "       [106,   4, 158,  57, 159,   1, 499,   0,  16,   0],\n",
              "       [  0,   0,   0,   0,   0,  31,   0, 936,   0,  33],\n",
              "       [  4,   1,  38,  15,   8,  12,   9,   5, 906,   2],\n",
              "       [  0,   0,   1,   0,   2,  15,   0,  51,   1, 930]])"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ql-TQxuYiqPl"
      },
      "source": [
        "That confusion matrix is hard to comprehend, let's make it prettier using the function we created before."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DLr6daZAbzRi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 825
        },
        "outputId": "c708302f-4cba-4a91-cd14-2da15294c231"
      },
      "source": [
        "# Make a prettier confusion matrix\n",
        "make_confusion_matrix(y_true=test_labels, \n",
        "                      y_pred=y_preds,\n",
        "                      classes=class_names,\n",
        "                      figsize=(15, 15),\n",
        "                      text_size=10)"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x1080 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tH3FhuGEjTu9"
      },
      "source": [
        "That looks much better! (one of my favourites sights in the world is a confusion matrix with dark squares down the diagonal)\n",
        "\n",
        "Except the results aren't as good as they could be...\n",
        "\n",
        "It looks like our model is getting confused between the `Shirt` and `T-shirt/top` classes (e.g. predicting `Shirt` when it's actually a `T-shirt/top`).\n",
        "\n",
        "> 🤔 **Question:** Does it make sense that our model is getting confused between the `Shirt` and `T-shirt/top` classes? Why do you think this might be? What's one way you could investigate?\n",
        "\n",
        "We've seen how our models predictions line up to the truth labels using a confusion matrix, but how about we visualize some?\n",
        "\n",
        "Let's create a function to plot a random image along with its prediction.\n",
        "\n",
        "> 🔑 **Note:** Often when working with images and other forms of visual data, it's a good idea to visualize as much as possible to develop a further understanding of the data and the outputs of your model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2XIuAjgJri9e"
      },
      "source": [
        " import random\n",
        "\n",
        "# Create a function for plotting a random image along with its prediction\n",
        "def plot_random_image(model, images, true_labels, classes):\n",
        "  \"\"\"Picks a random image, plots it and labels it with a predicted and truth label.\n",
        "\n",
        "  Args:\n",
        "    model: a trained model (trained on data similar to what's in images).\n",
        "    images: a set of random images (in tensor form).\n",
        "    true_labels: array of ground truth labels for images.\n",
        "    classes: array of class names for images.\n",
        "  \n",
        "  Returns:\n",
        "    A plot of a random image from `images` with a predicted class label from `model`\n",
        "    as well as the truth class label from `true_labels`.\n",
        "  \"\"\" \n",
        "  # Setup random integer\n",
        "  i = random.randint(0, len(images))\n",
        "  \n",
        "  # Create predictions and targets\n",
        "  target_image = images[i]\n",
        "  pred_probs = model.predict(target_image.reshape(1, 28, 28)) # have to reshape to get into right size for model\n",
        "  pred_label = classes[pred_probs.argmax()]\n",
        "  true_label = classes[true_labels[i]]\n",
        "\n",
        "  # Plot the target image\n",
        "  plt.imshow(target_image, cmap=plt.cm.binary)\n",
        "\n",
        "  # Change the color of the titles depending on if the prediction is right or wrong\n",
        "  if pred_label == true_label:\n",
        "    color = \"green\"\n",
        "  else:\n",
        "    color = \"red\"\n",
        "\n",
        "  # Add xlabel information (prediction/true label)\n",
        "  plt.xlabel(\"Pred: {} {:2.0f}% (True: {})\".format(pred_label,\n",
        "                                                   100*tf.reduce_max(pred_probs),\n",
        "                                                   true_label),\n",
        "             color=color) # set the color to green or red"
      ],
      "execution_count": 89,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RAAIrpcEumyE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "245aa5d9-246e-4dce-97cc-80f9388293b4"
      },
      "source": [
        "# Check out a random image as well as its prediction\n",
        "plot_random_image(model=model_14, \n",
        "                  images=test_data, \n",
        "                  true_labels=test_labels, \n",
        "                  classes=class_names)"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FNebpPbCw52S"
      },
      "source": [
        "After running the cell above a few times you'll start to get a visual understanding of the relationship between the model's predictions and the true labels.\n",
        "\n",
        "Did you figure out which predictions the model gets confused on?\n",
        "\n",
        "It seems to mix up classes which are similar, for example, `Sneaker` with `Ankle boot`.\n",
        "\n",
        "Looking at the images, you can see how this might be the case.\n",
        "\n",
        "The overall shape of a `Sneaker` and an `Ankle Boot` are similar.\n",
        "\n",
        "The overall shape might be one of the patterns the model has learned and so therefore when two images have a similar shape, their predictions get mixed up."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pOwM1rqhx6p3"
      },
      "source": [
        "### What patterns is our model learning?\n",
        "\n",
        "We've been talking a lot about how a neural network finds patterns in numbers, but what exactly do these patterns look like?\n",
        "\n",
        "Let's crack open one of our models and find out.\n",
        "\n",
        "First, we'll get a list of layers in our most recent model (`model_14`) using the `layers` attribute."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kcwMsgFuySTi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6bd5834b-a25c-41ad-f309-2678c8afbfc4"
      },
      "source": [
        "# Find the layers of our most recent model\n",
        "model_14.layers"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<keras.layers.core.flatten.Flatten at 0x7fc85b3ecc50>,\n",
              " <keras.layers.core.dense.Dense at 0x7fc85b329c10>,\n",
              " <keras.layers.core.dense.Dense at 0x7fc85b3922d0>,\n",
              " <keras.layers.core.dense.Dense at 0x7fc85b627f10>]"
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w9si0o-h4oO1"
      },
      "source": [
        "We can access a target layer using indexing."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DXuQmsNX1mGR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0fbcc1f6-87a4-4386-91c8-3a459561540c"
      },
      "source": [
        "# Extract a particular layer\n",
        "model_14.layers[1]"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.layers.core.dense.Dense at 0x7fc85b329c10>"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W6Cftaib4uG-"
      },
      "source": [
        "And we can find the patterns learned by a particular layer using the `get_weights()` method.\n",
        "\n",
        "The `get_weights()` method returns the **weights** (also known as a weights matrix) and biases (also known as a bias vector) of a particular layer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WdmZy5xi1srE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7c7ad9a-d9b2-4dbd-fc73-e6c6c6ae2f72"
      },
      "source": [
        "# Get the patterns of a layer in our network\n",
        "weights, biases = model_14.layers[1].get_weights()\n",
        "\n",
        "# Shape = 1 weight matrix the size of our input data (28x28) per neuron (4)\n",
        "weights, weights.shape"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[ 0.7150263 , -0.06077093, -0.99763095, -1.0484313 ],\n",
              "        [ 0.2773212 , -0.471554  , -0.52916455,  0.02329255],\n",
              "        [ 0.7752433 ,  0.5402759 , -1.128857  , -0.7426156 ],\n",
              "        ...,\n",
              "        [-0.3945342 ,  0.47628632, -0.2264153 ,  0.2550593 ],\n",
              "        [-0.40515798,  0.61810046,  0.23928414, -0.50387603],\n",
              "        [ 0.23884593,  0.11606961, -0.12131374,  0.04352392]],\n",
              "       dtype=float32), (784, 4))"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yCjuNSD73oG0"
      },
      "source": [
        "The weights matrix is the same shape as the input data, which in our case is 784 (28x28 pixels). And there's a copy of the weights matrix for each neuron the in the selected layer (our selected layer has 4 neurons).\n",
        "\n",
        "Each value in the weights matrix corresponds to how a particular value in the input data influences the network's decisions.\n",
        "\n",
        "These values start out as random numbers (they're set by the [`kernel_initializer` parameter](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dense) when creating a layer, the default is [`\"glorot_uniform\"`](https://www.tensorflow.org/api_docs/python/tf/keras/initializers/GlorotUniform)) and are then updated to better representative values of the data (non-random) by the neural network during training.\n",
        "\n",
        "![neural network supervised learning weight updates](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-fashion-mnist-learning.png)\n",
        "*Example workflow of how a supervised neural network starts with random weights and updates them to better represent the data by looking at examples of ideal outputs.*\n",
        "\n",
        "Now let's check out the bias vector."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ndG-h2yz1z2_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dcc4828c-8dfb-4ab4-ec87-ac8bc185fd1a"
      },
      "source": [
        "# Shape = 1 bias per neuron (we use 4 neurons in the first layer)\n",
        "biases, biases.shape"
      ],
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 2.4485964e-02, -6.1471871e-04, -2.7230152e-01,  8.1124878e-01],\n",
              "       dtype=float32), (4,))"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3JRQFh3U374U"
      },
      "source": [
        "Every neuron has a bias vector. Each of these is paired with a weight matrix.\n",
        "\n",
        "The bias values get initialized as zeroes by default (using the [`bias_initializer` parameter](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dense)).\n",
        "\n",
        "The bias vector dictates how much the patterns within the corresponding weights matrix should influence the next layer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_QCUb7GeSGYF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "66331bde-1967-4984-86ae-1b9144f41fe0"
      },
      "source": [
        "# Can now calculate the number of paramters in our model\n",
        "model_14.summary()"
      ],
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_14\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " flatten_3 (Flatten)         (None, 784)               0         \n",
            "                                                                 \n",
            " dense_37 (Dense)            (None, 4)                 3140      \n",
            "                                                                 \n",
            " dense_38 (Dense)            (None, 4)                 20        \n",
            "                                                                 \n",
            " dense_39 (Dense)            (None, 10)                50        \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 3,210\n",
            "Trainable params: 3,210\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "trRRZLIRyLXe"
      },
      "source": [
        "Now we've built a few deep learning models, it's a good time to point out the whole concept of inputs and outputs not only relates to a model as a whole but to *every* layer within a model.\n",
        "\n",
        "You might've already guessed this, but starting from the input layer, each subsequent layer's input is the output of the previous layer.\n",
        "\n",
        "We can see this clearly using the utility [`plot_model()`](https://www.tensorflow.org/api_docs/python/tf/keras/utils/plot_model)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YJD0GqGl3NY0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        },
        "outputId": "89978ea4-3673-48e0-d44c-5954fff5ce64"
      },
      "source": [
        "from tensorflow.keras.utils import plot_model\n",
        "\n",
        "# See the inputs and outputs of each layer\n",
        "plot_model(model_14, show_shapes=True)"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OY5HO72ATJR4"
      },
      "source": [
        "## How a model learns (in brief)\n",
        "\n",
        "Alright, we've trained a bunch of models, but we've never really discussed what's going on under the hood. So how exactly does a model learn?\n",
        "\n",
        "A model learns by updating and improving its weight matrices and biases values every epoch (in our case, when we call the `fit()` fucntion).\n",
        "\n",
        "It does so by comparing the patterns its learned between the data and labels to the actual labels.\n",
        "\n",
        "If the current patterns (weight matrices and bias values) don't result in a desirable decrease in the loss function (higher loss means worse predictions), the optimizer tries to steer the model to update its patterns in the right way (using the real labels as a reference).\n",
        "\n",
        "This process of using the real labels as a reference to improve the model's predictions is called [**backpropagation**](https://en.wikipedia.org/wiki/Backpropagation).\n",
        "\n",
        "In other words, data and labels pass through a model (**forward pass**) and it attempts to learn the relationship between the data and labels. \n",
        "\n",
        "And if this learned relationship isn't close to the actual relationship or it could be improved, the model does so by going back through itself (**backward pass**) and tweaking its weights matrices and bias values to better represent the data.\n",
        "\n",
        "If all of this sounds confusing (and it's fine if it does, the above is a very succinct description), check out the resources in the extra-curriculum section for more."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LXmMG6fcpoIp"
      },
      "source": [
        "## Exercises 🛠\n",
        "\n",
        "1. Play with neural networks in the [TensorFlow Playground](https://playground.tensorflow.org/) for 10-minutes. Especially try different values of the learning, what happens when you decrease it? What happens when you increase it?\n",
        "2. Replicate the model pictured in the [TensorFlow Playground diagram](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.001&regularizationRate=0&noise=0&networkShape=6,6,6,6,6&seed=0.51287&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&discretize_hide=true&regularizationRate_hide=true&percTrainData_hide=true&dataset_hide=true&problem_hide=true&noise_hide=true&batchSize_hide=true) below using TensorFlow code. Compile it using the Adam optimizer, binary crossentropy loss and accuracy metric. Once it's compiled check a summary of the model.\n",
        "![tensorflow playground example neural network](https://raw.githubusercontent.com/mrdbourke/tensorflow-deep-learning/main/images/02-tensorflow-playground-replication-exercise.png)\n",
        "*Try this network out for yourself on the [TensorFlow Playground website](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.001&regularizationRate=0&noise=0&networkShape=6,6,6,6,6&seed=0.51287&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false&regularization_hide=true&discretize_hide=true&regularizationRate_hide=true&percTrainData_hide=true&dataset_hide=true&problem_hide=true&noise_hide=true&batchSize_hide=true). Hint: there are 5 hidden layers but the output layer isn't pictured, you'll have to decide what the output layer should be based on the input data.*\n",
        "3. Create a classification dataset using Scikit-Learn's [`make_moons()`](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html) function, visualize it and then build a model to fit it at over 85% accuracy.\n",
        "4. Create a function (or write code) to visualize multiple image predictions for the fashion MNIST at the same time. Plot at least three different images and their prediciton labels at the same time. Hint: see the [classifcation tutorial in the TensorFlow documentation](https://www.tensorflow.org/tutorials/keras/classification) for ideas.\n",
        "5. Recreate [TensorFlow's](https://www.tensorflow.org/api_docs/python/tf/keras/activations/softmax) [softmax activation function](https://en.wikipedia.org/wiki/Softmax_function) in your own code. Make sure it can accept a tensor and return that tensor after having the softmax function applied to it.\n",
        "6. Train a model to get 88%+ accuracy on the fashion MNIST test set. Plot a confusion matrix to see the results after.\n",
        "7. Make a function to show an image of a certain class of the fashion MNIST dataset and make a prediction on it. For example, plot 3 images of the `T-shirt` class with their predictions.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oksgPs-meGHj"
      },
      "source": [
        "## Extra curriculum 📖\n",
        "* Watch 3Blue1Brown's neural networks video 2: [*Gradient descent, how neural networks learn*](https://www.youtube.com/watch?v=IHZwWFHWa-w). After you're done, write 100 words about what you've learned.\n",
        "  * If you haven't already, watch video 1: [*But what is a Neural Network?*](https://youtu.be/aircAruvnKk). Note the activation function they talk about at the end.\n",
        "* Watch [MIT's introduction to deep learning lecture 1](https://youtu.be/njKP3FqW3Sk) (if you haven't already) to get an idea of the concepts behind using linear and non-linear functions.\n",
        "* Spend 1-hour reading [Michael Nielsen's Neural Networks and Deep Learning book](http://neuralnetworksanddeeplearning.com/index.html).\n",
        "* Read the [ML-Glossary documentation on activation functions](https://ml-cheatsheet.readthedocs.io/en/latest/activation_functions.html). Which one is your favourite?\n",
        "  * After you've read the ML-Glossary, see which activation functions are available in TensorFlow by searching \"tensorflow activation functions\"."
      ]
    }
  ]
}