week-4/neural_networks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week 4 - Neural Networks\n",
    "\n",
    "The type of Artificial Neural Network (ANN) we will use today is the multilayer perceptron (MLP). It is a feedforward neural network, where the input data is fed in only one direction (forward) through the network (without loops), and the output is generated at the end. In this scenario:\n",
    "- The leftmost layer is the input layer\n",
    "- The middle layer(s) are hidden layer(s)\n",
    "- The rightmost layer is the output layer\n",
    "\n",
    "The architecture of ANNs allows them to learn complex patterns from data by automatically extracting statistically significant features. This lets them be used to solve complex problems and uncover patterns and relationships within large datasets too complicated for traditional approaches.\n",
    "\n",
    "Fun fact! Neural networks with non-linear activation functions can learn non-linear relationships. A neural network with infinite neurons can approximate any function - but that would be a pretty big network... For more information, check out [Universal Approximation Theorem](https://en.wikipedia.org/wiki/Universal_approximation_theorem)!\n",
    "\n",
    "This notebook demonstrates how to implement an ANN with the following sections:\n",
    "1. Loading the Dataset\n",
    "2. NN Implementation with Scikit-Learn\n",
    "3. NN Implementation with Pytorch\n",
    "    1. Defining the Model\n",
    "    2. Training the NN\n",
    "    3. Evaluation\n",
    "4. NN Implementation From Scratch\n",
    "    1. Activation Functions\n",
    "    2. Loss Functions\n",
    "    3. Foward Propagation \n",
    "    4. Backpropagation\n",
    "    5. Putting It All Together"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Loading the Dataset\n",
    "\n",
    "Before loading the dataset we need to import the following python packages. From the \"Introduction to Python\" session, we have introduced the various packages commonly used in machine learning: Numpy for numerical computations and supports working with arrays and matrices, Matplotlib for visualising data such as through graphical representations, Scikit-learn for using built-in models and datsets, Seaborn for more data visualisation, and lastly tqdm for adding process bars to loops. Feel free to check out the [introduction-to-python](https://github.com/UCLAIS/ML-Tutorials-Season-4/tree/main/week-0/introduction-to-python) session for more information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import fetch_openml\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from seaborn import heatmap\n",
    "from tqdm.notebook import tqdm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set random seeds for reproducibility\n",
    "np.random.seed(42)\n",
    "torch.manual_seed(42)\n",
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this gives live loss plots -- recommended\n",
    "from livelossplot import PlotLosses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now also make sure we're using out computer GPU for best performance. Make sure it says \"Using cuda device\" below. If not, go to \"Runtime\" -> \"Change runtime type\" in google colab and change to GPU. This will make model training a lot faster!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cpu device\n"
     ]
    }
   ],
   "source": [
    "device = (\n",
    "    \"cuda\"\n",
    "    if torch.cuda.is_available()\n",
    "    else \"cpu\"\n",
    ")\n",
    "print(f\"Using {device} device\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this demonstration, we will be using the [MNIST](https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html) dataset, which includes 28x28 grayscale images of handwritten digits (0 through 9). The following function loads this dataset as numpy arrays to represent the images and an integer value for the label. Initially, the value of each pixel takes values between 0 and 255 - this may result in very large results from forward propagation computations, so it is important to scale this to between 0 and 1 by dividing by 255.\n",
    "\n",
    "![title](media/MNIST.jpeg)\n",
    "\n",
    "Since we are showing classification between only two classes in this session, we will filter out images that corresponds outside the two."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_mnist_dataset():\n",
    "    # Load the datadet from SkDataset\n",
    "    X, y = fetch_openml(\"mnist_784\", version=1, return_X_y=True, as_frame=False)\n",
    "    y = y.astype(np.int64)\n",
    "\n",
    "    # Scale values between [0, 1]\n",
    "    X = X / 255.0\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below plots a confusion matrix, which evaluates the performance of a classification model by displaying the number of instances where we have true positive, true negative, false positive, and false negative predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_confusion_matrix(true_labels, pred_labels):\n",
    "    fig, ax = plt.subplots(figsize=(10, 10))\n",
    "    cm = confusion_matrix(true_labels, pred_labels)\n",
    "    heatmap(cm, annot=True, ax=ax, cmap=\"Blues\")\n",
    "    ax.set_xlabel(\"Predicted labels\")\n",
    "    ax.set_ylabel(\"True labels\")\n",
    "    ax.set_title(\"Confusion Matrix\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following loads and splits the mnist dataset into training and testing. Each set would contain a series of examples (a pair of features and labels) that are fed into the model firstly for training to update the parameters for learning, and then the results are confirmed by the test set to show how well the model is performing. test_size of 0.2 means that 20% of the loaded dataset is used for testing and 80% is used for training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_mnist, y_mnist = load_mnist_dataset()\n",
    "X_mnist_train, X_mnist_test, y_mnist_train, y_mnist_test = train_test_split(\n",
    "    X_mnist, y_mnist, test_size=0.2, random_state=42\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Neural Network Implemented with Scikit-Learn\n",
    "\n",
    "MLPClassifier is a sklearn class that stands for Multi-Layer Perceptron Classifier with a prebuilt neural network-based classification algorithm that uses a multi-layer feedforward neural network. In this example, we have two hidden layers, each with 100 neurons and the algorithm will, at most, iterate through the training dataset 1000 times. Below is a graph showing how the loss has decreased throughout the iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 93.19%\n"
     ]
    }
   ],
   "source": [
    "# Import the packages and classes needed in this example\n",
    "\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "\n",
    "# Use the mnist dataset\n",
    "\n",
    "mlp = MLPClassifier(hidden_layer_sizes=(10, 10), max_iter=1000)\n",
    "\n",
    "# Train the neural network\n",
    "mlp.fit(X_mnist_train, y_mnist_train)\n",
    "\n",
    "\n",
    "# Plot the loss curve\n",
    "plt.plot(mlp.loss_curve_)\n",
    "plt.title(\"Loss curve\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.show()\n",
    "\n",
    "# Plot the predictions\n",
    "y_pred = mlp.predict(X_mnist_test)\n",
    "plot_confusion_matrix(y_mnist_test, y_pred)\n",
    "\n",
    "# Accuracy\n",
    "print(f\"Accuracy: {np.mean(y_mnist_test == y_pred) * 100:.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Neural Network Implemented with PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyTorch is an ML framework developed by Meta AI, that includes built-in functions for building an NN by layers. The following code shows how we can define our model as a series of linear layers with ReLU activation functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Define our model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we us PyTorch to define the model. Pytorch gives us a lot of flexibility including how many layers, the number of neurons in each layer, activation function, etc. More about the possible models and layers is available in the [documentation](https://pytorch.org/docs/stable/nn.html#linear-layers)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sequential(\n",
      "  (0): Linear(in_features=784, out_features=100, bias=True)\n",
      "  (1): ReLU()\n",
      "  (2): Linear(in_features=100, out_features=100, bias=True)\n",
      "  (3): ReLU()\n",
      "  (4): Linear(in_features=100, out_features=100, bias=True)\n",
      "  (5): ReLU()\n",
      "  (6): Linear(in_features=100, out_features=100, bias=True)\n",
      "  (7): ReLU()\n",
      "  (8): Linear(in_features=100, out_features=10, bias=True)\n",
      "  (9): Softmax(dim=1)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Define our model with 3 hidden layers\n",
    "num_input_features, num_hidden_neurons, num_classes = X_mnist.shape[1], 100, 10\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(num_input_features, num_hidden_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(num_hidden_neurons, num_hidden_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(num_hidden_neurons, num_hidden_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(num_hidden_neurons, num_hidden_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(num_hidden_neurons, num_classes),\n",
    "    nn.Softmax(dim=1)\n",
    ")\n",
    "\n",
    "# Move model to GPU is present\n",
    "model = model.cuda() if device == \"cuda\" else model\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Training our neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we define the hyperparameter. Feel free to experiment with those!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 1e-2\n",
    "batch_size = 32\n",
    "num_epochs = 250"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the cross_entropy loss function. This is best for multi-class classification problems such as this case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_fun(pred, target):\n",
    "    return nn.functional.cross_entropy(pred, target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also used the Adam optimeter here. This updates our weights based on the gradient values it receives in 'loss.backward()'. The specifics of how it does this is not too important. Just know this is an extended version of gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "optim = torch.optim.Adam(model.parameters(), lr=learning_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we set up our model for training and plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#Keep track of losses\n",
    "plotlosses = PlotLosses()\n",
    "\n",
    "# Convert our training data to tensors\n",
    "X_mnist_train_tensor = torch.from_numpy(X_mnist_train).float().to(device)\n",
    "y_mnist_train_tensor = torch.from_numpy(y_mnist_train).long().to(device)\n",
    "\n",
    "# Change model to training mode\n",
    "model.train();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now actually train our model! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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41RIAAIgCoixM3GoJAABEA1EWJqIMAABEA1EWpuBGf5YvAQBAJBFlYfIwUwYAAKKAKAtT29WXRBkAAIgcoixM7CkDAADRQJSFicNjAQBANBBlYQrOlPlYvgQAABFElIXJ7XRIapkpW7XriKrrmkweEQAA6AmIsjAFly//trZMX3r2I/334o0mjwgAAPQERFmYgsuXa/ZUSZK2H6o1cTQAAKCnIMrCFDynLKimgeVLAADQfURZmNwnRVmzSSMBAAA9CVEWphNnyrz1zJQBAIDuI8rCFNzoH1Tb6Jc/YJg0GgAA0FMQZWE6cflSko6xhAkAALqJKAtTcPlyTFGmklwtv/ey2R8AAHQTURamS4fladLAPpp76WClJ7kkEWUAAKD7iLIw9euTogXfOE9TR+QpI8kpiSswAQBA9xFl3RCaKeMKTAAA0E1EWTekM1MGAAAihCjrhoxk9pQBAIDIIMq6gT1lAAAgUoiybgjuKeP+lwAAoLuIsm4IzpR565kpAwAA3UOUdUNopszHTBkAAOgeoqwbMpLZUwYAACKDKOuGdA/nlAEAgMggyrqBc8oAAECkEGXd0HZOGVEGAAC6hyjrhuBMGYfHAgCA7iLKuiF49WVjc0ANTX6TRwMAAOIZUdYN6R6nbLaW37OvDAAAdAdR1g12u01p7uBmf5YwAQBA1xFl3cQVmAAAIBKIsm5quwKTmTIAANB1RFk3MVMGAAAigSjrptD9L5kpAwAA3UCUdVNG8KyyembKAABA1xFl3cRMGQAAiASirJvaTvVnpgwAAHQdUdZNXH0JAAAigSjrJq6+BAAAkUCUdVNwT5m3npkyAADQdURZN6W6HZLEDckBAEC3EGXd5HEGoyxg8kgAAEA8I8q6KcnV8k/Y0MxMGQAA6DqirJuSXCxfAgCA7iPKuik0U8byJQAA6AairJva9pQxUwYAALqOKOum4PKlrzkgwzBMHg0AAIhXRFk3BZcvpZYwAwAA6AqirJuCM2WS5GNfGQAA6CKirJtcDrscdpskjsUAAABdR5RFQJIzeAUmUQYAALqGKIuAtrPKWL4EAABdQ5RFgIeZMgAA0E1EWQRwqj8AAOguoiwCPMEo40gMAADQRURZBLTdaomZMgAA0DVEWQQkcaslAADQTURZBARnyjg8FgAAdBVRFgFt979kpgwAAHQNURYBnFMGAAC6iyiLADb6AwCA7iLKIsAT3OjP8iUAAOgioiwCPKGZMpYvAQBA1xBlEcCRGAAAoLuIsghgoz8AAOguoiwCQhv92VMGAAC6iCiLgNA5ZSxfAgCALiLKIiB0oj83JAcAAF1ElEUAG/0BAEB3EWURwEZ/AADQXURZBHg40R8AAHQTURYBoZkyrr4EAABdRJRFgMfJif4AAKB7iLIIaNtTxkwZAADoGqIsAtrOKWOmDAAAdA1RFgFJrcuXjf6A/AHD5NEAAIB4RJRFQHCmTJJ8bPYHAABdQJRFQLsoYwkTAAB0AVEWAQ67TS6HTRLHYgAAgK4hyiKk7VZLzJQBAIDwEWUR4uFYDAAA0A1EWYQkcaslAADQDURZhHBTcgAA0B1EWYSEbrXERn8AANAFRFmEtJ3qT5QBAIDwEWUR0ranjOVLAAAQPqIsQoJHYnCiPwAA6AqiLELY6A8AALqDKIsQD0diAACAbiDKIoSZMgAA0B1EWYSEbrPEnjIAANAFRFmEcKI/AADoDqIsQli+BAAA3UGURUjwRH8OjwUAAF1BlEVIaKaMPWUAAKALiLIICe4p87F8CQAAuoAoixBmygAAQHcQZRHicbLRHwAAdB1RFiHJ7pYoK69uUJOfMAMAAOEhyiJkbFEv9UpxaX9VvZ5dut3s4QAAgDhDlEVIZopLP7pmpCTpySXbtOmA1+QRAQCAeEKURdA1pYWaOiJPTX5DP3ljo9nDAQAAcYQoiyCbzaZvXjJIkrTjUK3JowEAAPGEKIuwVLdTktTYzGZ/AADQeURZhLlbb7dElAEAgHAQZREWjDIfx2IAAIAwEGUR5jlupswwDJNHAwAA4kVYUTZv3jxNmDBB6enpys3N1XXXXactW7ac8XXLli3TuHHjlJSUpIEDB+rZZ5/t8oCtLjhTJkmNzJYBAIBOCivKli1bpjlz5mjlypV655131NzcrGnTpqm2tuMrDXfu3Kkrr7xSF110kdasWaP7779fd9xxh/7yl790e/BW5HYcF2XsKwMAAJ3kDOfJb775ZrvPX3zxReXm5mr16tWaPHnyKV/z7LPPql+/fnriiSckScOHD9fHH3+sn//857r++uu7NmoL8xw3U+ZrDijdxLEAAID40a09ZdXV1ZKkrKysDp/z0Ucfadq0ae0eu+KKK/Txxx+rqampO3+9JdlsttBsGTNlAACgs8KaKTueYRi66667dOGFF2rUqFEdPq+8vFx5eXntHsvLy1Nzc7MOHz6sgoKCk17j8/nk8/lCn3u98XXLIrfTrkZ/gCgDAACd1uWZsttvv11r167VggULzvhcm83W7vPgVYknPh40b948ZWZmhj6Ki4u7OkxThI7FIMoAAEAndSnK5s6dq0WLFum9995TUVHRaZ+bn5+v8vLydo9VVFTI6XSqT58+p3zNfffdp+rq6tDH3r17uzJM03g4QBYAAIQprOVLwzA0d+5cLVy4UEuXLlVJSckZXzNp0iT99a9/bffY22+/rfHjx8vlcp3yNR6PRx6PJ5yhWUroVH+/3+SRAACAeBHWTNmcOXP0+9//Xn/4wx+Unp6u8vJylZeXq76+PvSc++67T7Nnzw59ftttt2n37t266667tGnTJv3mN7/RCy+8oHvuuSdy34XFBDf6+5qYKQMAAJ0TVpQ988wzqq6u1iWXXKKCgoLQx6uvvhp6zoEDB7Rnz57Q5yUlJVq8eLGWLl2qsWPH6pFHHtGTTz7ZI4/DCPK4uNUSAAAIT9jLl2cyf/78kx67+OKL9cknn4TzV8U1jsQAAADh4t6XUcDVlwAAIFxEWRR4nA5JzJQBAIDOI8qiwM2RGAAAIExEWRS0LV9yJAYAAOgcoiwKODwWAACEiyiLAqIMAACEiyiLgtDhsUQZAADoJKIsCjyu1qsvOTwWAAB0ElEWBRweCwAAwkWURQFXXwIAgHARZVHg4UR/AAAQJqIsCjg8FgAAhIsoiwLufQkAAMJFlEUB974EAADhIsqigOVLAAAQLqIsCtoOj+XqSwAA0DlEWRR4XK0zZRweCwAAOokoiwIPh8cCAIAwEWVRwNWXAAAgXERZFHD1JQAACBdRFgVcfQkAAMJFlEUBy5cAACBcRFkUeJgpAwAAYSLKoiC0fOkPyDAMk0cDAADiAVEWBcEok1jCBAAAnUOURYHnuCjjAFkAANAZRFkUBG+zJLGvDAAAdA5RFgU2m+24+18SZQAA4MyIsijhCkwAABAOoixKOEAWAACEgyiLkrYDZP0mjwQAAMQDoixKWL4EAADhIMqihOVLAAAQDqIsSrj/JQAACAdRFiUep0MSUQYAADqHKIuS4DllnOgPAAA6gyiLktDyZRNXXwIAgDMjyqIkdPUlM2UAAKATiLIo4epLAAAQDqIsSrj6EgAAhIMoi5Lg1ZfMlAEAgM4gyqKEE/0BAEA4iLIo4d6XAAAgHERZlDBTBgAAwkGURQmHxwIAgHAQZVHSdngsUQYAAM6MKIuS4PKlj5kyAADQCURZlLg5EgMAAISBKIsSDo8FAADhIMqipO3qS47EAAAAZ0aURQn3vgQAAOEgyqKE5UsAABAOoixKODwWAACEgyiLklCUcSQGAADoBKIsStyOliMxODwWAAB0BlEWJUmuln/ausZmk0cCAADiAVEWJbkZSZIkb0MzYQYAAM6IKIuSzGSX0j1OSVJZVb3JowEAAFZHlEVR397JkqT9VQ0mjwQAAFgdURZFhb1ao+woM2UAAOD0iLIo6huMsqo6k0cCAACsjiiLouDyZRnLlwAA4AyIsihi+RIAAHQWURZFbcuXRBkAADg9oiyKglFW7m1QM7dbAgAAp+E0ewA9WW66Ry6HTU1+QwdrfKFIAwAgXvj9fjU1NZk9DEtzu92y27s/z0WURZHdblNBZrL2HKlTWVU9UQYAiBuGYai8vFxVVVVmD8Xy7Ha7SkpK5Ha7u/XnEGVRVtgrSXuO1Gn/0XpNGGD2aAAA6JxgkOXm5iolJUU2m83sIVlSIBBQWVmZDhw4oH79+nXr34koi7K+vVIkHWGzPwAgbvj9/lCQ9enTx+zhWF5OTo7KysrU3Nwsl8vV5T+Hjf5R1narJaIMABAfgnvIUlJSTB5JfAguW/r9/m79OURZlPXtlSSJs8oAAPGHJcvOidS/E1EWZS3Ll1IZM2UAAOA0iLIoY/kSAIDYueSSS3TnnXeaPYwuIcqiLDfdI0mqa/Sr1tds8mgAAIBVEWVRlupxKsXtkCQdqvGZPBoAAGBVRFkM5LTOlh06RpQBABArR48e1ezZs9W7d2+lpKRo+vTp2rZtW+jru3fv1owZM9S7d2+lpqZq5MiRWrx4cei1X/7yl5WTk6Pk5GQNHjxYL774YlTHyzllMZCT5tHuyjpmygAAcckwDNU3de+4h65Kdjm6fHXjzTffrG3btmnRokXKyMjQ97//fV155ZXauHGjXC6X5syZo8bGRr3//vtKTU3Vxo0blZaWJkn64Q9/qI0bN+rvf/+7srOz9dlnn6m+Prr7w4myGAjOlB1mpgwAEIfqm/wa8eBbpvzdG398hVLc4edKMMY+/PBDnX/++ZKkl19+WcXFxXr99df1pS99SXv27NH111+v0aNHS5IGDhwYev2ePXt09tlna/z48ZKkAQMGdP+bOQOWL2MgtHzJTBkAADGxadMmOZ1OTZw4MfRYnz59NHToUG3atEmSdMcdd+gnP/mJLrjgAj300ENau3Zt6Lnf/OY39corr2js2LH63ve+pxUrVkR9zMyUxUBOGlEGAIhfyS6HNv74CtP+7q4wDKPDx4PLobfccouuuOIKvfHGG3r77bc1b948PfbYY5o7d66mT5+u3bt364033tC7776ryy67THPmzNHPf/7zLn8vZ8JMWQwwUwYAiGc2m00pbqcpH13dTzZixAg1Nzfrn//8Z+ixyspKbd26VcOHDw89VlxcrNtuu02vvfaa7r77bj3//POhr+Xk5Ojmm2/W73//ez3xxBP69a9/3fV/xE5gpiwGstO4+hIAgFgaPHiwrr32Wt1666167rnnlJ6ernvvvVd9+/bVtddeK0m68847NX36dA0ZMkRHjx7VkiVLQsH24IMPaty4cRo5cqR8Pp/+9re/tYu5aGCmLAaYKQMAIPZefPFFjRs3TldffbUmTZokwzC0ePFiuVwuSS03EJ8zZ46GDx+uz33ucxo6dKiefvppSS03Gb/vvvs0ZswYTZ48WQ6HQ6+88kpUx2szOlp0tRCv16vMzExVV1crIyPD7OGErayqXuf/dIlcDpu2PDJddjs3eAUAWFdDQ4N27typkpISJSUlmT0cyzvdv1c4DcNMWQz0SXNLkpr8hqrrm0weDQAAsCKiLAY8Tod6pbRMlXJWGQAAOBWiLEY4FgMAAJwOURYj3P8SAACcDlEWI1yBCQCIN3FwLaAlROrfiSiLkWyWLwEAcSJ4ZERdXZ3JI4kPjY2NkiSHo2t3Hwji8NgYYaYMABAvHA6HevXqpYqKCklSSkpKl0/W7+kCgYAOHTqklJQUOZ3dyyqiLEZyONUfABBH8vPzJSkUZuiY3W5Xv379uh2uRFmMMFMGAIgnNptNBQUFys3NVVMTZ2yejtvtlt3e/R1hRFmMBKOMc8oAAPHE4XB0e68UOoeN/jESjLLK2kY1+QMmjwYAAFgNURYjfVLd8jjtMgypvLrB7OEAAACLIcpixGazqW/vZEnS3qNcYgwAANojymKoqHeKJGnf0XqTRwIAAKyGKIuhotaZsn1HmCkDAADtEWUxFIoyZsoAAMAJiLIYYvkSAAB0hCiLoeLQTBnLlwAAoD2iLIaCM2Xl3gY1NnNWGQAAaEOUxVB2WstZZQHOKgMAACcgymLIZrOFNvtzVhkAADgeURZjbZv9iTIAANCGKIsxjsUAAACnQpTFGMdiAACAUyHKYqw4i2MxAADAyYiyGAvOlO09wkwZAABoQ5TFWHBP2cGaBvma/SaPBgAAWAVRFmN9Ut1yO+0yDKnC6zN7OAAAwCKIshiz2WzKy/BIkg56OUAWAAC0IMpMkJeeJEk6yEwZAABoRZSZIC8zGGXMlAEAgBZEmQnaZsqIMgAA0IIoM0F+JnvKAABAe0SZCfIy2FMGAADaI8pMkMvyJQAAOAFRZoJ8NvoDAIATEGUmCJ5TVtvo1zFfs8mjAQAAVkCUmSDF7VR6klOSVF7NbBkAACDKTBPc7F/BEiYAABBRZprgEmY5UQYAAESUmYZjMQAAwPGIMpO0RRkzZQAAgCgzTT5RBgAAjkOUmSS4p4woAwAAElFmmlz2lAEAgOMQZSYJLl9W1DQoEDBMHg0AADAbUWaSnPSW5csmv6EjdY0mjwYAAJiNKDOJy2FX317JkqQdh2pNHg0AADAbUWaiofnpkqQtB2tMHgkAADAbUWaiIXmtUVbuNXkkAADAbESZiYa1zpRtLT9m8kgAAIDZiDIThWbKDtbIMLgCEwCAREaUmWhQbqocdpuq65s4rwwAgARHlJnI43SoJDtVEpv9AQBIdESZyYbmBfeVEWUAACQyosxkwX1lm4kyAAASGlFmsqH5aZKkrSxfAgCQ0Igykw3Nz5DUEmV+7oEJAEDCIspM1i8rRR6nXb7mgHYe5nZLAAAkKqLMZA67TWOKMiVJn+w+avJoAACAWYgyC5gwIEuS9M+dR0weCQAAMEvYUfb+++9rxowZKiwslM1m0+uvv37G17z88ssqLS1VSkqKCgoK9NWvflWVlZVdGW+PdG5JS5St2kWUAQCQqMKOstraWpWWluqpp57q1POXL1+u2bNn6+tf/7o2bNigP/3pT1q1apVuueWWsAfbU43r31t2m7TnSJ3KqxvMHg4AADCBM9wXTJ8+XdOnT+/081euXKkBAwbojjvukCSVlJTov/7rv/Too4+G+1f3WOlJLo0ozND6/V79a9cRXVNaaPaQAABAjEV9T9n555+vffv2afHixTIMQwcPHtSf//xnXXXVVdH+q+NKcF/ZKvaVAQCQkGISZS+//LJmzZolt9ut/Px89erVS7/85S87fI3P55PX62330dNNbN1X9i+iDACAhBT1KNu4caPuuOMOPfjgg1q9erXefPNN7dy5U7fddluHr5k3b54yMzNDH8XFxdEepunGt86UbTlYo6q6RpNHAwAAYs1mGEaXj5G32WxauHChrrvuug6f85WvfEUNDQ3605/+FHps+fLluuiii1RWVqaCgoKTXuPz+eTz+UKfe71eFRcXq7q6WhkZGV0druVd/LP3tLuyTn+4ZaLOPyvb7OEAAIBu8nq9yszM7FTDhL3RP1x1dXVyOtv/NQ6HQ5LUUQ96PB55PJ5oD81y+vdJ1e7KOu09Wmf2UAAAQIyFvXx57Ngxffrpp/r0008lSTt37tSnn36qPXv2SJLuu+8+zZ49O/T8GTNm6LXXXtMzzzyjHTt26MMPP9Qdd9yhc889V4WFXGV4vOLeyZKkfUfrTR4JAACItbBnyj7++GNNmTIl9Pldd90lSbrppps0f/58HThwIBRoknTzzTerpqZGTz31lO6++2716tVLl156qf7nf/4nAsPvWYqzUiRJe48wUwYAQKLp1p6yWAlnPTaevbH2gOb84RON699bf/nm+WYPBwAAdFM4DcO9Ly2kqHX5kpkyAAASD1FmIcHly4oanxqa/CaPBgAAxBJRZiG9U1xKdbdcmbq/is3+AAAkEqLMQmw2G5v9AQBIUESZxRT1bo0yjsUAACChEGUWE9zsv4+ZMgAAEgpRZjHB5UsOkAUAILEQZRYTPNWfWy0BAJBYiDKLYaM/AACJiSizmOCesqN1TTrmazZ5NAAAIFaIMotJT3KpV4pLErNlAAAkEqLMgvq3LmHuOlxr8kgAAECsEGUWNDQ/XZK0ubzG5JEAAIBYIcosaGh+y13kN5d7TR4JAACIFaLMgoa3zpRtYaYMAICEQZRZUHD5cveROtU1cgUmAACJgCizoD5pHuWke2QY0taDx8weDgAAiAGizKKGBTf7H2BfGQAAiYAos6hhXIEJAEBCIcosiiswAQBILESZRQ077gpMwzBMHg0AAIg2osyizspNk8Nu09G6JlXU+MweDgAAiDKizKKSXA6VZKdKkn701w061Ikw21zu1YxfLtd7WyqiPTwAABBhRJmFfeOigbLbpMXryjX1F8u0u/L098J8e8NBrdtfrYWf7I/RCAEAQKQQZRY2c0Kx/m/OhRqUk6qquib95QyxVVXXJEnyNjTFYngAACCCiDKLG12UqW9MHihJ+mj74dM+t6q+UZJUXU+UAQAQb4iyOHD+oGxJ0po9Var1dXzbpergTBlRBgBA3CHK4kBxVoqKeierOWBo1a4jHT6vqjXGquu5XyYAAPGGKIsTF7TOln20vbLD51TVtSxfsqcMAID4Q5TFifPP6iNJ+vA0+8qCe8kamwNqaPLHZFwAACAyiLI4MWlgS5RtKPOGZsSOZxhG6OpLiX1lAADEG6IsTuRmJOms3DQZxqmXMOsa/WoOtN2OiSVMAADiC1EWRy4ZkiNJ+tvaAyd9reqEmTGOxQAAIL4QZXHk8+f0lSS9s/Fg6PiLoBOXNL1cgQkAQFwhyuLIyMJMDctPV6M/oL+uLWv3tRMjjZkyAADiC1EWZ64/p0iS9JdP9rV7/MTlS/aUAQAQX4iyOHPt2YVy2G1as6dK2w8dCz1edeJMWR1RBgBAPCHK4kxuepImD245SPbPq9tmy4L3vQxipgwAgPhClMWhWROKJUl/+nifmvwBSewpAwAg3hFlceiy4XnKTnPr8DGf/rGpQlLb8mV+RpIkrr4EACDeEGVxyOWw6/pxLRv+X121R1Lb8mW/rBRJzJQBABBviLI4dcOEfpKkZVsPqayqPjRT1q9PS5SxpwwAgPhClMWpkuxUnTcwSwFDWrhmf2hmjJkyAADiE1EWx64YmS9J+mT30ZOijBuSAwAQX5xmDwBdV1rcS5L06d4q1TX6JbUtX9b4mhUIGLLbbWYNDwAAhIGZsjg2oiBDTrtNlbWNqm9qibLi3i1RZhgtYQYAAOIDURbHklwODS/ICH1ut0l9Ut1KcrW8rSxhAgAQP4iyOFdanBn6fWayS3a7TRlJLkls9gcAIJ4QZXFubHHv0O97pbgltcSZxEwZAADxhCiLc2NPmCmTpIxglHFWGQAAcYMoi3MDs9OU5mm5iLZXSkuMBeOM5UsAAOIHR2LEObvdpjFFmVqxvVK9gjNlSS1va3V9k5ZuqdAH2w5rS3mNLhmao69fWCKbjWMyAACwGqKsBxjfv7dWbK9UfmaypLbly+c/2KlDNb7Q85Z/dlif7Dmqn3+pVClu3noAAKyE/2XuAW6ZPFA5GUm6anSBpLbly2CQzRxfpPzMZD2z9DMtXleuQzU+vXzLeXI7Wb0GAMAq+F/lHiAjyaWvnNdfWanu0OdB3/vcUD36xVLdNXWIFtx6ntKTnFq166j+v8WbzBouAAA4BaKsB5o0qI/6pLo1Z8ogffPiQaHHxw/I0uMzx0qS5q/YpWeWbld5dYNJowQAAMezGYZhmD2IM/F6vcrMzFR1dbUyMjLO/ALIMIwON/T/7K3N+tV720OfTyzJ0o+uHalh+fzbAgAQSeE0DFGWgPwBQ8+9v11vri/Xuv3VMgzJYbdp1oRifXFckc4u7sUVmgAARABRhk7bX1WvR/66UW9uKA89NrwgQz/9wmiVFvcyb2AAAPQARBnCtmL7Yf1x1V69vfGg6hr9stukb14ySHdNHSqHnVkzAAC6gihDlx2pbdTDizZo0b/LJEmXD8/V/95wtlI9nJ4CAEC4wmkYrr5EO1mpbj1549l68saz5Xba9e6mCl3/zAr9c0el2UMDAKBHI8pwSteUFmrBrecpK9WtzeU1mvXrlfrGSx+rwssRGgAARANRhg6N699bb905Wf95Xj857Da9vfGgrnjifb25vvzMLwYAAGFhTxk6ZevBGt35yqfaeMArSZo2Ik8/vHqEirNSTB4ZAADWxUZ/RIWv2a9fvLNNz3+wQ/6AIZfDpkuG5urzZ/fVtBF5cjqYeAUA4HhEGaJqS3mNHlq0Xit3HAk9VtQ7Wf81eaBmTejHjc4BAGhFlCEmNpd79X+flunVVXt1pLZRktQvK0XfvWKorh5TwF0BAAAJjyhDTNU3+vXqqj361dLtOlTjkySVFvfSA1cO17klWSaPDgAA8xBlMEWtr1nPf7BDv35/h+oa/ZKk8wZm6daLBmrK0FzZuTMAACDBEGUwVUVNg554d5v+uGqvmgMt//EalJOqWy4aqM+f3VdJLofJIwQAIDaIMlhCWVW95q/YpQX/3KMaX7MkqU+qW1+Z1F//MbGfctOTTB4hAADRRZTBUmoamvTqqr168cNd2l9VL0ly2m26bHiubpjQT5OH5HDTcwBAj0SUwZKa/QEtXl+uFz/cqTV7qkKPF2Qm6YYJ/XTjxGJmzwAAPQpRBsvbUl6jV1ft1Wtr9qmqrkmS5HLYNH1UgWZP6q9x/XtzpAYAIO4RZYgbDU1+vbWhXC99tFurdx8NPX5WbpquLS3UNWML1b9PqokjBACg64gyxKX1+6v1u4926/VP98vXHAg9XlqUqRmlhZpRWqi8DJY3AQDxgyhDXPM2NOmt9eVa9O8yffjZYbWeqiGbTTqvpI+uGVuoz43MV+9Ut7kDBQDgDIgy9BiHanxavO6AFv27rN3ypsNu0/j+vXX58DxdPiJPJdkscQIArIcoQ4+090id/rq2TIs+LdPm8pp2XxuYk6qpw/N02fA8ndOvl5wObooOADAfUYYeb++ROr276aDe3XRQ/9xxJHTnAEnKSHJq8pAcXTosVxcPyVGfNI+JIwUAJDKiDAnF29CkZVsO6d1NB7Vs66HQERtSyz60c/q1LHNOHZGrQTlpHLUBAIgZogwJyx8w9Oneo3pv8yEt2VyhjQe87b7ev0+KLh+ep8uG5Wpsv15KcTtNGikAIBEQZUCrsqp6/WNzhf6x6aBWfFapRn/bURt2mzQkL12DctM0KDtVkwZla/yA3nKxHw0AECFEGXAKx3zNWr7tkN7ZWKEPth1SRY3vpOekJzk1eXCOpgzL1ZiiTA3okyq3k0gDAHQNUQZ0Qnl1g9bvr9bOw7XaeMCr97ceUmVtY7vnOO02jSjM0LkDsjShJEsTBmQpi/PRAACdRJQBXeAPGFq7r0rvba7Q8s8Oa+vBYzrmaz7peQP6pGhk30yNLMzQqMJMje6byUG2AIBTIsqACDAMQ/uO1mv17qP6164jWrXziLZVHDvlc4uzkjWmqJfG9G2JtGEFGcyoAQCIMiBajtY2akOZV+vLqrV+f8vHrsq6Uz43N92jofnpGlGYoTF9e2lMUaaKeidzJAcAJBCiDIih6vomrd9frbX7qrV2X5U2HfB2GGq9U1waHZxRK8rUmKJM5WckEWoA0EMRZYDJan3N2nqwRpsO1Gh9WbXW7avW5nKvmvwn/7hlp3k0sjCjZY9a6161flkphBoA9ABEGWBBvma/tpTXaO2+lkhbu79aWw/WyB84+Ucw3ePU8NYLCUYWZmhk3wydlZPGPT0BIM4QZUCcaGjya+MBrzaUebWxrFobyrzafKCm3SG3QR6nXcPy0zWiMFOj+mZoZGGmhuWnK8nlMGHkAIDOIMqAONbkD+izimPaUObVhrJqbdjv1cYD3lMez+Gw2zQoJ1WjCjM1orAl1EYUZigz2WXCyAEAJyLKgB4mEDC050id1rfOpm0o82rD/uqTDrsNGpKXpvMHZevy4XmaNKiPHHb2pwGAGYgyIAEYhqGDXl/LbFrrrNr6/V7tr6pv97zcdI++PLG/vjF5oJLdLHUCQCwRZUACO1LbqJU7KvX+1kP6+/pyVdc3SZIKM5P042tH6fIReSaPEAASB1EGQJLU2BzQ39cf0KNvbtH+qnrZbdLTXx6nz43KN3toAJAQwmkYrq8HejC3065rx/bVP+6+WNefU6SAId2xYI2Wbzts9tAAACcgyoAEkORy6NEvjtH0Uflq9Af0rZdXn/JqTgCAeYgyIEE47DY9ccNYlWSnytvQrIWf7DN7SACA4xBlQALxOB2aPam/JOm3H+1WHGwpBYCEQZQBCeaL44qU6nbos4pj+vCzSrOHAwBoRZQBCSY9yaXrxxVJkuav2GXuYAAAIUQZkICCS5hLNh+Ut6HJ5NEAACSiDEhIZ+Wmq2+vZAUMaf3+arOHAwAQUQYkrNF9MyURZQBgFUQZkKBGF7VE2br9XpNHAgCQiDIgYY1ipgwALIUoAxJUcPly5+FaNvsDgAUQZUCCykp1q2+vZEnSBpYwAcB0RBmQwEb1zZAkrdtfZe5AAABEGZDIxhT1ksRmfwCwAqIMSGBs9gcA6yDKgAR2/Gb/Gjb7A4CpiDIggWWlupWd5pHUEmYAAPMQZUCCG5idKokoAwCzEWVAghuQnSKJKAMAsxFlQIIryU6TJO0iygDAVEQZkOBKmCkDAEsgyoAEF5wp23m4VoZhmDwaAEhcRBmQ4Pr3aZkp8zY060hto8mjAYDERZQBCS7J5QjdA3NXJUuYAGAWogxA6ArMHYeIMgAwC1EGQCWtZ5UxUwYA5iHKAGhAHw6QBQCzEWUANDAnGGV1Jo8EABIXUQYgNFO2i2MxAMA0RBkAFWelyGG3qb7JrwPVDWYPBwASElEGQC6HXYNzWw6RXbe/2uTRAEBiIsoASJLO7tdLkrRmT5Wp4wCAREWUAZAknV3cW5K0Zs9Rk0cCAImJKAMgqW2mbO2+ajX7A+YOBgASEFEGQJI0KCdN6R6n6pv82nKwxuzhAEDCIcoASJLsdpvGsq8MAExDlAEIObu4lySiDADMQJQBCDm7X+tm/71s9geAWCPKAISMbZ0p23GoVkdrG80dDAAkGKIMQEjvVLeG5adLkn7z4U6TRwMAiYUoA9DOnZcPliQ9/8EOHaiuN3k0AJA4iDIA7VwxMl/nDshSQ1NAP3tri9nDAYCEQZQBaMdms+mBq4ZLkl77ZL9+v3K3ySMCgMRAlAE4SWlxL900qb8k6Qevr9cPXl+nJk75B4CoIsoAnNLD14zUd68YKptN+v3KPZr9wr+4IhMAoogoA3BKNptNc6acpV9/ZbxS3Q59tKNS1/xquRb9u4x7YwJAFNgMwzDMHsSZeL1eZWZmqrq6WhkZGWYPB0g4W8prdMtLq7T3SMvVmMVZybr1ooH60rhiJbsdJo8OAKwrnIYJe6bs/fff14wZM1RYWCibzabXX3/9jK/x+Xx64IEH1L9/f3k8Hg0aNEi/+c1vwv2rAZhkaH66/jb3In3n8iHKSnVr75F6Pfh/G3TB/yzR8+/vUEOT3+whAkDcc4b7gtraWpWWluqrX/2qrr/++k69ZubMmTp48KBeeOEFnXXWWaqoqFBzc3PYgwVgnsxkl759+WB9Y/JA/Wn1Xj3/wQ7tPVKv/168Sb/5cKduuWigZo4vUnqSy+yhAkBc6tbypc1m08KFC3Xdddd1+Jw333xTN9xwg3bs2KGsrKwu/T0sXwLW0+wP6LVP9usX727VgeoGSVK6x6mvXViiWycPVJon7P/PBwA9TlSXL8O1aNEijR8/Xo8++qj69u2rIUOG6J577lF9fccnhft8Pnm93nYfAKzF6bBr5oRivXfPJfrvz4/SoJxU1fia9b//2KaLH31PTy3ZpsPHfGYPEwDiRtT/r+yOHTu0fPlyJSUlaeHChTp8+LC+9a1v6ciRIx3uK5s3b55+9KMfRXtoACIgyeXQlyf2140T+unv68v187e3aOfhWv387a168h+f6erSAt00aYBKW292DgA4tagvX06bNk0ffPCBysvLlZmZKUl67bXX9MUvflG1tbVKTk4+6TU+n08+X9v/w/Z6vSouLmb5EogDTf6A/ra2TPNX7Na/91aFHh9TlKn/OLefpo8qUGYK+84AJIZwli+jPlNWUFCgvn37hoJMkoYPHy7DMLRv3z4NHjz4pNd4PB55PJ5oDw1AFLgcdn3+7CJ9/uwifbq3Si+t2KW/rT2gtfuqtXbfOt23cJ1GFGQozeNUTUOzslLdOis3TVeOLtC5JV3bdwoAPUHU95RdcMEFKisr07Fjx0KPbd26VXa7XUVFRdH+6wGYaGxxLz0+a6w+uu9S3X/lMA3JS5NhSBvKvPrnziPaeMCr5Z8d1vwVuzTr1x/piXe3KhCw/NGJABAVYS9fHjt2TJ999pkk6eyzz9bjjz+uKVOmKCsrS/369dN9992n/fv366WXXgo9f/jw4TrvvPP0ox/9SIcPH9Ytt9yiiy++WM8//3yn/k6uvgR6jgpvg1btOqqAYSgtyalDXp+Wf3ZYi/5dJkkqLcrUF84pUmGvZG0/dEx5GR5dPaZQLgc3IAEQf8JpmLCjbOnSpZoyZcpJj990002aP3++br75Zu3atUtLly4NfW3z5s2aO3euPvzwQ/Xp00czZ87UT37yk1PuJ+vuNwQgPv159T49sHCdfM0n38JpYHaq7p0+TNNG5pswMgDouqhGmRmIMiAxlFc36G9ry/Tm+nLVN/k1IDtVK7dXqrL1RuhfOLuvHr52pDI4oBZAnCDKAPQYNQ1Nenrpdj23bLsCRst9N3/71XM1MCfN7KEBwBlZ6vBYAOiO9CSXvv+5YfrTbZNUnJWsvUfqNfO5j7SxjEOlAfQsRBmAuDCuf5YWfusCjSjI0OFjjbrx+ZU62rqsCQA9AVEGIG5kp3m04BvnaUCfFFXXN+mDzw6bPSQAiBiiDEBcyUx26ZKhuZKk1buOmDwaAIgcogxA3JkwoOXk/1W7jpo8EgCIHKIMQNwZP6C3JGlzuVfHfM0mjwYAIoMoAxB38jKSVJyVrIAhrdnDbBmAnoEoAxCXxvdnCRNAz0KUAYhL4/q3LGGu3s1mfwA9A1EGIC4FN/uv2VOlZv/J98sEgHhDlAGIS4Nz05SR5FRdo1+by2vMHg4AdBtRBiAu2e02DStouY/c9kPHTB4NAHQfUQYgbg3okyJJ2l1ZZ/JIAKD7iDIAcat/n1RJ0q7KWpNHAgDdR5QBiFv9W2fK9jBTBqAHIMoAxK3+WcGZMqIMQPwjygDErX6tM2WHj/lUy+2WAMQ5ogxA3MpMdql3iksSm/0BxD+iDEBcC27233OEzf4A4htRBiCuBTf7s68MQLwjygDEteBMGcuXAOIdUQYgrvXPCh4gy/IlgPhGlAGIawOyOdUfQM/gNHsAANAd/VrPKiurrte/dh7ROxvLtfXgMfma/frFrLEqyEw2eYQA0DlEGYC4lp3mVqrbodpGv2Y+91G7r/3t3wd06+SBJo0MAMLD8iWAuGaz2VSS0zJbZrdJ140t1EWDsyVJe4+ypAkgfjBTBiDu3X/lcL27sUL/MbGfzspN04J/7dEH2w5r7xGiDED8IMoAxL3zB2Xr/EHZoc+Le7feqJwoAxBHWL4E0OP0az0mY9/RehmGYfJoAKBziDIAPU5BryTZbZKvOaBDNT6zhwMAnUKUAehxXA576CgMljABxAuiDECPFFzC5ApMAPGCKAPQIxVntc6UVdabPBIA6ByiDECPxEwZgHhDlAHokYqzOBYDQHwhygD0SMEo20eUAYgTRBmAHil4gOwBb4MamwMmjwYAzowoA9AjZae5lexyyDCk/VVs9gdgfUQZgB7JZrOFrsDkHpgA4gFRBqDHCi5hrt1XZe5AAKATiDIAPdalw3MlSb9c8pm2HqwxeTQAcHpEGYAe68YJ/TR5SI58zQHN/cMaNTT5zR4SAHSIKAPQY9ntNj32pVJlp7m15WCNXli+0+whAUCHiDIAPVpOukf3Th8uSXpl1R4FAobJIwKAUyPKAPR4V40uULrHqb1H6vXRjkqzhwMAp0SUAejxkt0OXTO2UJL06qq9Jo8GAE6NKAOQEGZNKJYkvbmhXNV1TSaPBgBORpQBSAij+2ZqeEGGGpsD+u1Hu8weDgCchCgDkBBsNpu+dsEASdIv3t2qdzce1P6qer26ao8OH/OZOzgAkOQ0ewAAECtfHFekT/Yc1YJ/7dW3Xv5EzYGAAoZ01ZjD+tV/nGP28AAkOGbKACQMm82mH187ShcNzlajvyXIJGnp5gr5mjlYFoC5iDIACcXlsOu5r4zTo9eP0TvfmazsNI9qG/1atfOo2UMDkOCIMgAJJ8Xt1MwJxRqcl65Lh+VIkv6x+aDJowKQ6IgyAAnt0mEtNy1fsrlChsFp/wDMQ5QBSGgXDs6Ry2HT7so67Thca/ZwACQwogxAQkvzODWxpI8k6WvzV2n0w2/p0Tc3mzwqAImIKAOQ8C4f3rKEubuyTjUNzXp22XZtOuA1eVQAEg3nlAFIeDdO7Kf6poB6pbj0j00H9e6mCv3kjY369VfG6/VP92tUYaZKi3uZPUwAPZzNiIOdrV6vV5mZmaqurlZGRobZwwHQg+09UqfLHlumRn9AmckuVdc3Kcll14Jbz9PZ/XqbPTwAcSachmH5EgCOU5yVoq9fVCJJqq5vkttpV0NTQF//7cfaxYUAAKKI5UsAOMHcS89SU3NAxVkpunZsob7ywr+0bn+1bnx+pZ6fPV6j+maaPUQAPRDLlwBwBodqfJr164+041Ctklx2/eyLpZpRWmj2sADEAZYvASCCctI9WvitCzRlaI4amgKau2CNXv7nbrOHBaCHIcoAoBMyk136/2+aoJsm9ZckPbBwvR5/e4uq6hpNHhmAnoLlSwAIg2EY+p83t+jZZdslSW6nXVePLtCtkwdqeAH//QSgvXAahigDgDAZhqE/r96nF5bv1ObymtDjE0uyNHlIjqaOyNOQvHQTRwjAKogyAIgBwzD0733Vev6DHfr7ugMKtP63qd0m3Td9uG65qCT0mMNuM2+gAExDlAFAjO09Uqclmyv07qaD+mDbYUnSsPx07T1SJ6fDrv/+/ChdPYYrNoFEQ5QBgEkMw9DvVu7Wj/+6Uc2B9v/1etvFgzSmKFO9U9yaMKC3nA6utQJ6OqIMAEy2udyrtfuqNbIwQ39ZvV+/+XBnu68XZCbpxnP76YYJxcrNSDJplACijSgDAIv5y+p9ev3T/fI1BfTZoWM6UttylIbTbtMVI/P1n+f113kDs2SzsfcM6EmIMgCwMF+zX2+uL9fvPtqtj3cfDT0+KCdVFw3O0dn9eumy4XlK83AnPCDeEWUAECc2HfDq9yt3a+Ga/apr9IceT09y6oYJxRpRmKGMJJfG989SZorLxJEC6AqiDADiTE1Dk5ZsrtCne6v03uYK7aqsa/d1t9OuaSPyNKO0UBcNzlaKm1k0IB4QZQAQxwIBQ0s2V2jRv8t0tK5R+6vqteNQbejrbqddpUWZGtU3U2OKMjW6b6ZKstM4Cw2wIKIMAHoQwzC0ocyrv3yyT+9uOqi9R+pPek6K26FRhS2hNrooQ0Py0tW/Tyr70gCTEWUA0EMZhqHth2r1771VWre/Wuv3V2tDmVf1Tf5TPj8/I0mj+ma0xFrfTA3NT1d+RhJnpAExQpQBQALxBwxtP3RM6/ZVh0Jtx+Ha0LEbJ3LYberbK1lD89M1PD9dQ/MzdFZumnLSPeqV7JKdZVAgYogyAICq65u09WCN1u1rCbV1+6u1q7JWTf6O/2vf7bRrYHaqBuWkKTfDo5x0j3LSPMpu/TU33aOsVDczbUAnEWUAgFMKBAxV1Pi04/AxbT5Qoy3lNdpc7tXOw7XyNjR36s+w2aSsFHdLsKV7lJ12fLy5lZOW1Pq4W71T3My8IaERZQCAsDU2B1RWVa/PKo5pV2WtDh3z6XBNow4d8+lQjU+Hj/lUecynQBj/q+G025SR7FKqx6E0j0vpHqfSkpxKa/013dP2+1SPs93X05OcSvO4lJbkVIrLQdwhLoXTMFyWAwCQ1LJ0OSA7VQOyUzt8jj9g6Ehtow63hlow1g7V+Foi7rjHj9Y1qbn1+UdqJenkq0Y7y2aT0txt8ZbW+pHsdijZ1frhdiip9fcpboeS2n3NftzXnEp2OZTktsvjcMjttMvttHOkCExHlAEAOs1ht4WWLYcXnP65Tf6AKo81ytvQpJqGZh3zNavW16xjDc2qaf31mK9Jx3zNoa8fa/21pqFZtY0tv/oDhgxDqvG1vC5a7LaWMHU77O1+dQU/7+rXHDa5HC2fu0783GGX23nC5w67XK2PBf88l4NoTAREGQAgKlwOu/Izk5SfmdTlP8MwDPmaA+2ircbXpGOt0VbfGFB9k18NTX7VnfB5faNf9cf/2vr7hqa2z4/fwBMwpIamgBqaAhH47iPPYbfJ1Rp0x4efy2GT2+loF3ttUWgLRZ2rXTCeHH3t/rx2nx/3PGf7v99pt8lpt8tul5z2lnB02m0sNXcRUQYAsCybzaYkV8uyZE66J6J/tmEYavIbavQH1NgcUFPrr77jft/oD6ipOSDfCc9p/1yj9bn+0O99Jzy3yR9Qo99Q04mft/6+qbn9543NATWfsHnPHzDkDxiWjcbj2Wwt+wkdrdEWjLXQr472j9ttNjkdthOed8LrHC3Pc9htcthawq/lV4Uet9uCz1Ho6w67TTZb8Pdtj9tb/4wkl11fntjf7H8ySUQZACBB2Wy2lpkkp12KbO9FxPHRGIy5toBsCTjfcZHXFpJGa+QdH4ZGu0A8/nWhr/tPiM4TXhP8M49/vr+Dqz4MQ61jNCRZOyLTk5xEGQAA6JjVo1FqCUd/wFBz4MRfW4Kt2d/2eMA4/vPAKV4XaPf8do8HP/e3/Dn+gCG/0bLXMDiDGHw8YKjtOQGjZYyGIX+g5UgYv9Hy3JbfS0lO65y5R5QBAIAusbUuOzodZo+kZ7BOHgIAACQwogwAAMACiDIAAAALIMoAAAAsgCgDAACwAKIMAADAAogyAAAACyDKAAAALIAoAwAAsACiDAAAwAKIMgAAAAsgygAAACyAKAMAALAAogwAAMACiDIAAAALIMoAAAAsgCgDAACwAKIMAADAAogyAAAACyDKAAAALIAoAwAAsACiDAAAwAKIMgAAAAsgygAAACyAKAMAALAAogwAAMACiDIAAAALIMoAAAAsgCgDAACwAKfZA+gMwzAkSV6v1+SRAAAAdF6wXYItczpxEWU1NTWSpOLiYpNHAgAAEL6amhplZmae9jk2ozPpZrJAIKCysjKlp6fLZrNF5e/wer0qLi7W3r17lZGREZW/A13De2NNvC/WxXtjTbwv1hXN98YwDNXU1KiwsFB2++l3jcXFTJndbldRUVFM/q6MjAx+WCyK98aaeF+si/fGmnhfrCta782ZZsiC2OgPAABgAUQZAACABRBlrTwejx566CF5PB6zh4IT8N5YE++LdfHeWBPvi3VZ5b2Ji43+AAAAPR0zZQAAABZAlAEAAFgAUQYAAGABRFmrp59+WiUlJUpKStK4ceP0wQcfmD2khPLwww/LZrO1+8jPzw993TAMPfzwwyosLFRycrIuueQSbdiwwcQR91zvv/++ZsyYocLCQtlsNr3++uvtvt6Z98Ln82nu3LnKzs5WamqqrrnmGu3bty+G30XPc6b35eabbz7pZ+i8885r9xzel8ibN2+eJkyYoPT0dOXm5uq6667Tli1b2j2HnxlzdOa9sdrPDVEm6dVXX9Wdd96pBx54QGvWrNFFF12k6dOna8+ePWYPLaGMHDlSBw4cCH2sW7cu9LVHH31Ujz/+uJ566imtWrVK+fn5mjp1augWXIic2tpalZaW6qmnnjrl1zvzXtx5551auHChXnnlFS1fvlzHjh3T1VdfLb/fH6tvo8c50/siSZ/73Ofa/QwtXry43dd5XyJv2bJlmjNnjlauXKl33nlHzc3NmjZtmmpra0PP4WfGHJ15bySL/dwYMM4991zjtttua/fYsGHDjHvvvdekESWehx56yCgtLT3l1wKBgJGfn2/89Kc/DT3W0NBgZGZmGs8++2yMRpiYJBkLFy4Mfd6Z96KqqspwuVzGK6+8EnrO/v37Dbvdbrz55psxG3tPduL7YhiGcdNNNxnXXntth6/hfYmNiooKQ5KxbNkywzD4mbGSE98bw7Dez03Cz5Q1NjZq9erVmjZtWrvHp02bphUrVpg0qsS0bds2FRYWqqSkRDfccIN27NghSdq5c6fKy8vbvUcej0cXX3wx71GMdea9WL16tZqamto9p7CwUKNGjeL9irKlS5cqNzdXQ4YM0a233qqKiorQ13hfYqO6ulqSlJWVJYmfGSs58b0JstLPTcJH2eHDh+X3+5WXl9fu8by8PJWXl5s0qsQzceJEvfTSS3rrrbf0/PPPq7y8XOeff74qKytD7wPvkfk6816Ul5fL7Xard+/eHT4HkTd9+nS9/PLLWrJkiR577DGtWrVKl156qXw+nyTel1gwDEN33XWXLrzwQo0aNUoSPzNWcar3RrLez01c3JA8Fmw2W7vPDcM46TFEz/Tp00O/Hz16tCZNmqRBgwbpt7/9bWjTJe+RdXTlveD9iq5Zs2aFfj9q1CiNHz9e/fv31xtvvKEvfOELHb6O9yVybr/9dq1du1bLly8/6Wv8zJiro/fGaj83CT9Tlp2dLYfDcVLxVlRUnPT/bBA7qampGj16tLZt2xa6CpP3yHydeS/y8/PV2Nioo0ePdvgcRF9BQYH69++vbdu2SeJ9iba5c+dq0aJFeu+991RUVBR6nJ8Z83X03pyK2T83CR9lbrdb48aN0zvvvNPu8XfeeUfnn3++SaOCz+fTpk2bVFBQoJKSEuXn57d7jxobG7Vs2TLeoxjrzHsxbtw4uVyuds85cOCA1q9fz/sVQ5WVldq7d68KCgok8b5Ei2EYuv322/Xaa69pyZIlKikpafd1fmbMc6b35lRM/7mJ+KUDceiVV14xXC6X8cILLxgbN2407rzzTiM1NdXYtWuX2UNLGHfffbexdOlSY8eOHcbKlSuNq6++2khPTw+9Bz/96U+NzMxM47XXXjPWrVtn3HjjjUZBQYHh9XpNHnnPU1NTY6xZs8ZYs2aNIcl4/PHHjTVr1hi7d+82DKNz78Vtt91mFBUVGe+++67xySefGJdeeqlRWlpqNDc3m/Vtxb3TvS81NTXG3XffbaxYscLYuXOn8d577xmTJk0y+vbty/sSZd/85jeNzMxMY+nSpcaBAwdCH3V1daHn8DNjjjO9N1b8uSHKWv3qV78y+vfvb7jdbuOcc85pd8ksom/WrFlGQUGB4XK5jMLCQuMLX/iCsWHDhtDXA4GA8dBDDxn5+fmGx+MxJk+ebKxbt87EEfdc7733niHppI+bbrrJMIzOvRf19fXG7bffbmRlZRnJycnG1VdfbezZs8eE76bnON37UldXZ0ybNs3IyckxXC6X0a9fP+Omm2466d+c9yXyTvWeSDJefPHF0HP4mTHHmd4bK/7c2FoHDgAAABMl/J4yAAAAKyDKAAAALIAoAwAAsACiDAAAwAKIMgAAAAsgygAAACyAKAMAALAAogwAAMACiDIA6IKlS5fKZrOpqqrK7KEA6CGIMgAAAAsgygAAACyAKAMQlwzD0KOPPqqBAwcqOTlZpaWl+vOf/yypbWnxjTfeUGlpqZKSkjRx4kStW7eu3Z/xl7/8RSNHjpTH49GAAQP02GOPtfu6z+fT9773PRUXF8vj8Wjw4MF64YUX2j1n9erVGj9+vFJSUnT++edry5Yt0f3GAfRYRBmAuPSDH/xAL774op555hlt2LBB3/nOd/Sf//mfWrZsWeg53/3ud/Xzn/9cq1atUm5urq655ho1NTVJaompmTNn6oYbbtC6dev08MMP64c//KHmz58fev3s2bP1yiuv6Mknn9SmTZv07LPPKi0trd04HnjgAT322GP6+OOP5XQ69bWvfS0m3z+AnsdmGIZh9iAAIBy1tbXKzs7WkiVLNGnSpNDjt9xyi+rq6vSNb3xDU6ZM0SuvvKJZs2ZJko4cOaKioiLNnz9fM2fO1Je//GUdOnRIb7/9duj13/ve9/TGG29ow4YN2rp1q4YOHap33nlHl19++UljWLp0qaZMmaJ3331Xl112mSRp8eLFuuqqq1RfX6+kpKQo/ysA6GmYKQMQdzZu3KiGhgZNnTpVaWlpoY+XXnpJ27dvDz3v+GDLysrS0KFDtWnTJknSpk2bdMEFF7T7cy+44AJt27ZNfr9fn376qRwOhy6++OLTjmXMmDGh3xcUFEiSKioquv09Akg8TrMHAADhCgQCkqQ33nhDffv2bfc1j8fTLsxOZLPZJLXsSQv+Puj4hYPk5OROjcXlcp30ZwfHBwDhYKYMQNwZMWKEPB6P9uzZo7POOqvdR3Fxceh5K1euDP3+6NGj2rp1q4YNGxb6M5YvX97uz12xYoWGDBkih8Oh0aNHKxAItNujBgDRxEwZgLiTnp6ue+65R9/5zncUCAR04YUXyuv1asWKFUpLS1P//v0lST/+8Y/Vp08f5eXl6YEHHlB2drauu+46SdLdd9+tCRMm6JFHHtGsWbP00Ucf6amnntLTTz8tSRowYIBuuukmfe1rX9OTTz6p0tJS7d69WxUVFZo5c6ZZ3zqAHowoAxCXHnnkEeXm5mrevHnasWOHevXqpXPOOUf3339/aPnwpz/9qb797W9r27ZtKi0t1aJFi+R2uyVJ55xzjv74xz/qwQcf1COPPKKCggL9+Mc/1s033xz6O5555hndf//9+ta3vqXKykr169dP999/vxnfLoAEwNWXAHqc4JWRR48eVa9evcweDgB0CnvKAAAALIAoAwAAsACWLwEAACyAmTIAAAALIMoAAAAsgCgDAACwAKIMAADAAogyAAAACyDKAAAALIAoAwAAsACiDAAAwAKIMgAAAAv4fzwJ9eNs4peFAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss\n",
      "\tloss             \t (min:    1.480, max:    2.303, cur:    1.480)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for _ in range(num_epochs):\n",
    "    # Forward pass\n",
    "    pred = model(X_mnist_train_tensor)\n",
    "\n",
    "    # Compute loss\n",
    "    loss = loss_fun(pred, y_mnist_train_tensor)\n",
    "\n",
    "    # Backward pass\n",
    "    optim.zero_grad() # Reset gradients\n",
    "    loss.backward()\n",
    "\n",
    "    # Gradient descent step\n",
    "    optim.step() \n",
    "\n",
    "    # Update live plot\n",
    "    plotlosses.update({\"loss\": loss.item()})\n",
    "    plotlosses.send()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the loss is not a perfect \"L\" shape in this case, and we plateau a couple times around epochs 50-90 and 100-110. This is likely because we get stuck in a saddle point during our optimization stage. Proves to show sometimes it is best to wait longer for the model to train rather than stopping preemptively. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Evaluating the output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 96.12%\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Change model to evaluation model\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    pred = model(torch.from_numpy(X_mnist_test).float().to(device))\n",
    "    y_pred = pred.argmax(dim=1).cpu().numpy()\n",
    "    plot_confusion_matrix(true_labels=y_mnist_test, pred_labels=y_pred)\n",
    "\n",
    "# Accuracy\n",
    "print(f\"Accuracy: {np.mean(y_mnist_test == y_pred) * 100:.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Neural Network Implemented From Scratch\n",
    "\n",
    "Feel free to skip this section of the notebook if it is too advanced for you! This part shows how you could create your own NN without the use of any built-in functions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Activation Functions\n",
    "\n",
    "Activation functions are used to allow relationships that are non-linear in nature. There are many activation functions, but the most common are the sigmoid function, the tanh function, and the rectified linear unit (ReLU) function. \n",
    "\n",
    "The sigmoid function is defined as follows:\n",
    "\n",
    "$$\\sigma(z) = \\frac{1}{1+e^{-z}}$$\n",
    "\n",
    "The tanh function is defined as follows:\n",
    "\n",
    "$$\\text{tanh}(z) = \\frac{e^z - e^{-z}}{e^z + e^{-z}}$$\n",
    "\n",
    "The ReLU function is defined as follows:\n",
    "\n",
    "$$\\text{ReLU}(z) = \\text{max}(0,z)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "\n",
    "def tanh(z):\n",
    "    return (np.exp(z) - np.exp(-z)) / (np.exp(z) + np.exp(-z))\n",
    "\n",
    "\n",
    "def relu(z):\n",
    "    return np.maximum(0, z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Loss Functions\n",
    "\n",
    "Loss functions are used to evaluate how well the model performs. We aim to minimise the loss function as much as possible. There are many loss functions, but the most common two are the mean squared error (MSE) and the binary cross entropy (BCE). The MSE is used for regression problems, while the BCE is used for classification problems.\n",
    "\n",
    "The MSE is defined as:\n",
    "\n",
    "$$\\text{MSE}(\\bf{y}, \\bf{\\hat{y}}) = \\frac{1}{n}\\sum_{i=1}^{n}(y_i - \\hat{y_i})^2$$\n",
    "\n",
    "where $y_i$ is the true value and $\\hat{y_i}$ is the predicted value.\n",
    "\n",
    "The BCE is defined as:\n",
    "\n",
    "$$BCE = -y_1\\log(\\hat{y_1}) - (1 - y_1)\\log(1 - \\hat{y_1})$$\n",
    "\n",
    "where $y_i$ is the true value and $\\hat{y_i}$ is the predicted value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mse_loss(y_true, y_pred):\n",
    "    return np.mean((y_true - y_pred) ** 2)\n",
    "\n",
    "\n",
    "def bce_loss(y_true, y_pred):\n",
    "    # the epsilon value is used to avoid log(0) which is undefined\n",
    "    epsilon = 1e-15\n",
    "    y_pred = np.clip(y_pred, epsilon, 1 - epsilon)\n",
    "    return -y_true * np.log(y_pred) - (1 - y_true) * np.log(1 - y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Forward Propagation\n",
    "\n",
    "Forward propagation is a series of computations that takes the input layer and produces a prediction. This can be described mathematically in the following steps:\n",
    "\n",
    "1. Get the output from the neuron $$z = Wx + b$$\n",
    "2. Pass the output through an activation function A $$\\hat{y} = A(z)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward(X, W, b):\n",
    "    # This example is very simple, but we can have multiple hidden layers\n",
    "    z = X @ W + b\n",
    "    yhat = sigmoid(z)\n",
    "    return yhat, z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Backpropagation\n",
    "\n",
    "Backpropagation is used to update the weights and biases. These are done by computing the partial derivatives of the loss function with respect to the weights and biases. The formulae we use for this are:\n",
    "\n",
    "$$ W_{n+1} = W_n - \\alpha \\frac{\\partial L}{\\partial W_n} $$\n",
    "$$ b_{n+1} = b_n - \\alpha \\frac{\\partial L}{\\partial b_n} $$\n",
    "\n",
    "where $\\alpha$ is the learning rate.\n",
    "\n",
    "This is done is essentially four steps:\n",
    "1. Calculate $\\frac{\\partial L}{\\partial \\hat{y}}$ using the derivative of the loss function\n",
    "2. Calculate $\\frac{\\partial \\hat{y}}{\\partial z}$ using the derivative of the activation function\n",
    "3. Calculate $\\frac{\\partial z}{\\partial W}$ and $\\frac{\\partial z}{\\partial b}$ using the derivative of the forward pass\n",
    "4. Use the chain rule to calculate $\\frac{\\partial L}{\\partial W}$ and $\\frac{\\partial L}{\\partial b}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def d_mse_loss(y_true, y_pred):\n",
    "    grad = -2 * (y_true - y_pred) / len(y_true)\n",
    "    return grad\n",
    "\n",
    "\n",
    "def d_sigmoid(z):\n",
    "    grad = sigmoid(z) * (1 - sigmoid(z))\n",
    "    return grad\n",
    "\n",
    "\n",
    "def backward(X, y, z, yhat, W, b):\n",
    "\n",
    "    dL_dyhat = d_mse_loss(y, yhat)\n",
    "    dyhat_dz = d_sigmoid(z)\n",
    "    dz_dw = X\n",
    "    dz_db = 1\n",
    "\n",
    "    dL_dz = dL_dyhat * dyhat_dz\n",
    "    dL_dw = dz_dw.T @ dL_dz\n",
    "    dL_db = np.sum(dL_dz * dz_db, axis=0)\n",
    "\n",
    "    dL_dw = dL_dw\n",
    "    dL_db = dL_db\n",
    "\n",
    "    return dL_dw, dL_db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Putting it all together\n",
    "Now that we have set up all the components, we can assemble these pieces in our training function. This iterates over the number of epochs set, each time creating a random batch of 200 data points from arrays X and Y while ensuring that the selected indices are unique, applying forward propagation through the neural network, as well as backpropagation to update the parameters. The loss calculated in each epoch is saved into loss_history so that we can plot it on a graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def training(X, Y, W, b, step_size, max_it):\n",
    "\n",
    "    loss_history = []\n",
    "    for i in tqdm(range(max_it)):\n",
    "\n",
    "        idx = np.random.choice(X.shape[0], 200, replace=False)\n",
    "        X_batch = X[idx]\n",
    "        Y_batch = Y[idx].reshape(-1, 1)\n",
    "\n",
    "        yhat, z = forward(X_batch, W, b)\n",
    "        loss = mse_loss(Y_batch, yhat)\n",
    "        loss_history.append(loss)\n",
    "        dL_dw, dL_db = backward(X_batch, Y_batch, z, yhat, W, b)\n",
    "        W = W - step_size * dL_dw\n",
    "        b = b - step_size * dL_db\n",
    "\n",
    "    return W, b, loss_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below combines the steps mentioned previously: spliting the dataset into test and training sets, defining the initial set-up for the neural network, training and lastly evaluating the performance looking at the loss graph. Feel free to change the learning rate, loss function and activation function used to explore how this might affect the output!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b0eb11b0ff6a49d1a033dabd6911a749",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/2500 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 0.03327761134328305\n",
      "Accuracy: 95.89%\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the step size, maximum number of epochs, and classes\n",
    "step_size = 0.01\n",
    "max_iter = 2500\n",
    "class1 = 0\n",
    "class2 = 1\n",
    "\n",
    "\n",
    "# Our example is binary, so let's simplify the problem and only look at 2 classes\n",
    "X_subset = X_mnist_train[(y_mnist_train == class1) | (y_mnist_train == class2)]\n",
    "Y_subset = y_mnist_train[(y_mnist_train == class1) | (y_mnist_train == class2)]\n",
    "XT_subset = X_mnist_test[(y_mnist_test == class1) | (y_mnist_test == class2)]\n",
    "YT_subset = y_mnist_test[(y_mnist_test == class1) | (y_mnist_test == class2)]\n",
    "\n",
    "\n",
    "# We need to convert our labels to 0/1\n",
    "Y_subset[Y_subset == class1] = 0\n",
    "Y_subset[Y_subset == class2] = 1\n",
    "YT_subset[YT_subset == class1] = 0\n",
    "YT_subset[YT_subset == class2] = 1\n",
    "\n",
    "# Set initial weights and biases to random values\n",
    "initial_W = np.random.randn(X_subset.shape[1], 1)\n",
    "initial_b = np.random.randn(1)\n",
    "\n",
    "# Train the model\n",
    "W, b, loss = training(X_subset, Y_subset, initial_W, initial_b, step_size, max_iter)\n",
    "\n",
    "# Compute predictions and the model accuracy\n",
    "y_pred, _ = forward(XT_subset, W, b)\n",
    "final_loss = mse_loss(y_pred, YT_subset.reshape(-1, 1))\n",
    "accuracy = np.mean(np.round(y_pred.flatten()) == YT_subset)\n",
    "\n",
    "# Print results\n",
    "print(f\"Final loss: {final_loss}\")\n",
    "print(f\"Accuracy: {accuracy * 100:.2f}%\")\n",
    "\n",
    "# Plot loss graph\n",
    "fig = plt.figure(figsize=(10, 6))\n",
    "plt.plot(loss)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}