kampala2020/DSA2020-DeepLearningPractical.ipynb

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  "metadata": {
    "anaconda-cloud": {},
    "kernelspec": {
      "display_name": "Python [Root]",
      "language": "python",
      "name": "Python [Root]"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.5.6"
    },
    "colab": {
      "name": "DSA-DL.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "1F1_3qC8RDRR"
      ]
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QUO6t7SpRDP1",
        "colab_type": "text"
      },
      "source": [
        "# Deep learning lab - DSA \n",
        "By: _Benjamin Akera_  &  _Andreas Damianou_     \n",
        "25 July 2020 "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6oNunMjClP2F",
        "colab_type": "text"
      },
      "source": [
        "In this tutorial we will introduce the concept of deep learning by starting from the fundamentals block, which is a logistic regression model. We will implement this model from scratch to understand its behaviour, and then add more layers to obtain a deep model. \n",
        "\n",
        "We will then show how complicated architectures and optimization can be achieved with `keras`, which abstracts all the low-level functionalities.\n",
        "\n",
        "We will focus on image problems with convolutional neural networks, and explain how transfer learning can help us achieve good results. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QxMokgOaRDP1",
        "colab_type": "text"
      },
      "source": [
        "### First import necessary helper libraries for this tutorial and define helper functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yrUh511RRDP3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "outputId": "bf8b65ce-32d8-4f66-d092-963b0fb45320"
      },
      "source": [
        "### Download the data for future use\n",
        "\n",
        "!wget \"http://ec2-3-135-230-66.us-east-2.compute.amazonaws.com/dsa/train.zip\"\n",
        "!unzip 'train.zip'"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-07-25 14:33:33--  http://ec2-3-135-230-66.us-east-2.compute.amazonaws.com/dsa/train.zip\n",
            "Resolving ec2-3-135-230-66.us-east-2.compute.amazonaws.com (ec2-3-135-230-66.us-east-2.compute.amazonaws.com)... 3.135.230.66\n",
            "Connecting to ec2-3-135-230-66.us-east-2.compute.amazonaws.com (ec2-3-135-230-66.us-east-2.compute.amazonaws.com)|3.135.230.66|:80... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 814615952 (777M) [application/zip]\n",
            "Saving to: ‘train.zip.1’\n",
            "\n",
            "train.zip.1         100%[===================>] 776.88M  22.6MB/s    in 36s     \n",
            "\n",
            "2020-07-25 14:34:08 (21.8 MB/s) - ‘train.zip.1’ saved [814615952/814615952]\n",
            "\n",
            "Archive:  train.zip\n",
            "replace train/cgm/train-cgm-738.jpg? [y]es, [n]o, [A]ll, [N]one, [r]ename: n\n",
            "replace train/cgm/train-cgm-704.jpg? [y]es, [n]o, [A]ll, [N]one, [r]ename: N\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OfUp6F8OhxlM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import os\n",
        "os.environ['KERAS_BACKEND'] = 'tensorflow' "
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R1CVWSJaRDP6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ApJCa62VRDP9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Define helper functions for later\n",
        "\n",
        "def plot_point(func, t, xmin, xmax):\n",
        "    N = 10\n",
        "    x = np.zeros((N,1))+t\n",
        "    x = x[:,0]\n",
        "    y = np.linspace(0,func(t),N)\n",
        "    plt.plot(x,y, 'k--', linewidth=1)\n",
        "    \n",
        "    x = np.linspace(xmin, t, N)\n",
        "    y = np.zeros((N,1))+func(t)\n",
        "    plt.plot(x,y, 'k--', linewidth=1)"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sCmRP5KlRDQB",
        "colab_type": "text"
      },
      "source": [
        "### Define the activation function and its derivative"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "01dds3Jhlz__",
        "colab_type": "text"
      },
      "source": [
        "A deep learning model is, losely speaking, a hierarchy of dot products (involving weight parameters) passed through activations (non-linearities):\n",
        "$$f(x; w) = activation(w x) $$\n",
        "\n",
        "This gives us a function the shape of which changes as we change the weights. We want to find a good setting of the weights such that our function $f$ \"fits\" our observed data well. To find the weights we first define a loss function which we then minimize by computing its gradients with respect to the weights. \n",
        "\n",
        "To get started, let's fist define and plot an activation and its derivative."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9MhwMrZpRDQB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Sigmoid activation function\n",
        "def activation(x):\n",
        "    return 1/(1+np.exp(-x))\n",
        "\n",
        "# Derivative of activation wrt input x\n",
        "def activation_derivative(x):\n",
        "    # the activation of the sigmoid function conveniently can be written in terms of its outputs.\n",
        "    f = activation(x)\n",
        "    return f*(1-f)\n",
        "\n",
        "# Derivative of activation wrt input x but expressed when activation(x) is given as argument instead of x\n",
        "def activation_derivative_f(f):\n",
        "    return f*(1-f)\n"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JxmVo_TcRDQE",
        "colab_type": "text"
      },
      "source": [
        "### Plots to explore the activation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6S4UBbZARDQE",
        "colab_type": "text"
      },
      "source": [
        "First, plot the activation for input domain between -10 and 10"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "snw3m9x7RDQF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "ab130e1d-f00c-490e-973c-9379765d6f7d"
      },
      "source": [
        "x1 = np.linspace(-10, 10, 500)\n",
        "plt.plot(x1, activation(x1))\n",
        "plt.xlabel('x'); plt.ylabel('activation(x)')"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'activation(x)')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WbONfeI9RDQJ",
        "colab_type": "text"
      },
      "source": [
        "Let's see what happens with low, intermediate and high values:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i4HsRo1TRDQJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "de1cfd50-736a-4522-b2f5-d58494e1bcfe"
      },
      "source": [
        "x1 = np.linspace(-10, 10, 500)\n",
        "plt.plot(x1, activation(x1))\n",
        "plt.xlabel('x'); plt.ylabel('activation(x)')\n",
        "plot_point(activation, x1[150], -10, 10)\n",
        "plot_point(activation, x1[250], -10, 10)\n",
        "plot_point(activation, x1[470], -10, 10)"
      ],
      "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": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8d6amg3oRDQN",
        "colab_type": "text"
      },
      "source": [
        "Repeat but for the space -20 to 20"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j6eh5dUbRDQO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "d905644e-c22b-4c1d-ec37-fdd3faa4264d"
      },
      "source": [
        "x2 = np.linspace(-20, 20, 500)\n",
        "plt.plot(x2, activation(x2))\n",
        "plt.xlabel('x'); plt.ylabel('activation(x)')\n",
        "plot_point(activation, x1[150], -20, 20)\n",
        "plot_point(activation, x1[250], -20, 20)\n",
        "plot_point(activation, x1[470], -20, 20)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QwwKtipcRDQQ",
        "colab_type": "text"
      },
      "source": [
        "Explore the derivative"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vUS2cc_XRDQQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "78d167bf-2c6a-445c-f824-bcb97ca7a861"
      },
      "source": [
        "plt.plot(x1, activation(x1))\n",
        "plt.plot(x1, 4*activation_derivative(x1), '--')\n",
        "plt.plot(np.zeros((5,1)), np.linspace(0,1,5), '--')\n",
        "plt.legend(['activation','activation_derivative','decision boundary'])\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('activation(x)')"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'activation(x)')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nZ3PgwAE6dOhAaGgogwYNuqCsPn36cOrUKY4fP05qaiqBgYG0b9+eoqIinnrqKTZu3IjFYiE5ObnKu5TSn9PIkSP5+9//zueff17WdrB69WpWrFjB66+/Dhgztx47dqz2c1HFfwvLp8MDm6GVA6rcLrkaNrwMh9dDpGPbO+b9nMAX25N4cERnJvWXNgFhv4szETjBxbweQUWLjWitefLJJ7n//vvP2Z6QkICPj0+lZU2YMIEvv/ySkydPlt3tfPbZZ6SmprJ9+3bc3NwICwur9vsLCQmhRYsW/PbbbyxevJjZs2eXxbVkyRK6du1a5fl2O/Kj0W20ZTfHlNcmCrwCIf2IY8qz2bg/lRe/jWN0z9Y8NKKzQ8sWFz+pGnKQ6tYjAEhLSwMqX0MA7F+PoFRV6xH8+OOPnD59mpKSEhYuXMiwYcNq/H1ddtllLFq0CDDesEuNGjWKefPmkZ1tzLuTnJzMqVOnqi1v0qRJLFq0iC+//JIJEyYAxs8uODgYNzc31q9fz9GjR6v83sqX9a9//YuMjAx69epVFtc777xD6ay6O3furPH3XEZrOPwjhA+ttNtojbm4wiPxMPQxx5QHHD+bx4OLdtKllR9vTIySNQNEjUkicJDRo0dTXFxM9+7dmTVr1gXrEURFRZW9sY8dO5alS5eWNRafb9KkSXz66adMnGj0Oy+/HsGoUaMqXI+gtLG4VPn1CKKioujXr1+t1iN4++23ee+994iMjCQ5Obls+8iRI7n11lvLGpLHjx9f5Zt2qZ49e5KVlUVISEhZm8Ntt91GTEwMkZGRfPLJJ3TrZnz6btGiBZdddhkRERE89tiFb5zjx49n0aJFZT8ngL/97W8UFRXRq1cvevbsyd/+9rcaf89lUvdB9skqewuVenP4m7w5/E37ynXzrH1M5ymxah5eHEthsZX/3N4PH1k1TNSCrEcgmiS7/ma2fADfPQ4zf4PA0KqPrYmc0/DlPRB9tzH1RB28s/YAb/ywnzcmRHFzv3YOClBcjGQ9AiFqI+JmaBZqVxJYdtDokTXuknHVl+sVaKxydnBtnRJBbOJZ3lp7gBt6t+WmviG1LkcISQQCgBdffJEvvvjinG0TJkzg6aefdlJEDYBPEHQdbdehyw8a4xXsSgQWF2PuoYQLqwXtVVhs5YkvfyPYz4N/jIuosEFfCHtJIhAAPP300037Tf98Gcmw5ytjRLFfK8eXHz4E9n0LGUkQUPMqnf9sOMS+lCw++lM0/p5ujo9PNCnSWCxERQ5vgNXPQF6aOeV3sI2zSNxS41MPpGTx7voDjI1qy4juJiQp0eRIIhCiIsc2G2sPBDloPML5WkUao4w9/Gt0mjF6+Hd8PFx5bmzDmFNKNH5SNSRERRK3GJ/aHTV+4HwurnDbF9Ufd55vd59ga0IaL90YSZCvhwmBiaZI7ghMUDqZWm1ceumlVe6v7ZTO57vrrrvqfSbP2kxh7RQ5p+H0fmg/0O5T3r/qfd6/6v3qDzxfQRaUFNl1aH5RCS+vjKd7G38m9W9f82sJUQlJBA1M+empK1LbKZ0bm9IprJ3i1F6wuEKHwXaf4uXqhZerV/UHlpfwM7zSAY79atfhczceJvlsHs+N7SGrjAmHkkTgIC+++CJdunTh8ssvZ9++fWXbDx06xOjRo+nXrx9Dhgwpm3soJSWFG2+8kaioKKKiosoSQOmn5hMnTjB06FB69+5NRERE2Qjk0imdAd58800iIiKIiIjgrbfeAoy5frp37859991Hz549GTly5Dkjjstbs2YN0dHRdOnShW+++QYwprO4++67iYyMpE+fPqxfvx4w1j2YMWNG2bnXXXcdGzZsKIu5ommtK5vCurJpp8+fwvof//gHDz30UNl5c+fO5eGHH67x76bGwofArGPQrn/1x9osil/EovhFNbtOcHfQVrsajFMy83l/wyGuiWjNIFlvWDjYRdlGcPequy/YNipsFJO7TSavOI/pa6ZfsP+GS25g3CXjSM9P55ENj5yzb/7o+VVeb/v27SxatIjY2FiKi4vp27cv/foZa9tOnTqV2bNn07lzZ7Zs2cL06dNZt24dDz74IMOGDWPp0qWUlJSUzdlT6n//+x+jRo3i6aefpqSkhNzc3AuuOX/+fLZs2YLWmoEDBzJs2DACAwM5cOAACxcuZO7cuUycOJElS5Zw++23XxB3QkICW7du5dChQ1xxxRUcPHiQ9957D6UUu3fvJj4+npEjR7J/f9UrapVOa/3iiy/y+OOPM3fuXJ555pmyKazvvPPOc9YhKJ122t/fn9OnTzNo0CCuv/56wJjC+uOPP2bQoEFkZ2cTFRXFa6+9hpubG/Pnz+eDDz6oMhaHca984ryKfJ/wPQCTu022/yTv5sZkdolbqz30vfUHKSqxMusaB01+J0Q5ckfgAJs2beLGG2/E29sbf3//sje17OxsfvnlFyZMmEDv3r25//77OXHiBADr1q3jgQceAIwZQAMCAs4ps3///syfP5/nn3+e3bt34+fnd87+n376iRtvvBEfHx98fX256aabyu4awsPD6d27N2BMM52QkFBh3BMnTsRisdC5c2c6duxIfHw8P/30U1nS6NatG6GhodUmgvOntS693s8//8wtt9wCGFNYl9Ja89RTT9GrVy+uuuqqc6adLj+Fta+vL1deeSXffPMN8fHxFBUVlS3UY5qifPh4LBxcY+51SrUfAElboYpqsMS0XBZuPcbE/u0JbVGzBCWEPS7KO4KqPsF7uXpVuT/QM7DaOwB7Wa1WmjVrRmxsbI3PHTp0KBs3buTbb7/lrrvu4pFHHrF7OUsPjz96k7i4uFRaNXT+aNSqRqe6urqeU2dffproqqa1rqjMqqadPn8K6ylTpvDSSy/RrVs37r77wjs9h0vZA0c2Qv8p5l8LjAbpHZ/AmQPQsuKuqu+sO4BSir9ceUn9xCSaHFPvCJRSo5VS+5RSB5VSsyrY30EptV4ptVMp9ZtSqvLVwRuwoUOHsmzZMvLy8sjKyuLrr78GwN/fn/Dw8LKpG7TW7Nq1C4ARI0bwn//8B4CSkhIyMjLOKfPo0aO0atWK++67jylTprBjx45z9g8ZMoRly5aRm5tLTk4OS5cuPWe1M3t88cUXWK1WDh06xOHDh+natStDhgwpm256//79HDt2jK5duxIWFkZsbCxWq5XExES2bq2+OqOyKawrm3a6IgMHDiQxMZH//e9/ZXcXpjpu+zm37Wv+tcCY2fSaf4FXxYsWHU7NZsmOZG4fGEqbgBo2RgthJ9MSgVLKBXgPuAboAdyilDp/BMwzwOda6z7AZKAW/e+cr2/fvkyaNImoqCiuueaac6aJ/uyzz/joo4+IioqiZ8+eZQ2jb7/9NuvXrycyMpJ+/foRFxd3TpkbNmwgKiqKPn36sHjxYmbOnHnBNe+66y4GDBjAwIEDmTJlStlqYfbq0KEDAwYM4JprrmH27Nl4enoyffp0rFYrkZGRTJo0iQULFuDh4cFll11GeHg4PXr04MEHH6Rv3+rfKCubwrqyaacrM3HiRC677DICAwNr9P3VyvGdxkI0tZj2oVYC2sHA+8G3ZYW731l3EHcXC9Ov6FQ/8YgmybRpqJVSg4HntdajbK+fBNBav1zumA+Aw1rrV23Hv6G1rrIjvUxD3fRcd911PPzww4wYMcJhZVb6N/PeIGjWvlaDvWot87hRJdX56nM2J6blMvz1DdxzWRhPXyujiEXdVDUNtZlVQyFAYrnXSbZt5T0P3K6USgJWAn+pqCCl1FSlVIxSKiY1NdWMWEUDdPbsWbp06YKXl5dDk0ClrFYjCYTXfCW3OomZD/+bCIU552z+cNNhLAruvbxj/cYjmhxnNxbfAizQWr9huyP4r1IqQmt9ThcKrfUcYA4YdwROiFM4QbNmzartseRQFkut7wQW/L4AgLsi7qr5ySH9jPEEJ3ZBqHFDfDq7gEXbErmpTztaBzhuRTMhKmLmHUEyUH4cfDvbtvLuBT4H0FpvBjyBoNpcrLGttCacp9K/lTqMZP4x6Ud+TPqxdieH2Npbkv/oELDg5wQKS6xMHSZ3A8J8ZiaCbUBnpVS4UsodozF4xXnHHANGACilumMkghrX/Xh6enLmzBlJBqJaWmvOnDmDp2cFn7KXTYOPr6//oHyDIaA9JG8HIKegmE82JzC6Z2s6tWwk8zOJRs20qiGtdbFSagbwPeACzNNa71FKvQDEaK1XAI8Cc5VSDwMauEvX4t28Xbt2JCUlIe0Hwh6enp60a1dBr6CkGGPaB2cI6VvWdfWrHUlk5hczZYjcDYj6YWobgdZ6JUYjcPltz5b7Og64rK7XcXNzIzw8vK7FiKYs7yykHYLetzrn+lf+DVzcsFo1C35JIKpdAH07XPyTC4qGwdmNxUI0DCeMgX60rdlYjFIernVcGyCoMwA/7U/lUGoO/zcpStYhFvVGEoEQUG5Ece0SweyrZtc9hm0fsmtbNkG+EYyJbFP38oSwkyQCIcBYOnLQn40ZQZ2kcPMH9Ej14dahY/BwdXFaHKLpkUQgBEDnq4xHLc3eZdwRTIuaVusy9qpLiLL8ROQAWX1M1C+ZhlqIwlxIT4A6dD/ecmILW05Uv8BMZQqKS1iZ1pYglUmwPl3rcoSoDUkEQhz9Gd6OMp6dZE3cKTbnhxovbOMJhKgvkgiESN4BKGjdy2khLNp2jEz/rmhXT+PuRIh6JG0EQhzfaXTf9PR3yuUT03LZdOA0D13VGTUsAdxk3QFRvyQRCHF8J3Ss24yjzTxqP/jri5hElIIJ0e0lCQinkEQgmrbM45B9ss4rkv3fFf9Xq/OKS6x8HpPEsC4tCWnmZQxsW/N3GPMatJDFaET9kDYC0bR5+MGEBdBllFMuv/FAKicz85nc39Zl1OIGh9Ya8x4JUU8kEYimzcMPet4Izes2V9Vb29/ire1v1fi8L2KSaOHjzpXdWhkbgrqAm7dRXSVEPZGqIdG0xX8LzUKhdUSditmVuqvG52TkFbF27yluHdgBd1fbZzIXV6P30vEdVZ8shAPJHYFourSG5TNgiwPmCaqF73afoLDEyo19zlvBNaQvnPgNSoqdEpdoeiQRiKbr7FHIS/tjhbB6tnRnMh1b+tCrXcC5OzoMhnbRRmxC1AOpGhJNV2k9fC1nHK2L5LN5bDmSxqNXd7lwuuke1xsPIeqJJALRdCXvABd3CO5Z56Ja+bSq0fHLdhrLd9/QO6Tyg6xWsMhNuzCfJALRdB3fCa0iwNW9zkW9MuQVu4/VWrN0ZzLRoYF0aOFd8UFfz4SUOJjyQ51jE6I6kghE03XLQsg+Ve+X3XM8k4OnsvnnuCp6KnkGGImquADquvqZENWQ+07RdHn4OWz07qtbX+XVra/adeyyncm4uSiu61XFKmRt+4C1CFL2OCQ+IaoiiUA0TUc2wrp/QkG2Q4qLT4snPi2+2uOsVs3K3ScY2rklzbyrqJIqnfJCBpaJeiCJQDRN8Svhl3fB1bNeL7sz8SzHM/K5tqq7AYBmHcC7hQwsE/VC2ghE03R8J7SJMkby1qNvfzuBu4uFq3pU08tIKRg8A/yr6FUkhINIIhBNT0mxMctnv7vq9bJWq+a7308wtEtL/D3dqj9hyCPmByUEdiYCpZQFiALaAnnA71rr+u9uIYQjnN4HxXkOHUgW6h9a7TE7E9M5kZHPE6O72V9w5gmj15B38zpEJ0TVqkwESqlOwBPAVcABIBXwBLoopXKBD4CPtdZWswMVwmEyksDdz6FTSzx/6fPVHvPNbydwd7UwonuwfYVmnYQ3u8HoV2HQtLoFKEQVqrsj+CfwH+B+rbUuv0MpFQzcCtwBfGxOeEKYoMsomHXMqIevJ6W9hYZ1aYmfPdVCAH6twa+NNBgL01WZCLTWt1Sx7xRQ8wnYhWgIHDx1w/O/PG88V3JnsONYOimZBVWPHahI2z7ShVSYzq7/BqXUP5RSruVe+yul5psXlhAmKS6EuVdC3HKHFns08yhHM49Wuv+PaqGazUlE2z5w+gDkZ9YxQiEqZ+/HIldgi1Kql1LqamAbsN28sIQwyak9kLwd6rFZq7Ra6IquLfH1qGFHvbZ9AW30chLCJHYlAq31k8DjwBaM9oBrtdbvVneeUsZkAqAAACAASURBVGq0UmqfUuqgUmpWJcdMVErFKaX2KKX+V5PghaixZFt9ex0Xq6+J7cfSOZVVwJjIGlYLgbEuwY1zILi74wMTwsbe7qNDgX8DLwCRwDtKqXu11serOMcFeA+4GkgCtimlVmit48od0xl4ErhMa51ua4AWwjzHd4JXc2Pkbj1Zveck7i4WruxWiz9vr2YQNcnxQQlRjr33qa8DE0rfxJVSNwHrgKo6RA8ADmqtD9vOWQTcAMSVO+Y+4D2tdTqUNUALYZ7jO41uow7uMdStecX/ClprVselcOklLezvLXS+tMOQFAO9JtYhQiEqZ28iGKy1Lil9obX+Sin1YzXnhACJ5V4nAQPPO6YLgFLqZ8AFeF5rver8gpRSU4GpAB061N8nOXGR0Rpa9TSlWuiJAU9UuH1/SjZHz+Ry/9A6zHIatwLWPAedRoBPi9qXI0QlqmwjUErdrpSylE8CpbTWZ5RSnZRSl9fh+q5AZ2A4cAswVynVrIJrzdFaR2uto1u2bFmHy4kmTSm4aU69Ds5aveckSsFVPepQ61k68O2EdCMV5qjujqAFsFMptR2jl1DpyOJLgGHAaaDCRmAgGWhf7nU727bykoAtWusi4IhSaj9GYthWk29CCLsU5YObObONztpk/Bucv1LZ6rgU+rRvRrBfHa7bJsp4Pr4TLrmq9uUIUYkq7wi01m8DfYGFQEtghO11MnCH1vpmrfWBSk7fBnRWSoUrpdyBycCK845ZhnE3gFIqCKOq6HDtvhUhqrFiBswZbkrRKTkppOSknLPt+Nk8didnMLJn67oV7hkALTpDstwRCHNU20Zgqxb6wfawm9a6WCk1A/geo/5/ntZ6j1LqBSBGa73Ctm+kUioOKAEe01qfqek3IYRdkrdDcI96u9wPcUZiGFndlNP2aNsHEn6qezlCVMDe7qMtMXr4hJU/R2t9T1Xnaa1XAivP2/Zsua818IjtIYR5ctOM3jd9bq+3S66OO8klwb50bOlb98Kueg7cKlnoXog6srfX0HJgE7AG45O7EI1L6Xw9If3q5XIZuUX8ejiN+4d2dEyBAe0cU44QFbA3EXhrrSvuHydEY1A6g2eb3qYUH9Uy6pzX6/alUGLVdW8fKG/TG9AsFCLHO65MIbA/EXyjlBpjq+oRovFpPwiGP2WM1DXBQ/0eOuf16j0ptPL3oFdIgOMusnsJ+LeVRCAczt5EMBN4SilVCBTZtmmttb85YQnhYOFDjEc9yC8q4cf9qdzUNwSLxYEjmNv2gf3fGQPj6nEtBXHxs3fSOT+ttUVr7Wn72k+SgGg08jOM2TtLiqo/tpYeXv8wD69/GICfD54mt7CEkT0cWC0E0LY35J6BjMTqjxWiBuxenUMpdb1S6nXb4zozgxLCoY5shA+GwvFY0y5xtuAsZwvOAka1kJ+HK4M6Ong6iNIRxsmyYplwLHsXpnkFo3oozvaYqZR62czAhHCY5B1gcYXWkaZfqsSqWbM3hSu6BePu6thV0GgVAR4BkJPq2HJFk2dvG8EYoHfpIvVKqY+BnRhTSAvRsCVvNyabM2l6ifJ2HEvnTE4hI3s6YBDZ+Vw94IkEhy+zKURN/qLKd7dwYFcIIUxktdqmnq6f8QOlaw8M62LS5IiSBIQJ7P2rehlj8rkFtruB7cCL5oUlhIOkHYKCTNNXJBvYZiAD2wys+9oD1UncCnNHwJlD5pQvmiR7ew0tBAYBXwFLMNYnWGxmYEI4hH8I3LEUOl9t6mWmRU3jila3cfRMruN7C5Xn5g3JMdJgLByquvUIutme+wJtMKaNTgLa2rYJ0bC5e0OnK8HPxDdnG4esPVCdlt3A1fOPKTOEcIDqGosfwVgZ7I0K9mngSodHJIQj7fgEgntCO3PbCKatmcaOo+n0af9g3dYeqI6LK7Tu9ceUGUI4QJWJQGs91fblNVrr/PL7lFLmd8EQoi6K8uHbR2HQA6Yngqz8PLIK8hw7t1BlQvoaCc5aAhYX868nLnr2Nhb/Yuc2IRqOE7ugpBDaDTD9Umm5hYCD1h6oTtgQo7orP8P8a4kmoco7AqVUa4xF6L2UUn2A0glO/AGZHF00bIlbjOf25ieC9JxCvNxdHLP2QHW6X2c8hHCQ6toIRgF3Yaw3/Ga57VnAUybFJIRjJG2FwDDwNbHxFmPtgcz8YtoG1HNtaWGu0RguRB1V10bwMfCxUupmrfWSeopJCMc4+Xu9VAut25dCUVY3rugVZvq1yiyfYYwpmLG1/q4pLlp2TTGhtV6ilLoW6Al4ltv+glmBCVFnM2KMwWQmW70nhebFV/Pk4BGmX6tMYBjs/K+xBKd38/q7rrgo2Tvp3GxgEvAXjHaCCUCoiXEJUXcurqa/SeYXlbBhXypX92jl2LUHqtN+oPGctK3+rikuWvb2GrpUa30nkK61/jswGOhiXlhC1NEv78Kav5t+mZ8OnCavqIQ4/Sp3r7rb9OuVCekHyuWPBnEh6sDe2UfzbM+5Sqm2wBmMkcZCNEy7PwdP8+dGXB13Ej9PV/zNmluoMu7e0KYXHJNEIOquJmsWNwNeA3ZgjCqea1pUQtRFYY7RUHz5w6ZeprjEypq9p7iyWzCZzlg58tK/GLOrClFH9jYW/8P25RKl1DeAp9ZaRrOIhil5B+iSP+rRTbL9aDppOYWM6tmaL5JNvVTFIm52wkXFxcjexuLflFJPKaU6aa0LJAmIBi3J1qWyXbSpl1kdl4K7q4WhZq09YI9T8ZAS57zri4uCvVVDYzF6DX2ulLICi4HPtdbHTItMiNpSFmMaBhN7DGmt+X7PSS6/JAhfD1dGhY0y7VpV+my80XA88WPnXF9cFOxdj+Co1vpfWut+wK1AL+CIqZEJUVuXPwx3fWPqJfaeyCIpPY9RtiUpJ3ebzORuk029ZoXaDzR6Dmld/9cWFw27171TSoUqpR4HFgHdgMdNi0qI2qqnxtPvbWsPjOhuJIK84jzyivOqOcsE7QdC1gnISKz/a4uLhr1tBFuApYALMEFrPUBrXdEaBUI4V8xH8FakMeLWRKvjUogODSTI1wOA6WumM33NdFOvWaEOtgZx6UYq6sDeO4I7tdZ9tdYva60PmxqREHVx9Gdjnn6vQNMukZiWy94TmeYuSWmvVhHg4W9830LUUnXTUN+utf4UuNY219A5tNZvVnCaEM6hNST8DB2HgzKvY//3e04CMLJnPaw9UB2LC9y+BFpc4uxIRCNW3R2Bj+3Zr4JHtROvK6VGK6X2KaUOKqVmVXHczUoprZQyt7+fuLidOQQ5pyD0UlMvszouhW6t/Qht4VP9wfWh/QCZeE7USXXTUH9g+3KN1vqce0+l1GVVnauUcgHeA67GWPB+m1JqhdY67rzj/ICZgFRyiro5+pPxHFrln2adnMkuICYhjRlXNKBP4IW5sHUOtOsPYeZ97+LiZW8bwTt2bitvAHBQa31Ya12I0dvohgqO+wfwKpBfwT4h7NeyOwyaDkGdTbvE2r2nsGouWJv4hktu4IZLKvrzrgcu7rDxNfj9S+dcXzR61bURDAYuBVoqpR4pt8sfowdRVUKA8n3akoBzxvwrpfoC7bXW3yqlHqsijqnAVIAOHTpUc1nRZHUY+EcvGpN8v+ckIc286NnW/5zt4y4ZZ+p1q+TiCh0GG+0jQtRCdXcE7hhtAa6c2z6QCYyvy4WVUhaM5S8fre5YrfUcrXW01jq6ZUsnDucXDVdeOqTsMXUcQWZ+EZsOnGZ0RGvUeY3R6fnppOenm3btaoVdBqf3QfYp58UgGq3q2gh+BH5USi3QWh+tYdnJQPtyr9vZtpXyAyKADbZ/qtbACqXU9VrrmBpeSzR18Sth+XSY9jO0jjDlEmviUigssTIm8sIZ2B/ZYNwwzx8935RrVytsiPGc8BNE3OScGESjZW8bwYe2aagBUEoFKqW+r+acbUBnpVS4UsodmAysKN2ptc7QWgdprcO01mHAr4AkAVE7R34En5YQ3MO0S6zcfZI2AZ70ad+s+oPrW5soY+xEpjOmQRWNnb2TzgVprc+WvtBapyulgqs6QWtdrJSaAXyP0Z4wT2u9Ryn1AhCjtV5R1flC2E1rOLwBwoeBxe5ZU2okK7+IjQdSuX1gaP0uSWkvFzf46wHjWYgasjcRWJVSHUpnG1VKhWEsTlMlrfVKYOV5256t5NjhdsYixLlS4yE7xRhIZpK1e09RWGxlTGQDGE1cGUkCopbs/fj0NPCTUuq/SqlPgR+BJ80LS4gaOLzBeO443LRLfLv7BK39PenbwbypK+os5wx8NAp2LXZ2JKKRsXeFslW2Ub9TgZ3AMv5Yx1gI5+p9GwR1gWbtqz+2FrILivlxfyq3DuhQabXQpK6TTLl2jXgFQtphOPgDRDWAeESjYVciUEpNwRj92w6IBQYBm4ErzQtNCDt5+sMlI0wrfu3eFAqLrVzb68LeQqVGh4827fp2s1iMu6JD64xutCa1l4iLj71/KTOB/sBRrfUVQB/gbNWnCFEPTu6GH18zddrplbtPEOznQb8qqoVO5pzkZM5J02KwW6crIfc0pPzu7EhEI2JvIsjXWucDKKU8tNbxQFfzwhLCTnu/gfUvmlZ8TkExG/alck1E6yp7Cz256Ume3NQAms06DjeeD61zZhSikbG311CSbRzBMuAHpVQ6UNMBZkI43uH10LaPabNvro0/RUFxxYPIGiT/NtDvbmje0dmRiEbE3sbiG21fPq+UWg8EAKtMi0oIe+SmQdI2GFrpNFV1tnxnMm0CPOkf1oimeR77lrMjEI2MvXcEZWzTTgjhfAfXgrZC51GmFJ+WU8iP+1O59/LwhjmIrCo5p6GkEPzbOjsS0QhItwLReGUmQ0B7o2rIBN/uPkGxVXND7xBTyjdNcSG8HQWbZAFBYZ8a3xEI0WBc/hAMnmFaN8nlO5PpHOxL9zZ+1R77p55/MiWGWnF1h/ChsP97GPOaqct2iouD3BGIxknbZjhxMeezTGJaLjFH0xnXJ+SCKacrMrz9cIa3H25KLLXSZRRkHINTcdUfK5o8SQSicVr3T/hoJFhLTCl+xa7jAFwfZV8d+5GMIxzJOGJKLLXSxTbAbd93zo1DNAqSCETjtH8VWNzAUt1CeTWntWbZzmSiQwNp39zbrnNe2PwCL2x+weGx1Jpfa6PtZL907hPVk0QgGp+MJGPkbJeRphQfdyKTA6eyuaFPI2skPt+YN+DmD50dhWgEpLFYND7x3xrPXceYUvyS7cm4uSiubSyDyCrTrp+zIxCNhNwRiMYnbgW07A5BnR1edGGxlaU7k7iqeyua+7g7vPx6t/dr+Pnfzo5CNHByRyAan14TwdXTlKLX7k0hPbeIif3NmdK63h3+EXb+F6LvAQ9fZ0cjGihJBKLx6Wden/3FMYm09vdkaOeWNTpvaq+pJkVURz1vhG1z4cD3EHGzs6MRDZRUDYnGZd8qyE41pegTGXls3J/K+H7tcKnhlBKD2w5mcNvBpsRVJx0GgW8r2LPM2ZGIBkwSgWg8ctNg8W2w+V1Til+yPQmrhgnR7Wp8bnxaPPFp8SZEVUcWF+h+PRxYDQXZzo5GNFCSCETjsX8VWIuhx/UOL9pq1Xwek8Sgjs0JbeFT4/Nf3foqr2591eFxOUTPGyEw3Oh2K0QFpI1ANB6/f2WbZK6vw4veciSNY2m5PHy143siOV3opfDnX50dhWjA5I5ANA5ZKcaqW5ETTJlE7bMtR/H3dGV0z0Y+dqAipT+vonwoLnBuLKJBkkQgGoeETaBLIGqyw4s+lZnPqt9PMjG6PV7ujp+yokE4cwhe6wR7ljo7EtEASSIQjUPkeHg4Dlo6fqns/209RonW3D4o1OFlNxjNO4JPEMR+5uxIRAMkbQSi8Qhw/Nw/hcVWPttyjGFdWhIWVPNG4lIz+850YFQmUAp63wbrX4Szx6BZB2dHJBoQuSMQDd+6F2HxHWC1Orzo7/ecJDWrgD8NDqtTOb2De9M7uLdjgjJLabXarkXOjUM0OJIIRMNmLYGdn0JxvikrkX2yOYEOzb0Z1qVmI4nPF3sqlthTsY4JyizNOhgrl8V+9sfCPkIgVUOioTu4BrKOw+iXHF70zmPpbEtI55lru9d5cfq3d7wNwPzR8x0RmnlGPAcW+bcX55K/CNGwbfvImCKh67UOL3rOxsP4eboyeUATqi9vF+3sCEQDZGrVkFJqtFJqn1LqoFJqVgX7H1FKxSmlflNKrVVKXcTdNkSNpR81pkboe6exILsDJZzOYdWek9w+KBRfjyb2eejMIVg2HXLOODsS0UCYlgiUUi7Ae8A1QA/gFqVUj/MO2wlEa617AV8C/zIrHtEIufvCsCegr+NnG/3wp8O4WSzcfWmYw8tu8EoKjXaCHR87OxLRQJh5RzAAOKi1Pqy1LgQWATeUP0BrvV5rnWt7+StQ89m+xMXLpwVc8SQ0c+zaAGeyC/giJokb+4QQ7G/OugYNWnB3CBsCMfOgpNjZ0YgGwMxEEAIklnudZNtWmXuB7yraoZSaqpSKUUrFpKaaMwWxaGCObIS45UavIQebu+kIhSVW7hsa7rAynxjwBE8MeMJh5Zlu4P2QkSiL2wuggTQWK6VuB6KBYRXt11rPAeYAREdHS7+3i53WsPpvUJAJ3cY6tOgz2QV8sjmB63q15ZJgP4eV2615N4eVVS+6XAP+7WDrHOh+nbOjEU5mZiJIBsrf07ezbTuHUuoq4GlgmNZaZsQSxt3AiVi47i2Hjx2Ys/EweUUlzBxxiUPL3Xx8M0DDXJymIi6ucOlfIDPJGKhnwhgN0XiYmQi2AZ2VUuEYCWAycGv5A5RSfYAPgNFa61MmxiIak5/fAp9giLrFocWezi7gk81HuT7KsXcDAHN+mwM0okQAMGiasyMQDYRpHwO01sXADOB7YC/wudZ6j1LqBaVU6coirwG+wBdKqVil1Aqz4hGNxIldxnTTgx4AN8c25H7w4yEKikt4cMRFuOZAbWkNB9caXUpFk2VqG4HWeiWw8rxtz5b7+iozry8aodwz0DoSou9xaLGJabl8vPko4/qE0Kmlr0PLbtTy0mHRbcYqZjf+x9nRCCeRikHRsHS6Eu7fBF7NHFrsa9/vQwF/Hen4aawbNe/m0O8u+G2xMYBPNEmSCETDsfdrYxUtB69AtvNYOit2Hee+IR1p28zLoWVfFC79i7HI/UYZz9lUSSIQDUPiVlh8O2yb69Bitdb889u9BPl6MG14J4eWXd6zg5/l2cHPVn9gQxQQAv3vg9j/QUqcs6MRTiCJQDif1rDm7+DTEvrd7dCiV+w6zvaj6Tw6soupcwqFB4QTHuC4AWr1buhfoXknyLygh7doAhrEgDLRxB1cA0d/gmteAw/HNeSezS3kH9/EEdW+GROjHTtNxfk2JG4AYHj74aZexzTezeHPW2U8QRMlv3XhXEX58N3jxqfRfo6dXO7VVfGk5xbx0o0RuNRxvYHqfLznYz7e08gncbNYoKQIfvvClKk9RMMliUA4V+5p8AqEa18HVw+HFbstIY2FWxO59/JwerYNcFi5F73938NXU2Dbh86ORNQjSQTCuQLawZS1RrdRB8kpKOaxL3YR0syLh66SwWM10u1a43ex9gXIkPaCpkISgXAOreGXdyHntMO7i/7z270cTcvl9QlReLtLM1iNKAXXvmlUDX33uLOjEfVEEoFwju3zYfXTsGepQ4v9IS6FhVuPMXVoRwZ3auHQspuM5uEw/AmI/wb2LHN2NKIeyMclUf9OH4Tvn4aOV0D0vQ4r9kRGHrOW/EaPNv48cnUXh5Vrj5eHvFyv1zPd4Blw4jcIMLe3lWgYJBGI+lVSDEungos7jHvfYd0VC4pLeODTHeQXlfDvW3rj4erikHLt1dqndb1ez3QubjBh/h+vtXZ4FZ5oOKRqSNSvTa9D8na47v/Av63Din1+xR5iE8/yxsQoh08xbY9VR1ax6shFuNqXtQRWPgYbX3N2JMJEckcg6lf0PeDdAiJucliR/92cwMKtifz5ik6MjmjjsHJrYvG+xQCMDh/tlOubRlkgPwO2zoVWEdBtjLMjEiaQOwJRP9KPGtVCvsEw4D6HFbvq95M8t2IPI7oF88jVMrOowykFY9+Gtr1hyRQ4+buzIxImkEQgzJd2BD66Glb8xaHFbjl8hgcX7SSqfTPevbWv6aOHmyw3L5i8EDz9YeFkyDrp7IiEg0kiEObKPAGf3GBMXXDZTIcVu/1oOlM+jqF9oBfz/tQfL/f6bRxucvzbwOT/QVEunN7v7GiEg0kbgTBPdip8epOx6tifVkBwN4cU++vhM9yzYBvBfh78996BBPq4O6RcUY2QvjDztz8mBrSWGOsYiEZPEoEwh9aw+DajWui2zyGkn0OKXR9/igc+205IMy8W3jeIYH/HrmtcW28Of9PZIdSP0iSw81OjAfnWz8GvlXNjEnUmiUCYQykY/bJRJdRhkEOKXPDzEV74Jo7ubfxZcPcAWvo5bpK6ugr0DHR2CPXLt7VRRfTR1XD7VxB0ibMjEnUgbQTCseJXwo+2JQ9D+jkkCeQXlfD00t08/3UcI7q34vP7BzeoJACw7OAylh1sQtMxdL4K7voGCnOMZHB4g7MjEnUgiUA4RkkxrH8JFt0C+74z1hlwgMOp2dz0/i98tuUY9w/ryOzb++Fj4kpjtbX84HKWH1zu7DDqV0g/uHe10SX4vzfC6QPOjkjUUsP7jxKNz5lDsHQaJG2FqFuNUcNudau7t1o1n205ysvfxePhauGjP0UzorvURTc4LToZ04jvWwlBtim/C7IdutKcMJ8kAlE3Rfnw0UiwFsHNH0Hk+DoXuT8liye/2s32o+kM6RzEv8b3ok2AlwOCFabw8IVeE42vj8ca3YVH/M1Yf1p6FTUKkghEzWkNSTHQLtr45H/dm9Cuf53nDjqZkc///bCfL7Yn4u/lxhsToripbwhKJjtrPLybG6OQv30UYhbA6JcgfKizoxLVkEQg7Kc1HF4PG16FxF9h0mfQ/TrocUOdij2Zkc+8n4/wyeYESqyauy4NZ8aVl9Bcxgc0Ps06wB3LjHUmfngOPh4L3a+HiZ/I7KUNmCQCUb2SYvh9CWydA8kx4B8CY16HzlfXqdjfkzOY9/MRVsQex6o110e15dGRXWnf3NtBgdef969639khNBxKGZMKdh0DWz/4YwprqxX2rzL+blzcnB2lKEcSgaiY1pB5HAJCjH/idf80/nmvfQP63FHrheZTswpYHpvMl9uTiD+Zhbe7C7cPCuXey8MbZQIo5eUqbRgXcPM8d1qRhE1GrzKfltD7Vug1GYK7y51CA6C01s6OoUaio6N1TEyMs8O4OBUXQuIWOLgG4pZDQSY8uh9cXOFsonEnUMOFZLTWHErN5oe4U6zZm8KOY+loDVHtAhjfrx3XR4UQ4N34Px0uil8EwORuk50cSQNmLYGDa2H7AuPOQJdA845wx1IIDHN2dBc9pdR2rXV0RfvkjqApK8g2Ptm7uBn/nKuegqIcUC7QcRj0vNH4Z8UVmtm3ZGGJVXPwVDbbEtLYesR4nMw0xhREhgTw0IgujIlsTedW9b94jJm+T/gekERQJYsLdBlpPLJSYN+3cGgd+Lcz9q/7J5zcDWGXQ4fB0KqnMfOpMJ0kgqYi7ywc2wyp+4ypAY7HQupe+NM3EHYZBHU1btc7XWn8I3r6V1mc1ao5mZlPwpkcDqXmEHc8k7gTmew7mUl+kRWAVv4eDAhvwaCOzbmyW7B0ARV/8GtlLFIUfc8f21w94cxB424BjA8kna6E2780XidvB69ACOhg3KUKhzH1p6mUGg28DbgAH2qtXzlvvwfwCdAPOANM0lonmBnTRUVr43bbxRWK8iDhZ8hMNh4ZyZCZBP2nQPexxqCvhbZPqz7B0KaX0ePHz7bWbuhg4wEUFls5m5XPqcwCUrMKSMnM51RWAaey8jmZkc/RM7kcTculsNhaFkqAlxs92/pz+8BQerT1Jzq0Oe2be0nXT2G/oX81HpknIGkbnNhlJIdSn98FGcfA4gaBoRAYbjQ8D7zf2H94A3g1B58gI2HI3YTdTEsESikX4D3gaiAJ2KaUWqG1jit32L1Autb6EqXUZOBVYJJZMTmc1sajtN68uAC01XhYS8BabCz159XM2H/6gPGGbS0yJmMrKTL+aIO7G/t//woKs6EwB12Ygy7IprhNX4o6j6G4MB+vpXdBYQ4qPx1LXhqWvHTS+v6ZU/0eQWWn0O2zm42wUBR6BZPn1Zp9h05xKPMYhfne+PZZwEm3dmRoH/KLrGSfKibz6zQy8lLIzC8iM6+YjLwi8opKKvx2A73daOXvSXiQD1d0Cya0hTdhLXwID/KhTYCnvOkLx/BvAz2uNx7l3TzX+B9KO2R8sElPgIwkY5/VCp/ebPzPlXL1hEEPwFXPGz3fPr8D3H3AzfuP547DIXyIMTAy/hvjHBd3o7rUxR2ahxvjY4oLjFX2Sre7uBsfwNx8wNXduL61yPh/L3s0nv8HM+8IBgAHtdaHAZRSi4AbgPKJ4AbgedvXXwLvKqWUNqEFe/G2YwR8P5M+Jb+h0Cg0FjRJqjUzPF8C4NX8fxJhjS/bp9DsUx15wO2faDTzix6niz6CAlwwPg1vI4L7XYxvYVnJn+lAyjnXXUc0M/XjaOBHptBCZZ6zf4X1cv5qnQEadrnej5cqBEABJdrCZyVX8/diFxRWVrgfIBdPMrQPaboVZ/Fj0y+e/PzTJixY6aOe46RuTgqBFOe7QjpwHGC37WruwCm83FzwdLPg7e5KgJcbAV5uhAf5EODlhr+n8TrA241gP0+C/T0I9vOgpZ8HHq4ySlQ4UYdBVU9iePcqyDoOuWmQl248Qmxto0U5cPaY7YNWrrHATmGO8cYfPgRyUmHJvReWOeplGDzdSDrvDbhw//XvQN874fhO+PDK83YqGD/P6Ep7ZCN8NtFIEBYXI0koRwVHzgAACQxJREFUC4yfD52ugANrYPmfbcnDlkCUgon/hXb9YO/XRhljXqvFD656ZiaCECCx3OskYGBlx2iti5VSGUAL4HT5g5RSU4GpAB06dKhVMC18PMgI7MaRAne0Mt7mQZHp2oLo4OYo4FTaYHYVhRppQBmf8s+6tWJoUBAKxYEzY0kpOWNLExZQkO7eljEtWqNQxJ6+g3hrDqDQykKJciPdM4TxAe1QKNZkPINFl2C1uFGiXLFa3MhxC+Ju71AUik/zP6XI4kGxxQvt7oNyccfV1cJTFoWLxcIOy3JcLAo3F4WrxUJri2KyRXGHi7Hf1TIQF4vC1UXZ3uxdznn2cLPg4WqRT+4mmD96vrNDaNosFmjfv/L9ngHwwM/nbtPauHsHo4r0z1uhON+4eygpNB7NO/6x/+aPbHfytn0lRX8kGv82MOJZW42ArcpWW6GlbTEm/xBjre7SGoPSWoPSqlnflkYjetlnYA3aFjcYXW6DutT1p1Qp07qPKqXGA6O11lNsr+8ABmqtZ5Q75nfbMUm214dsx5yuqEyQ7qNCCFEbVXUfNXMa6mSgfJ/DdrZtFR6jlHIFAjAajYUQQtQTMxPBNqCzUipcKeUOTAZWnHfMCuBPtq/HA+vMaB8QQghROdPaCGx1/jOA7zG6j87TWu9RSr0AxGitVwAfAf9VSh0E0jCShRBCiHpk6jgCrfVKYOV5254t93U+MMHMGIQQQlRNlqoUQogmThKBEEI0cZIIhBCiiZNEIIQQTVyjW49AKZUKHK3l6UGcN2q5gZC4akbiqrmGGpvEVTN1iStUa92yoh2NLhHUhVIqprKRdc4kcdWMxFVzDTU2iatmzIpLqoaEEKKJk0QghBBNXFNLBHOcHUAlJK6akbhqrqHGJnHVjClxNak2AiGEEBdqancEQgghziOJQAghmriLLhEopSYopfYopaxKqejz9j2plDqolNqnlBpVyfnhSqkttuMW26bQdnSMi5VSsbZHglIqtpLjEpRSu23Hmb4aj1LqeaVUcrnYxlRy3Gjbz/CgUmpWPcT1mlIqXin12/+3d66hVlRRHP/90dJQ8Ul6TSEFkawvmYmFhaiYSmhFxO2LlkFYCPkhwhAkMgiD+hBUQiU9sOxpXUTxkUYfQpPE6yO1e7WgK1eFHlpEprH6sPeN6Tjn3rneM3PUWT8Yzp6915m9Zu11Zs3ee85sSeslDaoiV4i9ujp/SX1iG7dGX7o+L10SdY6WtEPSd9H/n0iRmSbpdKJ9V6QdKwfdOm0XBV6O9tonaWIBOo1P2GGvpDOSllbIFGYvSWsknYqLdXXkDZG0VVJL/Bxc5bsLo0yLpIVpMl1iZlfUBtwAjAe+BCYl8icAzUAfYAxwFOiV8v0PgcaYXg08lrO+LwIrqpT9CAwr0HbPAE92IdMr2m4sYRHkZmBCznrNAnrH9CpgVb3sleX8gceB1THdCHxQQNs1ABNjegDwfYpe04ANRflT1nYB5gKbCIv1TgF2FaxfL+AE4Q9XdbEXcCcwETiQyHsBWBbTy9L8HhgCHIufg2N6cHfrv+J6BGZ2yMyOpBTNB9aZ2Vkz+wFoBf63GrXCYr7TgY9j1tvAPXnpGut7AHg/rzpyYDLQambHzOxvYB3BtrlhZlvM7Hzc3UlY7a5eZDn/+QTfgeBLM5TzQtFm1m5me2L6d+AQYU3wy4H5wDsW2AkMktRQYP0zgKNmdrFvLOgxZvYVYU2WJEk/qnYtugvYama/mNmvwFZgdnfrv+ICQSdcB/yU2G/jwh/KUOC3xEUnTaaW3AGcNLOWKuUGbJH0raRHc9QjyZLYPV9TpSuaxY55sohw95hGEfbKcv7/yURfOk3wrUKIQ1E3A7tSim+T1Cxpk6QbC1Kpq3apt081Uv1mrB726mC4mbXH9AlgeIpMTWyX68I0eSFpGzAipWi5mX1etD5pZNTxQTrvDUw1s+OSrgW2Sjoc7xxy0Qt4DVhJ+OGuJAxbLepJfbXQq8NekpYD54G1VQ5Tc3tdbkjqD3wCLDWzMxXFewjDH3/E+Z/PgHEFqHXJtkucA5wHPJ1SXC97XYCZmaTcnvW/LAOBmc28iK8dB0Yn9kfFvCQ/E7qlveOdXJpMTXSU1Bu4D7ilk2Mcj5+nJK0nDEv06AeU1XaSXgc2pBRlsWPN9ZL0EHA3MMPi4GjKMWpurxSynH+HTFts54EE38oVSVcRgsBaM/u0sjwZGMxso6RXJQ0zs1xfrpahXXLxqYzMAfaY2cnKgnrZK8FJSQ1m1h6Hyk6lyBwnzGV0MIowP9otyjQ01AQ0xic6xhAi+zdJgXiB2QHcH7MWAnn1MGYCh82sLa1QUj9JAzrShAnTA2mytaJiXPbeKvXtBsYpPF11NaFb3ZSzXrOBp4B5ZvZnFZmi7JXl/JsIvgPBl7ZXC161Is5BvAkcMrOXqsiM6JirkDSZ8PvPNUBlbJcmYEF8emgKcDoxJJI3VXvl9bBXBUk/qnYt2gzMkjQ4DuXOinndo4gZ8SI3wgWsDTgLnAQ2J8qWE574OALMSeRvBEbG9FhCgGgFPgL65KTnW8DiiryRwMaEHs1xO0gYIsnbdu8C+4F90QkbKvWK+3MJT6UcLUivVsI46N64ra7Uq0h7pZ0/8CwhUAH0jb7TGn1pbAE2mkoY0tuXsNNcYHGHnwFLom2aCZPutxegV2q7VOgl4JVoz/0knvbLWbd+hAv7wEReXexFCEbtwLl4/XqEMK/0BdACbAOGRNlJwBuJ7y6KvtYKPHwx9fsrJhzHcUpOmYaGHMdxnBQ8EDiO45QcDwSO4zglxwOB4zhOyfFA4DiOU3I8EDiO45QcDwSO4zglxwOB4/QQSbfGF/X1jf+kPSjppnrr5ThZ8T+UOU4NkPQc4R/F1wBtZvZ8nVVynMx4IHCcGhDfO7Qb+IvwKoJ/6qyS42TGh4YcpzYMBfoTVgfrW2ddHKdbeI/AcWqApCbCamVjCC/rW1JnlRwnM5flegSOcykhaQFwzszek9QL+FrSdDPbXm/dHCcL3iNwHMcpOT5H4DiOU3I8EDiO45QcDwSO4zglxwOB4zhOyfFA4DiOU3I8EDiO45QcDwSO4zgl51+Ws/vhK5DWqQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zrDE6M-Mm9kI",
        "colab_type": "text"
      },
      "source": [
        "Now that we understand how the activation function works (which provides the non-linearity in our network), let's use it inside a single-layer model. The model provides the necessary loss function which we use to obtain a fit to the data. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ARb908qyRDQT",
        "colab_type": "text"
      },
      "source": [
        "## Single layer"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_SRwWOimnNid",
        "colab_type": "text"
      },
      "source": [
        "Let's create some data to start with. We will use $X$ and $y$ to denote inputs and outputs respectively. In general inputs could be images and outputs labels (classification task); or inputs could be time of the year and outputs could be temperature (regression task). But here we will only create very simple toy data:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cundh81VRDQU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Create some toy data\n",
        "X = np.array([[0,0,1],\n",
        "              [0,1,1],\n",
        "              [1,0,1],\n",
        "              [1,1,1]])\n",
        "\n",
        "# Linear case\n",
        "y = np.array([[0],\n",
        "              [0],\n",
        "              [1],\n",
        "              [1]])\n",
        "\n",
        "# Fix the seed\n",
        "np.random.seed(1)"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6rKfyxIYn2VM",
        "colab_type": "text"
      },
      "source": [
        "Now let's create a single-layer model which fits the data. Our model will be composed of two parts. Firstly, the parametric fit function:\n",
        "$$f(x; w) = activation(wx)$$\n",
        "and then the loss function:\n",
        "$$Loss(x;w) = \\frac{1}{1} (f(x;w) - y)^2$$\n",
        "The loss function simply says that the further away I predict $f(x;w)$ from the true $y$ corresponding to $x$, the biggest the loss should be. The free parameter here (since my data $x,y$ is fixed) is the weights $w$. So I minimize the loss with respect to $w$ using gradient descent. We take small gradient towards the direction that minimizes the loss. \n",
        "\n",
        "For each step, we do a forward pass, meaning computing the value of $f(x;w)$ for the current setting of $w$, and a backward pass, meaning we use gradients to compute the changes we need to do in $w$ for the loss to be smaller. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ai_a4qwZRDQW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        },
        "outputId": "91d34ad9-772d-4b7e-b7c3-8a5c0e5454e0"
      },
      "source": [
        "# Initialize weight\n",
        "W0 = 2*np.random.random((3,1)) - 1\n",
        "error = []\n",
        "error_of_rounded = []\n",
        "fs = []\n",
        "\n",
        "# Optimize for 2000 iterations\n",
        "for i in range(200):\n",
        "    # FORWARD PASS: x -> f1 \n",
        "    f0 = X\n",
        "    f1 = activation(np.dot(f0, W0))\n",
        "    loss = (0.5 * (y-f1)**2 ).sum()\n",
        "    loss_of_rounded = (0.5 * (y-np.round(f1))**2 ).sum()\n",
        "    \n",
        "    # BACKWARDS PASS (derivatives of loss wrt W0)\n",
        "    e1 = y - f1   # Error contribution\n",
        "    delta_1 = e1 * activation_derivative_f(f1)  # The gradient contribution from activation\n",
        "    gradient_1 = np.dot(f0.T,delta_1)\n",
        "    \n",
        "    learning_rate = 0.2\n",
        "    \n",
        "    # Update the weights. This is simply adding the gradient multiplied by a learning rate\n",
        "    W0 += learning_rate * gradient_1\n",
        "\n",
        "    # Keep track of error\n",
        "    error.append(loss)\n",
        "    error_of_rounded.append(loss_of_rounded)\n",
        "    fs.append(f1)\n",
        "\n",
        "plt.plot(error)\n",
        "plt.xlabel('number of iterations')\n",
        "plt.ylabel('error in training data')\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(error_of_rounded)\n",
        "plt.xlabel('number of iterations')\n",
        "plt.ylabel('error in training data')"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'error in training data')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "bXDM6_nIRDQZ",
        "colab_type": "text"
      },
      "source": [
        "## Deep neural network"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VJH33m5hpr8h",
        "colab_type": "text"
      },
      "source": [
        "We will repeat exactly the same procedure, only now our model will comprise of more than one layers. That is, instead of calling $f(x;w)$ our output for input $x$, we will feed this to another parametric function first: $f_1(f_0(x;w_0);w_0)$. Since we have two sets of weights (for two functions), we have used subscripts. We can consider $f_1$ to be our final function, it just so happens to be a function which is defined by another function. \n",
        "\n",
        "We coud have defined an equivalent function $f_{0,1}(x; w_{0,1})$ directly, instead of decomposing it into two functions. However, the key intuition behind deep learning is that decomosability allows us to create __complicated and at the same time learnable functions__."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AwvM3feYRDQa",
        "colab_type": "text"
      },
      "source": [
        "Create some toy data again:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8S8prD4_RDQa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = np.array([[0,0,1],\n",
        "              [0,1,1],\n",
        "              [1,0,1],\n",
        "              [1,1,1]])\n",
        "\n",
        "# NON-linear case\n",
        "y = np.array([[0],\n",
        "               [1],\n",
        "               [1],\n",
        "               [0]])"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tZMFPmKfRDQc",
        "colab_type": "text"
      },
      "source": [
        "Define parameters and initialize them."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ABBzCF4nRDQd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Fix the seed\n",
        "np.random.seed(1)\n",
        "\n",
        "# randomly initialize our weights with mean 0\n",
        "W0 = 2*np.random.random((3,4)) - 1\n",
        "W1 = 2*np.random.random((4,1)) - 1\n"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2fMRqTe1RDQf",
        "colab_type": "text"
      },
      "source": [
        "Optimize!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-d3cpifoRDQf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "error = []\n",
        "error_of_rounded = []\n",
        "\n",
        "# Optimize\n",
        "for i in range(1000):\n",
        "    # FORWARD PASS: x -> f1 -> f2\n",
        "    f0 = X\n",
        "    f1 = activation(np.dot(f0, W0))\n",
        "    f2 = activation(np.dot(f1, W1))\n",
        "    # Normally we'd use the cross-entropy loss, but here we'll use sq. error to make derivatives easier.\n",
        "    loss = (0.5 * (y-f2)**2 ).sum()\n",
        "    loss_of_rounded = (0.5 * (y-np.round(f2))**2 ).sum()\n",
        "    \n",
        "    # BACKWARDS PASS\n",
        "    e2 = y - f2\n",
        "    delta_2 = e2 * activation_derivative_f(f2)\n",
        "\n",
        "    e1 = np.dot(delta_2, W1.T)\n",
        "    delta_1 = e1 * activation_derivative_f(f1)\n",
        "\n",
        "    gradient_0 = f0.T.dot(delta_1)\n",
        "    gradient_1 = f1.T.dot(delta_2)\n",
        "        \n",
        "    # Update the weights\n",
        "    learning_rate = 0.8\n",
        "    W0 += learning_rate * gradient_0\n",
        "    W1 += learning_rate * gradient_1\n",
        "\n",
        "    # Keep track of error\n",
        "    error.append(loss)\n",
        "    error_of_rounded.append(loss_of_rounded)"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qT5OYjojRDQk",
        "colab_type": "text"
      },
      "source": [
        "Plot the error per iteration of the optimization."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YUc1cuDLRDQl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        },
        "outputId": "009e875e-1cfb-429e-cf0f-562e9ef91b9e"
      },
      "source": [
        "plt.plot(error)\n",
        "plt.xlabel('number of iterations')\n",
        "plt.ylabel('error in training data')\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(error_of_rounded)\n",
        "plt.xlabel('number of iterations')\n",
        "plt.ylabel('error in training data')"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'error in training data')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "A8btBV7ERDQn",
        "colab_type": "text"
      },
      "source": [
        "### With Automatic differentiation\n",
        "For complicated models (eg. too many layers), it is tedious to compute all the gradients by hand. This is where automatic differentiation kicks in. It allows us to write code without having to worry about computing derivatives. \n",
        "\n",
        "In tensorflow, the way this is done is by defining our function as usual, but now we have to (a) declare which ones are the variables (the ones we wish to take derivatives for) (b) use tensorflow functions instead of pure numpy, so that the computation graph can be created. The computation graph is then used to compute derivatives using the chain rule automatically."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hrUe3zpuRDQo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import tensorflow as tf\n",
        "W0 = tf.Variable(2*tf.random.normal((3,4)) - 1, name=\"W0\")\n",
        "W1 = tf.Variable(2*tf.random.normal((4,1)) - 1, name=\"W1\")\n",
        "\n",
        "def activation_tf(x):\n",
        "    return 1/(1+tf.exp(-x))\n",
        "\n",
        "def fwd(X, W0, W1):\n",
        "    f1 = activation_tf(X @ W0)\n",
        "    f2 = activation_tf(f1 @ W1)\n",
        "    loss = tf.reduce_sum(0.5 * (y-f2)**2 )\n",
        "    return loss\n",
        "\n",
        "with tf.GradientTape() as tape:\n",
        "    loss = fwd(X, W0, W1) \n",
        "\n",
        "[g0_autograd, g1_autograd] = tape.gradient(loss, [W0, W1])\n"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1EdLsZlryxU9",
        "colab_type": "text"
      },
      "source": [
        "To convince ourselves taht this is the right thing to do, let's compute the derivatives manually, as we did before, and then compare them with the ones from autograd:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k4Vh8xpMyHha",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "W0_ = W0.numpy().copy()\n",
        "W1_ = W1.numpy().copy()\n",
        "\n",
        "\n",
        "f1 = activation(np.dot(X, W0_))\n",
        "f2 = activation(np.dot(f1, W1_))\n",
        "    \n",
        "e2 = y - f2\n",
        "delta_2 = e2 * activation_derivative_f(f2)\n",
        "\n",
        "e1 = np.dot(delta_2, W1_.T)\n",
        "delta_1 = e1 * activation_derivative_f(f1)\n",
        "\n",
        "gradient_0 = -f0.T.dot(delta_1)\n",
        "gradient_1 = -f1.T.dot(delta_2)"
      ],
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1VDGlUW5yL9S",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        },
        "outputId": "2eea3f87-87a6-4140-c6a9-a375ed713015"
      },
      "source": [
        "print(np.abs(g0_autograd.numpy() - gradient_0))\n",
        "print(np.abs(g1_autograd.numpy() - gradient_1))\n"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1.78103524e-09 6.17692623e-10 7.81120982e-11 1.14117448e-10]\n",
            " [1.75503772e-09 1.31487677e-09 6.02083779e-10 2.69472324e-09]\n",
            " [2.47110102e-09 1.85776916e-09 5.75190033e-10 2.71439658e-09]]\n",
            "[[7.57096229e-09]\n",
            " [9.24336433e-09]\n",
            " [2.03186193e-10]\n",
            " [5.13266264e-09]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DNmg_UpG1Ozb",
        "colab_type": "text"
      },
      "source": [
        "__Exercises__\n",
        "1. _[Medium]_ Embed the automatic differentiation loop inside the optimization loop, in order to minimize the loss.  \n",
        "2. _[Medium]_ Experiment with different settings for the learning rate, including a schedule which starts with bigger and then gradually reduces the learning rate. \n",
        "3. _[Hard]_ Experiment with deeper architectures, including different activation functions. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BKfRjQY6SYuE",
        "colab_type": "text"
      },
      "source": [
        "__Solution__ to 1. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TTR0XQuQScQC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "473d9f4b-c6f9-43dc-d85b-4fd5761f3cd1"
      },
      "source": [
        "# Fix the seed\n",
        "np.random.seed(1)\n",
        "tf.random.set_seed(1)\n",
        "\n",
        "# randomly initialize our weights with mean 0\n",
        "W0 = tf.Variable(2*tf.random.normal((3,4)) - 1, name=\"W0\")\n",
        "W1 = tf.Variable(2*tf.random.normal((4,1)) - 1, name=\"W1\")\n",
        "\n",
        "error = []\n",
        "error_of_rounded = []\n",
        "\n",
        "# Optimize\n",
        "for i in range(1,1000):\n",
        "    with tf.GradientTape() as tape:\n",
        "        loss = fwd(X, W0, W1) \n",
        "\n",
        "    [g0_autograd, g1_autograd] = tape.gradient(loss, [W0, W1])\n",
        "    \n",
        "    # Update the weights\n",
        "    learning_rate = 0.8\n",
        "    W0.assign(W0 -  learning_rate * g0_autograd)\n",
        "    W1.assign(W1 - learning_rate * g1_autograd)\n",
        "\n",
        "    # Keep track of error\n",
        "    error.append(loss)\n",
        "\n",
        "plt.plot(error)\n",
        "plt.xlabel('number of iterations')\n",
        "plt.ylabel('error in training data')\n",
        "\n"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'error in training data')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d3D5tJawaBKO",
        "colab_type": "text"
      },
      "source": [
        "__Solution to 2.__\n",
        "\n",
        "Replace `learning_rate = 0.8` with `learning_rate = 4. / np.log(i+1)`. This says that the learning rate should reduce logarithmically with the number of iterations. To avoid division by zero also please change the for loop to `for i in range(1,1001)`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tzvDMuMraaYv",
        "colab_type": "text"
      },
      "source": [
        "__Solution to 3.__\n",
        "(Notice how quickly it converges to a good solution when we use a more powerful model!)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EcnbwnFdactJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "78c080b4-5535-4652-aa55-3e4ec7c4bdcf"
      },
      "source": [
        "# Fix the seed\n",
        "np.random.seed(1)\n",
        "tf.random.set_seed(1)\n",
        "\n",
        "# randomly initialize our weights with mean 0\n",
        "W0 = tf.Variable(2*tf.random.normal((3,4)) - 1, name=\"W0\")\n",
        "W1 = tf.Variable(2*tf.random.normal((4,4)) - 1, name=\"W1\")\n",
        "W2 = tf.Variable(2*tf.random.normal((4,1)) - 1, name=\"W2\")\n",
        "\n",
        "def activation_tanh_tf(x):\n",
        "    return (tf.exp(x) - tf.exp(-x)) / (tf.exp(x) + tf.exp(-x))\n",
        "\n",
        "def fwd_deeper(X, W0, W1, W2):\n",
        "    f1 = activation_tf(X @ W0)\n",
        "    f2 = activation_tf(f1 @ W1)\n",
        "    f3 = activation_tanh_tf(f2 @ W2)\n",
        "    loss = tf.reduce_sum(0.5 * (y-f3)**2 )\n",
        "    return loss\n",
        "\n",
        "error = []\n",
        "\n",
        "# Optimize\n",
        "for i in range(1,1001):\n",
        "    with tf.GradientTape() as tape:\n",
        "        loss = fwd_deeper(X, W0, W1, W2) \n",
        "\n",
        "    [g0_autograd, g1_autograd, g2_autograd] = tape.gradient(loss, [W0, W1, W2])\n",
        "    \n",
        "    # Update the weights\n",
        "    learning_rate = 4. / np.log(i+1)\n",
        "    W0.assign(W0 -  learning_rate * g0_autograd)\n",
        "    W1.assign(W1 - learning_rate * g1_autograd)\n",
        "    W2.assign(W2 - learning_rate * g2_autograd)\n",
        "    \n",
        "    # Keep track of error\n",
        "    error.append(loss)\n",
        "\n",
        "plt.plot(error)\n",
        "plt.xlabel('number of iterations')\n",
        "plt.ylabel('error in training data')"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'error in training data')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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w5NqXuhyJmVnvKEWCf2VK8Kufc4I3M6sqRYLfee4Ag3NmcMntj3c7FDOznlGKBN9XESf+2Z7c+NDTXP/gH7sdjplZTyhFggf40MELWbDDTD5/yd0Mj4x2Oxwzs64rTYIfmNbHP7xrH+57Yi3n3fhIt8MxM+u60iR4gLe/dmfetNd8Tr/8ftas3dDtcMzMuqpUCV4Spx31Wl4aHuHzy+/udjhmZl1VqgQPsOfgbE46Yi8uuf1xfr5qdbfDMTPrmtIleIATD9uT1y2Yy3+78A7uevy5bodjZtYVpUzw0/oqnP0XQ8we6OeDy270pZNmtk0qZYIH2GX7mVz4kcXsuv1Mjjv3Zs697rfubdLMtimlTfAAu+24HReeuJjD996Jzy+/m499/1bWbRjudlhmZpOi1AkeYO7ANJYdexCfecfe/OzO1Rz11et44Im13Q7LzKxwpU/wkF0++ZE/25ML/voQnn9xmHd/7Xp+ettj3Q7LzKxQ20SCr1q85yu49ONLeO2uczn5B7dx6k9XsXHY3RqYWTltUwkesp4nv/c3h/DXS/bguzc8wgeW3cDjz77Y7bDMzLa6bS7BQ3YZ5f981z58/ZgDeeCJdbzrrOu47gFfSmlm5bJNJviqd/7pLvz0Y4cyf/Z0jj33Jk6/4n5eetmP/TOzctimEzxkXRv85O8O5b37L+ArVz7A2864lp/duZrRUV8zb2ZT2zaf4AG2m97P6R/Yn/NPOJiBaRVOvOAW3nrGNXzvpt/x/Esvdzs8M7OOqJfu7hwaGooVK1Z0NYbhkVEuvXM1y659iLsef57pfRUOe80gb9lnZxa/6hXsPm+7rsZnZlZP0sqIGBprXn/BGz4SOBPoA86JiH8pcntbQ39fhXfvv4Cj9tuVW3//LMtvX82ldz7O5Xc/AcCCHWay727bs/cr5/Inu8xhz51ms2CHmQxM6+ty5GZmjQprwUvqA+4H3go8CvwaODoixu2ovRda8GOJCB54ch03/OYpbvrtU9yzei0PP7We+q9ucM4MdttxJrtuP5N5s6Yzb9Z05s+ezrxZM5g3azpzBvqZPaOfWTOy94FpFSR1b6fMrBS61YJ/A/BgRDyUgvgB8G5gyj2JQxKv3nkOr955Dse9cREA6zcMc/8TWaJ/9OkXefSZF3n02Re4Z/XzPLV+I8+9OHHtvq8iZk3vY/aMfrab0c+M/goz+itM768wo78vvdfG6+f3VUR/RfRVKvRVoK9SSePa9N63abxu+T7Rp2y60n5JUJGoCKRsWkXZ/EqaX12mflmofiZ7r6Qfq0olTU/z2fSZbJ3Z95neEdWJtWm173ys5Zt/E5W21byO6o9nyzr8o2rbkCIT/ALg93XjjwIHF7i9STVrRj8HLNyRAxbuOOb8l0dGeeaFjTy9fiNPr9vI2g3DrN8wzLr0Wr9hmPUbRjYNbxweZePIKBteHuXZFzayYXiUjcOjbEivjcMj2fvIKD102mRK29wPwqafmIblqsOb/1Gp+/2qzRvj92W8n5zxfozGmjr+79Y462grjvHW3Dpj/GXHW3f+H9xx1z3mvmyN/c7//Y+3krzrnrfddH74kcXjLN25QmvweUhaCiwFWLhwYZej2Xqm9VXYac4AO80Z2OrrHh0NRiIYGQ2GR4ORkWx8eHQ0mzZSmzca9ePZ/NGA0QgisvJTkI2PVsfr5o+m+bFpfnXZ7Femtlw2TNSti+ydFCtA9bcpLZqGG3+xIn22Olz9XG24cV79OhrX27p80DhzvPWOuY66WPJss/mHeKxy6Hi/1eP9iMcYnxh/2XbWPfbS4657jOljxTbhOtpaNv9Kxt/vrfH951vvROsea8acgWJScZEJ/jFg97rx3dK0BhGxDFgGWQ2+wHhKo1IRFYTP65rZRIq8Dv7XwF6S9pA0HfggcHGB2zMzszqFteAjYljSx4BfkF0meW5E3FXU9szMrFGhNfiIuAy4rMhtmJnZ2NxVgZlZSTnBm5mVlBO8mVlJOcGbmZWUE7yZWUn1VHfBktYAj3T48fnAtvbcPe/ztsH7XH5bsr//KSIGx5rRUwl+S0haMV6PamXlfd42eJ/Lr6j9dYnGzKyknODNzEqqTAl+WbcD6ALv87bB+1x+hexvaWrwZmbWqEwteDMzqzPlE7ykIyXdJ+lBSZ/pdjxbi6TdJV0l6W5Jd0k6OU2fJ+kKSQ+k9x3TdEn6Svoe7pB0YHf3oHOS+iTdKml5Gt9D0k1p3/5f6n4aSTPS+INp/qJuxt0pSTtI+jdJ90q6R9Lish9nSaekv+tVkr4vaaBsx1nSuZKelLSqblrbx1XScWn5ByQd104MUzrBpwd7fw14B7APcLSkfbob1VYzDHwqIvYBDgH+Lu3bZ4ArI2Iv4Mo0Dtl3sFd6LQW+MfkhbzUnA/fUjX8BOCMi/jPwDHBCmn4C8EyafkZabio6E/h5ROwN7Ee276U9zpIWAB8HhiLidWTdiX+Q8h3n7wBHNk1r67hKmgecSva40zcAp1Z/FHLJHtE2NV/AYuAXdeOfBT7b7bgK2tefAm8F7gN2SdN2Ae5Lw98Cjq5bftNyU+lF9uSvK4EjgOVkj7X8I9DffMzJnjWwOA33p+XU7X1oc3+3B37bHHeZjzO15zXPS8dtOfD2Mh5nYBGwqtPjChwNfKtuesNym3tN6RY8Yz/Ye0GXYilM+pf0AOAmYOeIWJ1m/QHYOQ2X5bv4MvD3wGgafwXwbEQMp/H6/dq0z2n+c2n5qWQPYA3w7VSWOkfSLEp8nCPiMeCLwO+A1WTHbSXlPs5V7R7XLTreUz3Bl56k2cCPgE9ExPP18yL7SS/NZVCS3gU8GRErux3LJOoHDgS+EREHAOup/dsOlPI47wi8m+zHbVdgFq2ljNKbjOM61RN8rgd7T1WSppEl9wsi4sdp8hOSdknzdwGeTNPL8F0cChwl6WHgB2RlmjOBHSRVnz5Wv1+b9jnN3x54ajID3goeBR6NiJvS+L+RJfwyH+e3AL+NiDUR8TLwY7JjX+bjXNXucd2i4z3VE3xpH+wtScC/AvdExOl1sy4GqmfSjyOrzVen/0U6G38I8Fzdv4JTQkR8NiJ2i4hFZMfylxFxDHAV8P60WPM+V7+L96flp1RLNyL+APxe0mvSpDcDd1Pi40xWmjlE0nbp77y6z6U9znXaPa6/AN4macf0n8/b0rR8un0SYiucxHgncD/wG+B/dDuerbhfS8j+fbsDuC293klWe7wSeAD4d2BeWl5kVxT9BriT7AqFru/HFuz/YcDyNPwq4GbgQeBCYEaaPpDGH0zzX9XtuDvc1/2BFelY/wTYsezHGfgccC+wCjgPmFG24wx8n+wcw8tk/6md0MlxBf4q7fuDwPHtxOA7Wc3MSmqql2jMzGwcTvBmZiXlBG9mVlJO8GZmJeUEb2ZWUk7wNiVJulpS4c/slPTx1MPjBU3ThyR9JQ0fJumNW3GbiyR9aKxtmbWjf/OLmJWLpP6o9XmyOR8F3hIRj9ZPjIgVZNeuQ3bN/jrgP7ZSDIuADwHfG2NbZrm5BW+FSS3ReySdnfr+vlzSzDRvUwtc0vzUPQGS/lLST1Jf2Q9L+pikT6aOuG5M3adWHSvpttSn+BvS52elfrhvTp95d916L5b0S7IbTZpj/WRazypJn0jTvkl2883PJJ3StPxhkpanjuA+ApySYnmTpEFJP5L06/Q6NH3mNEnnSboeOC99P7+SdEt6Vf8L+BfgTWl9p1S3ldYxL30/d6TvY9+6dZ+bvteHJH287vu4VNLtad8+sGVH1aaUbt/t5Vd5X2Qt0WFg/zT+Q+DDafhq0t16wHzg4TT8l2R37M0BBsl6DvxImncGWadr1c+fnYb/C6lLVuCf67axA9ldzrPSeh8l3TnYFOdBZHcPzgJmA3cBB6R5DwPzx/jMYdTutD0N+HTdvO8BS9LwQrLuJqrLrQRmpvHtgIE0vBewonndY2zrLODUNHwEcFvduv+D7I7Q+WR9tUwD3lf9ntJy23f778KvyXu5RGNF+21E3JaGV5Il/c25KiLWAmslPQdckqbfCexbt9z3ASLiWklzJe1A1lfHUZI+nZYZIEuyAFdExNNjbG8JcFFErAeQ9GPgTcCteXZwDG8B9sm6WQFgrrJeQQEujogX0/A04KuS9gdGgFfnWPcSsqRNRPxS0iskzU3zLo2IDcAGSU+SdUV7J/AlSV8g+5H4VYf7ZFOQE7wVbUPd8AgwMw0PUysRDkzwmdG68VEa/2ab+9kIsj493hcR99XPkHQwWVe8k6ECHBIRLzXFQFMMpwBPkD3FqQI0LN+B5u+6PyLuV/b4t3cC/yjpyoj4/BZux6YI1+CtWx4mK41ArQfBdn0AQNISst73niPrae+k1Eshkg7IsZ5fAe9JvRvOAt6bpuW1lqykVHU5cFJ1JLXQx7I9sDoiRoFjyR5dN9b6mmM9Jq33MOCP0fScgHqSdgVeiIjzgf9D1hWxbSOc4K1bvgicKOlWsppxJ15Kn/8mted3/i+y0scdku5K4xOKiFvInp95M9lTs86JiHbKM5cA762eZCU9bzSdCL2b7CTsWL4OHCfpdmBvaq37O4CRdGL0lKbPnAYcJOkOspOxm3sI858CN0u6jezZnv/Yxn7ZFOfeJM3MSsoteDOzknKCNzMrKSd4M7OScoI3MyspJ3gzs5JygjczKykneDOzknKCNzMrqf8PugF1+Gh9fqgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IrdeJ8gSRDQ2",
        "colab_type": "text"
      },
      "source": [
        "## Deep Learning with Keras"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k2YPmUdwy6uu",
        "colab_type": "text"
      },
      "source": [
        "Being equipped with automatic differentiation, we can now define easily new, complicated loss functions and layers, and compose them in arbitrary ways as long as the chain rule applies. \n",
        "\n",
        "Many deep learning frameworks are built on this idea, and extend it with high-level APIs that allow us to easily create and compose layers and losses. Here we will use `Keras` which creates an API on top of Tensorflow. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1UmbM0OERDQ2",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "There are two ways to build Keras models: **sequential** and **functional**.\n",
        "\n",
        "The sequential API allows you to create models layer-by-layer for most problems. It is limited in that it does not allow you to create models that share layers or have multiple inputs or outputs.\n",
        "\n",
        "Alternatively, the **functional API**  allows you to create models that have a lot more flexibility as you can easily define models where layers connect to more than just the previous and next layers. In fact, you can connect layers to (literally) any other layer. As a result, creating complex networks such as siamese networks and residual networks become possible.\n",
        "\n",
        "[Documentation](https://keras.io/getting-started/sequential-model-guide/)\n",
        "\n",
        "[Sequential Vs Functional](https://jovianlin.io/keras-models-sequential-vs-functional/)\n",
        "\n",
        "#### Steps Involved\n",
        "\n",
        "1.   Start with Input node\n",
        "2.   Add layers (conv, Pooling, Dense, flatten etc)\n",
        "3. Compile Model (Loss function, optimizer, metrics)\n",
        "4. Fit Model (Means to train the model)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "02CN66odRDQ3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b515f3f4-6811-4dc4-8eac-4e5ccd9febc9"
      },
      "source": [
        "import keras\n",
        "from keras_preprocessing.image import ImageDataGenerator,array_to_img, img_to_array, load_img\n",
        "from keras.models import Sequential\n",
        "from keras.layers import Conv2D, MaxPooling2D, Flatten, Dropout, Dense, BatchNormalization, Activation, Input, ZeroPadding2D, AveragePooling2D\n",
        "from keras.optimizers  import RMSprop, SGD, Adam\n",
        "from keras.losses import sparse_categorical_crossentropy\n",
        "from keras import models\n",
        "import cv2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HdxbwobszrVL",
        "colab_type": "text"
      },
      "source": [
        "The data is from: https://arxiv.org/pdf/1908.02900.pdf originally hosted at: https://www.kaggle.com/c/cassava-disease/data?select=train.zip . We have already downloaded them from a mirror, in the beginning of this notebook."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LDsVqdqmRDQ5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "DATA_DIR = 'train/'\n",
        "IMG_SIZE = (200, 200)\n",
        "BATCH_SIZE = 300"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TdKxsipTRDQ8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import glob \n",
        "\n",
        "def get_class(class_name, label_name, data, labels, max_files=-1):\n",
        "    files = []\n",
        "    files.extend(glob.glob(DATA_DIR  + class_name + os.path.sep +  '*.jpg'))\n",
        "    data.extend([cv2.imread(file) for file in files][0:max_files])\n",
        "    labels.extend([label_name for file in files][0:max_files])\n",
        "\n",
        "data = []\n",
        "labels = []\n",
        "\n",
        "n_images = 400\n",
        "# classes = ['cbb', 'cmd', 'healthy']\n",
        "classes = ['cbb', 'healthy']\n",
        "for i in range(len(classes)):\n",
        "    get_class(classes[i], i, data, labels, n_images)    \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rx_hcqLBRDQ_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.array([cv2.resize(d, IMG_SIZE, interpolation = cv2.INTER_AREA) for d in data])\n",
        "labels = keras.utils.to_categorical(np.array(labels))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OtKyZbuARDRD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Shuffle data because labels are in order \n",
        "np.random.seed(1)\n",
        "perm = np.random.permutation(data.shape[0])\n",
        "data = data[perm]\n",
        "labels = labels[perm]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RIpfFBa77OAg",
        "colab_type": "text"
      },
      "source": [
        "Let's plot the first image to see what our data look like:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wsE7DRNLRDRE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "9458933c-b61d-4451-aac0-a6ddf41e47dd"
      },
      "source": [
        "plt.imshow(data[0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7ff9093d2630>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lXskqSD3RDRG",
        "colab_type": "text"
      },
      "source": [
        "Now we will build a deep learning model. Let's build a model that contains a convolutional layer, followed by a batch-norm layer, relu activation and then max-pooling. Let's actually do that sequence multiple times to obtain a deep model. For convenience, let's build a function that executes this sequence: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZTNB5CzYRDRH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def conv_bn_relu(layer, filters=32, kernel_size=(5,5), double_conv=False):\n",
        "    layer = Conv2D(filters, kernel_size)(layer)\n",
        "    if double_conv:\n",
        "        layer = Conv2D(filters, kernel_size)(layer)\n",
        "    layer = BatchNormalization(axis = 3)(layer)\n",
        "    layer = Activation('relu')(layer)\n",
        "    layer = MaxPooling2D((2, 2))(layer)\n",
        "    return layer"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "giSuWCEB7kyB",
        "colab_type": "text"
      },
      "source": [
        "Now we can define the inputs and outputs, and call the aforementioned function multiple times to build our deep model. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5MRDez4g9mHq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tf.random.set_seed(0)\n",
        "np.random.seed(0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a5F55uqPRDRK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_input = Input((*IMG_SIZE, 3))\n",
        "    \n",
        "# Zero-Padding: pads the border of X_input with zeroes\n",
        "X = ZeroPadding2D((3, 3))(X_input)\n",
        "\n",
        "X = conv_bn_relu(X, filters=32, kernel_size=(7,7), double_conv=True)\n",
        "X = conv_bn_relu(X, filters=32, kernel_size=(5,5), double_conv=True)\n",
        "X = conv_bn_relu(X, filters=64, kernel_size=(5,5), double_conv=True)\n",
        "X = conv_bn_relu(X, filters=128, kernel_size=(3,3), double_conv=True)\n",
        "X = conv_bn_relu(X, filters=256, kernel_size=(3,3), double_conv=True)\n",
        "\n",
        "# FLATTEN X (means convert it to a vector) + FULLYCONNECTED\n",
        "X = Flatten()(X)\n",
        "X = Dense(64, activation=\"relu\")(X)\n",
        "X = Dropout(0.2)(X)\n",
        "X = Dense(labels.shape[1], activation='softmax')(X)\n",
        "\n",
        "# Create model. This creates your Keras model instance, you'll use this instance to train/test the model.\n",
        "model = keras.models.Model(inputs = X_input, outputs = X)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R-i-vkjORDRM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "f12dc095-3435-4dad-9f1e-0963bb052628"
      },
      "source": [
        "model.compile(loss='binary_crossentropy', # 'categorical_crossentropy' if >2 classes\n",
        "              optimizer='rmsprop',\n",
        "              metrics=['accuracy'])\n",
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"model_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_1 (InputLayer)         (None, 200, 200, 3)       0         \n",
            "_________________________________________________________________\n",
            "zero_padding2d_1 (ZeroPaddin (None, 206, 206, 3)       0         \n",
            "_________________________________________________________________\n",
            "conv2d_1 (Conv2D)            (None, 200, 200, 32)      4736      \n",
            "_________________________________________________________________\n",
            "conv2d_2 (Conv2D)            (None, 194, 194, 32)      50208     \n",
            "_________________________________________________________________\n",
            "batch_normalization_1 (Batch (None, 194, 194, 32)      128       \n",
            "_________________________________________________________________\n",
            "activation_1 (Activation)    (None, 194, 194, 32)      0         \n",
            "_________________________________________________________________\n",
            "max_pooling2d_1 (MaxPooling2 (None, 97, 97, 32)        0         \n",
            "_________________________________________________________________\n",
            "conv2d_3 (Conv2D)            (None, 93, 93, 32)        25632     \n",
            "_________________________________________________________________\n",
            "conv2d_4 (Conv2D)            (None, 89, 89, 32)        25632     \n",
            "_________________________________________________________________\n",
            "batch_normalization_2 (Batch (None, 89, 89, 32)        128       \n",
            "_________________________________________________________________\n",
            "activation_2 (Activation)    (None, 89, 89, 32)        0         \n",
            "_________________________________________________________________\n",
            "max_pooling2d_2 (MaxPooling2 (None, 44, 44, 32)        0         \n",
            "_________________________________________________________________\n",
            "conv2d_5 (Conv2D)            (None, 40, 40, 64)        51264     \n",
            "_________________________________________________________________\n",
            "conv2d_6 (Conv2D)            (None, 36, 36, 64)        102464    \n",
            "_________________________________________________________________\n",
            "batch_normalization_3 (Batch (None, 36, 36, 64)        256       \n",
            "_________________________________________________________________\n",
            "activation_3 (Activation)    (None, 36, 36, 64)        0         \n",
            "_________________________________________________________________\n",
            "max_pooling2d_3 (MaxPooling2 (None, 18, 18, 64)        0         \n",
            "_________________________________________________________________\n",
            "conv2d_7 (Conv2D)            (None, 16, 16, 128)       73856     \n",
            "_________________________________________________________________\n",
            "conv2d_8 (Conv2D)            (None, 14, 14, 128)       147584    \n",
            "_________________________________________________________________\n",
            "batch_normalization_4 (Batch (None, 14, 14, 128)       512       \n",
            "_________________________________________________________________\n",
            "activation_4 (Activation)    (None, 14, 14, 128)       0         \n",
            "_________________________________________________________________\n",
            "max_pooling2d_4 (MaxPooling2 (None, 7, 7, 128)         0         \n",
            "_________________________________________________________________\n",
            "conv2d_9 (Conv2D)            (None, 5, 5, 256)         295168    \n",
            "_________________________________________________________________\n",
            "conv2d_10 (Conv2D)           (None, 3, 3, 256)         590080    \n",
            "_________________________________________________________________\n",
            "batch_normalization_5 (Batch (None, 3, 3, 256)         1024      \n",
            "_________________________________________________________________\n",
            "activation_5 (Activation)    (None, 3, 3, 256)         0         \n",
            "_________________________________________________________________\n",
            "max_pooling2d_5 (MaxPooling2 (None, 1, 1, 256)         0         \n",
            "_________________________________________________________________\n",
            "flatten_1 (Flatten)          (None, 256)               0         \n",
            "_________________________________________________________________\n",
            "dense_1 (Dense)              (None, 64)                16448     \n",
            "_________________________________________________________________\n",
            "dropout_1 (Dropout)          (None, 64)                0         \n",
            "_________________________________________________________________\n",
            "dense_2 (Dense)              (None, 2)                 130       \n",
            "=================================================================\n",
            "Total params: 1,385,250\n",
            "Trainable params: 1,384,226\n",
            "Non-trainable params: 1,024\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZrYIpYTOKC8B",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "b94a73d0-2bc5-4984-f13c-12b48af3fa65"
      },
      "source": [
        "keras.utils.plot_model(model)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QoaDQ0nz7sQr",
        "colab_type": "text"
      },
      "source": [
        "Train the model! *Warning:* This takes a bit of time. You can reduce the number of epochs or training set for a quick run, but keep in mind that this will harm accuracy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yIsrMKzgRDRO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 734
        },
        "outputId": "98fe82cd-2e5f-483a-f3be-a84b1dda51e3"
      },
      "source": [
        "history = model.fit(x=data, y=labels, batch_size=BATCH_SIZE, epochs=20, validation_split = 0.2, shuffle=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 572 samples, validate on 144 samples\n",
            "Epoch 1/20\n",
            "572/572 [==============================] - 39s 68ms/step - loss: 1.1840 - accuracy: 0.5262 - val_loss: 8.2011 - val_accuracy: 0.4653\n",
            "Epoch 2/20\n",
            "572/572 [==============================] - 4s 7ms/step - loss: 0.9561 - accuracy: 0.5017 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 3/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.6099 - accuracy: 0.6119 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 4/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5579 - accuracy: 0.6731 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 5/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5551 - accuracy: 0.6783 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 6/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5550 - accuracy: 0.6783 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 7/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5498 - accuracy: 0.6643 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 8/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5442 - accuracy: 0.6731 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 9/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5366 - accuracy: 0.7080 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 10/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5618 - accuracy: 0.6573 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 11/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5322 - accuracy: 0.7133 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 12/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5482 - accuracy: 0.6906 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 13/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5258 - accuracy: 0.6958 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 14/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5312 - accuracy: 0.7203 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 15/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5225 - accuracy: 0.7308 - val_loss: 7.1113 - val_accuracy: 0.5347\n",
            "Epoch 16/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5629 - accuracy: 0.6643 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 17/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5807 - accuracy: 0.6801 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 18/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5078 - accuracy: 0.7273 - val_loss: 7.1360 - val_accuracy: 0.5347\n",
            "Epoch 19/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.5254 - accuracy: 0.7308 - val_loss: 5.9915 - val_accuracy: 0.5347\n",
            "Epoch 20/20\n",
            "572/572 [==============================] - 4s 6ms/step - loss: 0.4763 - accuracy: 0.7552 - val_loss: 5.4659 - val_accuracy: 0.5347\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1F1_3qC8RDRR",
        "colab_type": "text"
      },
      "source": [
        "### Observations from training\n",
        "The training outcome depends on the random initialization and architecture that you pick. \n",
        "\n",
        "But we generally see that the performance is not great. The network is learning something, but you might notice tht it is quite unstable (different runs produce different results, based on initialization) and the validation error does not behave as expected. We migth also observe that the performance on validation data doesn't match the one of the training data, a possible sign of overfitting. \n",
        "\n",
        "Realistically, we would need:\n",
        "- More data  \n",
        "- Train for longer  \n",
        "- Consider a more elaborate architecture.  \n",
        "\n",
        "Instead, below we show another alternative: transfer learning. It allows us to leverage a model which is already treained on a different (but related) task so as to learn better in the current task.\n",
        "\n",
        "__Exercises__ \n",
        "Try to experiment a little bit with the \"training from scratch\" code that was given above. In addition to the aforementioned suggestions for better training you can try to: \n",
        "1. _[Easy]_ Play with the choice of dropout vs no dropout or a different regularization, and also change the dropout probability. \n",
        "2. _[Easy]_ Experiment with including vs not including a batch-norm layer.\n",
        "3. _[Medium]_ Try defining a different architecture. \n",
        "4. _[Hard]_ Plot together the training and validation loss (y-axis) with the number of epochs on the x-axis. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NIiqAJeeRDRR",
        "colab_type": "text"
      },
      "source": [
        "## Reusing deep neural networks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OT3frtqQRDRS",
        "colab_type": "text"
      },
      "source": [
        "Transfer learning is a machine learning technique where a model trained on one task is re-purposed on a second related task.\n",
        "\n",
        "It is common to perform transfer learning with predictive modeling problems that use image data as input.\n",
        "\n",
        "This may be a prediction task that takes photographs or video data as input.\n",
        "\n",
        "For these types of problems, it is common to use a deep learning model pre-trained for a large and challenging image classification task such as the ImageNet 1000-class photograph classification competition.\n",
        "\n",
        "The research organizations that develop models for this competition and do well often release their final model under a permissive license for reuse. These models can take days or weeks to train on modern hardware.\n",
        "\n",
        "These models can be downloaded and incorporated directly into new models that expect image data as input.\n",
        "\n",
        "\n",
        " [More info](https://machinelearningmastery.com/transfer-learning-for-deep-learning/)\n",
        " \n",
        " \n",
        " ![alt text](https://cdn-images-1.medium.com/max/1600/1*9GTEzcO8KxxrfutmtsPs3Q.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SPxYxQdkRDRS",
        "colab_type": "text"
      },
      "source": [
        "When we perform transfer learning, we use the following terminology:\n",
        "- **Source task** is the task we have already trained a model, called the **source model** or the **pre-trained model**. We assume we have solved this task well because we have an abundance of training data (the **source data**) and expertise to train the model.\n",
        "- **Target task** is the task we want to perform predictions on, but we can't train a model from scratch either because we have insufficient training data (i.e. **target data**) or because we're lacking epertise.\n",
        "\n",
        "We want to transfer knowledge from the source model to a target model. There are two dominant ways to perform transfer learning:  \n",
        "- Use the source model as feature extractor. For example forward propagated images of the target task into the source model, and use the top layers as features for a new, data-efficient classifier (such as a Gaussian process).\n",
        "- Fine-tune the source model by adding/dropping layers and freezing the existing layers that are learning generic, transferrable features. \n",
        "\n",
        "These two cases are demonstrated below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ietk0k6VRDRT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "outputId": "48873dd9-8f84-4261-eac5-cddf6a9cddc8"
      },
      "source": [
        "from IPython.display import HTML\n",
        "HTML('<img src=\"http://adamian.github.io/var/xfer_metamodel.gif\", width=\"50%\" height=50%>')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<img src=\"http://adamian.github.io/var/xfer_metamodel.gif\", width=\"50%\" height=50%>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o8_kFbgyRDRU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "outputId": "2504fd8e-dd0d-429e-b9ac-23806f352637"
      },
      "source": [
        "HTML('<img src=\"http://adamian.github.io/var/xfer_modelhandler.gif\", width=\"50%\" height=50%>')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<img src=\"http://adamian.github.io/var/xfer_modelhandler.gif\", width=\"50%\" height=50%>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kn4KTBQSRDRX",
        "colab_type": "text"
      },
      "source": [
        "Here we focus on the later case, i.e. fine-tuning. We will fine-tune the VGG-16 neural network which has been trained on the very large ImageNet databse.\n",
        "\n",
        "### VGG \n",
        "\n",
        "![alt text](https://neurohive.io/wp-content/uploads/2018/11/vgg16-1-e1542731207177.png)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LsGGkm0gRDRX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras.applications import VGG16"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3y1taZMeRDRa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Use imagenet weights\n",
        "vgg_conv = VGG16(weights='imagenet',\n",
        "                include_top = False, \n",
        "                input_shape = ((*IMG_SIZE,3)))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "JYNLhFqNuO2d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 799
        },
        "outputId": "64a8e461-e441-46d9-c6fb-e5626c4d241e"
      },
      "source": [
        "vgg_conv.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"vgg16\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_2 (InputLayer)         (None, 200, 200, 3)       0         \n",
            "_________________________________________________________________\n",
            "block1_conv1 (Conv2D)        (None, 200, 200, 64)      1792      \n",
            "_________________________________________________________________\n",
            "block1_conv2 (Conv2D)        (None, 200, 200, 64)      36928     \n",
            "_________________________________________________________________\n",
            "block1_pool (MaxPooling2D)   (None, 100, 100, 64)      0         \n",
            "_________________________________________________________________\n",
            "block2_conv1 (Conv2D)        (None, 100, 100, 128)     73856     \n",
            "_________________________________________________________________\n",
            "block2_conv2 (Conv2D)        (None, 100, 100, 128)     147584    \n",
            "_________________________________________________________________\n",
            "block2_pool (MaxPooling2D)   (None, 50, 50, 128)       0         \n",
            "_________________________________________________________________\n",
            "block3_conv1 (Conv2D)        (None, 50, 50, 256)       295168    \n",
            "_________________________________________________________________\n",
            "block3_conv2 (Conv2D)        (None, 50, 50, 256)       590080    \n",
            "_________________________________________________________________\n",
            "block3_conv3 (Conv2D)        (None, 50, 50, 256)       590080    \n",
            "_________________________________________________________________\n",
            "block3_pool (MaxPooling2D)   (None, 25, 25, 256)       0         \n",
            "_________________________________________________________________\n",
            "block4_conv1 (Conv2D)        (None, 25, 25, 512)       1180160   \n",
            "_________________________________________________________________\n",
            "block4_conv2 (Conv2D)        (None, 25, 25, 512)       2359808   \n",
            "_________________________________________________________________\n",
            "block4_conv3 (Conv2D)        (None, 25, 25, 512)       2359808   \n",
            "_________________________________________________________________\n",
            "block4_pool (MaxPooling2D)   (None, 12, 12, 512)       0         \n",
            "_________________________________________________________________\n",
            "block5_conv1 (Conv2D)        (None, 12, 12, 512)       2359808   \n",
            "_________________________________________________________________\n",
            "block5_conv2 (Conv2D)        (None, 12, 12, 512)       2359808   \n",
            "_________________________________________________________________\n",
            "block5_conv3 (Conv2D)        (None, 12, 12, 512)       2359808   \n",
            "_________________________________________________________________\n",
            "block5_pool (MaxPooling2D)   (None, 6, 6, 512)         0         \n",
            "=================================================================\n",
            "Total params: 14,714,688\n",
            "Trainable params: 14,714,688\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AdXmp4IVuO2i",
        "colab": {}
      },
      "source": [
        "### Add our custom layers\n",
        "\n",
        "tr_model = vgg_conv.output\n",
        "tr_model = Flatten()(tr_model)\n",
        "tr_model = Dense(64, activation='relu')(tr_model)\n",
        "tr_model = Dropout(0.5)(tr_model)\n",
        "tr_model = Dense(labels.shape[1], activation='softmax')(tr_model)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "U_RJoc2buO2q",
        "colab": {}
      },
      "source": [
        "new_model = models.Model(inputs=vgg_conv.input, outputs=tr_model)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "YMBd1QZyRO2D"
      },
      "source": [
        "### Freezing and Fine-tuning vgg16\n",
        "\n",
        "![alt text](https://blog.keras.io/img/imgclf/vgg16_modified.png)\n",
        "\n",
        "(Image: https://blog.keras.io/building-powerful-image-classification-models-using-very-little-data.html)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "y69GCXEouO2t",
        "colab": {}
      },
      "source": [
        "def print_layer_trainable():\n",
        "    for layer in new_model.layers:\n",
        "        print(\"{0}:\\t{1}\".format(layer.trainable, layer.name))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "78GINlpRuO2y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 408
        },
        "outputId": "be1ecc42-955d-420f-fafb-70cbedc28a3d"
      },
      "source": [
        "for i, layer in enumerate(new_model.layers):\n",
        "    print(i, layer.name)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0 input_2\n",
            "1 block1_conv1\n",
            "2 block1_conv2\n",
            "3 block1_pool\n",
            "4 block2_conv1\n",
            "5 block2_conv2\n",
            "6 block2_pool\n",
            "7 block3_conv1\n",
            "8 block3_conv2\n",
            "9 block3_conv3\n",
            "10 block3_pool\n",
            "11 block4_conv1\n",
            "12 block4_conv2\n",
            "13 block4_conv3\n",
            "14 block4_pool\n",
            "15 block5_conv1\n",
            "16 block5_conv2\n",
            "17 block5_conv3\n",
            "18 block5_pool\n",
            "19 flatten_2\n",
            "20 dense_3\n",
            "21 dropout_2\n",
            "22 dense_4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "WwGG3ysauO24",
        "colab": {}
      },
      "source": [
        "for layer in new_model.layers[:18]:\n",
        "    layer.trainable = False\n",
        "for layer in new_model.layers[18:]:\n",
        "    layer.trainable = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "SObfoWjxuO2-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 408
        },
        "outputId": "a56310fc-89d0-4bb5-9dc9-915484870879"
      },
      "source": [
        "print_layer_trainable()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False:\tinput_2\n",
            "False:\tblock1_conv1\n",
            "False:\tblock1_conv2\n",
            "False:\tblock1_pool\n",
            "False:\tblock2_conv1\n",
            "False:\tblock2_conv2\n",
            "False:\tblock2_pool\n",
            "False:\tblock3_conv1\n",
            "False:\tblock3_conv2\n",
            "False:\tblock3_conv3\n",
            "False:\tblock3_pool\n",
            "False:\tblock4_conv1\n",
            "False:\tblock4_conv2\n",
            "False:\tblock4_conv3\n",
            "False:\tblock4_pool\n",
            "False:\tblock5_conv1\n",
            "False:\tblock5_conv2\n",
            "False:\tblock5_conv3\n",
            "True:\tblock5_pool\n",
            "True:\tflatten_2\n",
            "True:\tdense_3\n",
            "True:\tdropout_2\n",
            "True:\tdense_4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "LjF2LP7nuO3D",
        "colab": {}
      },
      "source": [
        "new_model.compile(loss='categorical_crossentropy',\n",
        "              optimizer='rmsprop',\n",
        "              metrics=['accuracy'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "tZ0H7c6GuO3G",
        "colab": {}
      },
      "source": [
        "# history = new_model.fit_generator(\n",
        "#         train_generator,\n",
        "#         steps_per_epoch=2000 // batch_size,\n",
        "#         epochs=10,\n",
        "#         validation_data=validation_generator,\n",
        "#         validation_steps=800 // batch_size)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XIYTQEBo72LQ",
        "colab_type": "text"
      },
      "source": [
        "Warning! This will take time! "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yd_A0czkRDR2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 224
        },
        "outputId": "0b9e4ca4-f63a-4229-985a-87d4c53e7779"
      },
      "source": [
        "history = new_model.fit(x=data, y=labels ,batch_size=BATCH_SIZE, epochs=5, validation_split = 0.2, shuffle=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 572 samples, validate on 144 samples\n",
            "Epoch 1/5\n",
            "572/572 [==============================] - 35s 61ms/step - loss: 29.6630 - accuracy: 0.5192 - val_loss: 13.3621 - val_accuracy: 0.4653\n",
            "Epoch 2/5\n",
            "572/572 [==============================] - 3s 5ms/step - loss: 6.6645 - accuracy: 0.5962 - val_loss: 0.5325 - val_accuracy: 0.7986\n",
            "Epoch 3/5\n",
            "572/572 [==============================] - 3s 5ms/step - loss: 0.4170 - accuracy: 0.7955 - val_loss: 0.4768 - val_accuracy: 0.7500\n",
            "Epoch 4/5\n",
            "572/572 [==============================] - 3s 5ms/step - loss: 0.3148 - accuracy: 0.8112 - val_loss: 0.4729 - val_accuracy: 0.7708\n",
            "Epoch 5/5\n",
            "572/572 [==============================] - 3s 5ms/step - loss: 0.2738 - accuracy: 0.8392 - val_loss: 0.4696 - val_accuracy: 0.7847\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hPDhF_PURDR6",
        "colab_type": "text"
      },
      "source": [
        "Even though we only did fewer epochs the accuracy is already much better compared to learning from scratch!\n",
        "\n",
        "For convenience, we can save the model and load it later, as shown below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "z84U2qNPDUdQ",
        "colab": {}
      },
      "source": [
        "new_model.save('transfer_model.h5')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "NN9CC2gZtsLN",
        "colab": {}
      },
      "source": [
        "from keras.models import load_model\n",
        "new_model = load_model('transfer_model.h5')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n37uewO829bN",
        "colab_type": "text"
      },
      "source": [
        "__Exercises__ \n",
        "1. __[Easy]__ Perform transfer learning by changing the structure of the `new_model` to something of your choice. \n",
        "2. __[Hard]__ Try to make the network overfit by training for many more epochs. Show the overfitting pattern by plotting the training together with the validation loss curves (y-axis) versus the epoch number (x-axis). \n",
        "3. __[Medium]__ Check the keras documentation to figure out how to do predictions (hint: use the `.predict` function). Keep a few extra images for a test set and see how well your network predicts on those. \n",
        "4. __[Hard]__ Perform transfer learning with the 'feature extraction' method. You would need to extract features from a specific layer (after feeding your test inputs to the model), and use these features as the new \"inputs\" to a classifier of your choice, e.g. an SVM from sklearn. _Hint_: One way to extract features from layer `i` from the bottom is: \n",
        "```\n",
        "feature_model = Model(new_model.inputs, outputs=new_model.layers[-i].output) # Dense layer\n",
        "features = feature_model.predict(target_inputs) \n",
        "```\n",
        "To test this, you can use `target_inputs=data[0:10,:,:,:], target_outputs=labels[0:10,:]` to simulate a target task, but ideally you can use a separate target set. You can now train a sklearn model with `X=features, y = target_outputs`. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VaMYQj6M2-gg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}