Basics_Neural_Network.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Reference: Nielsen, Michael A. Neural networks and deep learning. Vol. 25. San Francisco, CA, USA: Determination press, 2015."
      ],
      "metadata": {
        "id": "FfohU5pZTYKI"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "d7WFfc1agTzp"
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import datasets"
      ],
      "metadata": {
        "id": "s5XUOIMp8mwo"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rc8qp5qI5zmq"
      },
      "source": [
        "### The core of a neural network\n",
        "\n",
        "$$\n",
        "a^\\prime = σ(wa + b)\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GxpRuYEB6seZ"
      },
      "source": [
        "#### Define activation function\n",
        "\n",
        "$$σ(z) = \\frac{1}{1+e^{-z}}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "kSSIVdVn66VG"
      },
      "outputs": [],
      "source": [
        "def sigmoid(z):\n",
        "  return 1.0/(1.0+np.exp(-z))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3rM1VUIv75xM"
      },
      "source": [
        "### Define the affine transformation\n",
        "\n",
        "$$z = wa+b = w^Ta +b = \\sum_{i=1}^n w_ia_i + b_i$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "QNWhrudu_Nxn"
      },
      "outputs": [],
      "source": [
        "def affine_transform(w, b, a):\n",
        "  return np.dot(w, a) +b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z-mtUMj_471B"
      },
      "source": [
        "### Define the weights\n",
        "\n",
        "$$\n",
        "a^l_j = σ(\\displaystyle\\sum_k w^l_{jk}a_k^{l-1} + b_j^l)\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o28EMhOi5A49"
      },
      "source": [
        "![nndl-weights2.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mUfThhQB5IZ0"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "-9uUvuUV_xIt"
      },
      "outputs": [],
      "source": [
        "class Network:\n",
        "  def __init__(self, sizes: list) -> None:\n",
        "    self.num_layers = len(sizes)\n",
        "    self.sizes = sizes\n",
        "    self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]\n",
        "    self.weights = [np.random.randn(y, x)\n",
        "                        for x, y in zip(self.sizes[:-1], self.sizes[1:])]\n",
        "      "
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Initialize the weights of a network"
      ],
      "metadata": {
        "id": "ho39eKn45ShA"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "IMWBpsFCB_rS"
      },
      "outputs": [],
      "source": [
        "net_01 = Network([2, 3, 2])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yj6JJ3k2Cq0c",
        "outputId": "660c8403-216f-40c1-deb5-dce8a1a7a036"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[array([[ 1.14416365, -0.05021131],\n",
              "        [-1.52412818,  0.08630249],\n",
              "        [-0.42046259, -0.81434719]]),\n",
              " array([[-1.42357829,  0.25377729,  0.68459482],\n",
              "        [ 0.54847535,  0.52033211, -0.37732298]])]"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "net_01.weights"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0WpG3pSUC4l9",
        "outputId": "d9d98d24-e86c-45a0-9d42-fbf65fc03861"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[array([[1.11999741],\n",
              "        [0.81070891],\n",
              "        [1.24811273]]), array([[ 1.33680914],\n",
              "        [-0.06552604]])]"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "net_01.biases"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Define the inputs"
      ],
      "metadata": {
        "id": "EFIkXFqN5QK0"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EnQAg_GlE9U4",
        "outputId": "3700b9e5-1a75-46af-a805-4bd4ef7a6274"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "x = np.array([1, 2]).reshape(2, -1)\n",
        "x\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AK1iCjz_Jjgk",
        "outputId": "ed900d03-f420-435f-a102-8dc632069eec"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "x.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Calculate the output of the second layer (hidden layer)\n",
        "\n",
        "$$a_1 = σ(z_1) = σ(w_{11}x_1+ w_{12}x_2 + b_1)$$\n",
        "\n",
        "$$a_2 = σ(z_2) = σ(w_{21}x_1+ w_{22}x_2 + b_2)$$\n",
        "\n",
        "$$a_3 = σ(z_3) = σ(w_{31}x_1+ w_{32}x_2 + b_3)$$"
      ],
      "metadata": {
        "id": "fj6KS_zZ6H50"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "izsrjNpqJqeE",
        "outputId": "7a93f58f-3321-4d61-cc92-b6ed006f74c9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "net_01.weights[0].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SQ7Ff_o7JvfQ",
        "outputId": "c21bfee9-8e78-407d-b1c7-589b1a18a7ea"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.04374102],\n",
              "       [-1.3515232 ],\n",
              "       [-2.04915698]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "a1=net_01.weights[0].dot(x)\n",
        "a1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VVArGwjMLngP",
        "outputId": "063c642c-2d51-4270-954b-4a47b08e97d5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2.16373843],\n",
              "       [-0.54081429],\n",
              "       [-0.80104425]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "a1_bias = a1 + net_01.biases[0]\n",
        "a1_bias"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### The activation function of the hidden layers can be sigmoid, reLu or Tanh\n",
        "\n",
        "$$a_1^3 = σ(z_1^3) = σ(w_{11}^2a_1^2+ w_{12}^2a_2^2 + b_1^2)$$\n",
        "\n",
        "$$a_2^3 = σ(z_2^3) = σ(w_{21}^2a_1^2+ w_{22}^2a_2^2 + b_2^2)$$"
      ],
      "metadata": {
        "id": "Hffk0KD184qI"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dLa5LRDZl3wD",
        "outputId": "108ef223-4a6a-4650-e840-ff490721a0ad"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.89694562],\n",
              "       [0.36799818],\n",
              "       [0.30980219]])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "a1_bias_sigm = sigmoid(a1_bias)\n",
        "a1_bias_sigm"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Calculate the outpus of the third layer (output layer)"
      ],
      "metadata": {
        "id": "GmbUOeJx67LQ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LnZcGrc3hjF3",
        "outputId": "6e347501-2426-4fbc-cfe2-befa970e4ab5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "net_01.weights[1].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Kxss-YDwKRu8",
        "outputId": "d16f512a-3ec8-4315-cd07-75a8465c6d5d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.97139376],\n",
              "       [ 0.56653835]])"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "a2=net_01.weights[1].dot(a1_bias_sigm)\n",
        "a2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_pl4CVGXL1Zo",
        "outputId": "40745c96-618e-471a-a99e-0d6551a53a71"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.36541539],\n",
              "       [0.50101231]])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "a2_bias = a2 + net_01.biases[1]\n",
        "a2_bias"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### The activation function of the output layer can use sigmoid or softmax."
      ],
      "metadata": {
        "id": "vj4I2_wZ8meU"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C68rEKfjmM11",
        "outputId": "980b36b9-94cf-4cc2-e0fb-69190c087f84"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.59035071],\n",
              "       [0.6226972 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "a2_bias_sigm = sigmoid(a2_bias)\n",
        "a2_bias_sigm"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Put all the above together"
      ],
      "metadata": {
        "id": "w_NVVDA39fVa"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TwJeMODeNUia"
      },
      "outputs": [],
      "source": [
        "\n",
        "import array\n",
        "def feed_forward(net, a:array) -> array:\n",
        "  for b, w in zip(net.biases, net.weights):\n",
        "    a = sigmoid(affine_transform(w, b, a))\n",
        "\n",
        "  return a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IYr8WiPfQgTi"
      },
      "outputs": [],
      "source": [
        "a_y = feed_forward(net_01, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8ysJgseEQ2Du",
        "outputId": "1784db81-dab1-461d-8612-54046e6b89f7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.62893018],\n",
              "       [0.38713388]])"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a_y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_F7YrLa1fqox"
      },
      "source": [
        "## Backpropagation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uYgv7UGzgRDB"
      },
      "source": [
        "### Cost function\n",
        "\n",
        "For a single training example:\n",
        "\n",
        "$$\n",
        "C=\\frac{1}{2}\\|y-a^L\\|^2=\\frac{1}{2}\\displaystyle\\sum_j (y_j - a_j^L)^2\n",
        "$$\n",
        "\n",
        "For the total training examples:\n",
        "\n",
        "$$\n",
        "C = \\frac{1}{2n}\\displaystyle\\sum_x \\|y(x) - a^L(x)\\|^2\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yNKdDzrcplMw"
      },
      "source": [
        "#### Get the error in the output layer\n",
        "\n",
        "$$\n",
        "\\delta_j^L = \\frac{∂C}{\\partial a_j^L}σ^\\prime(z_j^L)\n",
        "$$\n",
        "\n",
        "#### We have our loss function: $$C = \\frac{1}{2}\\displaystyle\\sum_j (y_j - a_j^L)^2$$\n",
        "\n",
        "$$\\frac{∂C}{∂a_j^L} = (a_j^L-y_j)$$\n",
        "\n",
        "$$\\delta_j^L = (a_j^L-y_j)\\odotσ^\\prime(z^L) = (a_j^L-y_j)\\odot(a_j^L(1-a_j^L))$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LdirNDozrPAp"
      },
      "source": [
        "#### Get the error in the next layer\n",
        "\n",
        "$$\n",
        "\\delta^l=((w^{l+1})^Tδ^{l+1})\\odot σ^\\prime(z^l)\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A9kCQA-YwWPk"
      },
      "source": [
        "#### Get the bias error\n",
        "\n",
        "$$\n",
        "\\frac{∂C}{\\partial b_j^l}=\\delta^l_j\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p-k6DmXdyFCB"
      },
      "source": [
        "#### Get the rate of weight changes\n",
        "\n",
        "$$\n",
        "\\frac{∂C}{\\partial w_{jk}^l}=a_k^{l-1}\\delta^l_j\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 1. 1 Calculate the error for the output layer (layer 3)"
      ],
      "metadata": {
        "id": "8Fdstu7Y99Em"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1.1.1 Get the ground truth y"
      ],
      "metadata": {
        "id": "ws5ZtJv7-D_K"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LdsG06bUlZnZ",
        "outputId": "8536bb36-c3e9-41b5-c1c6-5dd332020242"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2],\n",
              "       [3]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "### Let's say \n",
        "y_true = np.array([2, 3]).reshape(2, -1)\n",
        "y_true\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1.1.2 Get the derivative of sigmoid function"
      ],
      "metadata": {
        "id": "p2NqljTe-H8S"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "mtj6frujnYlC"
      },
      "outputs": [],
      "source": [
        "### Define the sigmoid derivative\n",
        "def sigmoid_prime(z):\n",
        "    \"\"\"Derivative of the sigmoid function.\"\"\"\n",
        "    return sigmoid(z)*(1-sigmoid(z))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1.1.3 Calculate $δ^L$"
      ],
      "metadata": {
        "id": "heZiYYIU-RZz"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tjxj-L-smmk6",
        "outputId": "5d4735d8-6438-4a96-8030-9e2a75058aa3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.340905  ],\n",
              "       [-0.55853635]])"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "delta_L = (a2_bias_sigm - y_true)*sigmoid_prime(a2_bias)\n",
        "delta_L"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yJaJ_n7JxM4j",
        "outputId": "f04430d0-ef35-4b76-af3f-010e2cab9b1a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.59035071],\n",
              "       [0.6226972 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ],
      "source": [
        "a2_bias_sigm"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 1.2 Update Weights and Bias for the output layer"
      ],
      "metadata": {
        "id": "PJjkssOF4kX2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1.2.1 Check the original weights for ourput layer"
      ],
      "metadata": {
        "id": "yPo3uapO-bYP"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OMjD0I7FxgLq",
        "outputId": "78a8a078-cfb6-410f-9105-5fc2e923f262"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.42357829,  0.25377729,  0.68459482],\n",
              "       [ 0.54847535,  0.52033211, -0.37732298]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "net_01.weights[1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UqgCFm6wxoZ0"
      },
      "outputs": [],
      "source": [
        "# why transpose\n",
        "#np.dot(delta_L, a2_bias_sigm)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_0BbTFajyw8f",
        "outputId": "bcc42b77-9c09-42e2-8269-3040cfdda97e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.59035071, 0.6226972 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "a2_bias_sigm.transpose()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1.2.2 Calculate the $∇$ for bias ($b_2$) and weightes ($w_2$)\n",
        "\n",
        "$$\\frac{∂C}{\\partial w_{jk}^l}=a_k^{l-1}\\delta^l_j$$\n",
        "\n",
        "$$\\frac{∂C}{\\partial b_j^l}=\\delta^l_j$$"
      ],
      "metadata": {
        "id": "Kumu6NBs-0Yr"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "c10mWphuq1MD"
      },
      "outputs": [],
      "source": [
        "nabla_b2 = delta_L\n",
        "nabla_w2 = np.dot(delta_L, a1_bias_sigm.transpose())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TTr5CAOh0fmu",
        "outputId": "f754c07a-8a48-43c6-8339-e599960d2c20"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.30577325, -0.12545242, -0.10561312],\n",
              "       [-0.50097673, -0.20554036, -0.17303578]])"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "nabla_w2"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1.2.3 Update $b_2$ and $w_2$"
      ],
      "metadata": {
        "id": "48OoISSI_zu7"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ki98MRKcqmc_",
        "outputId": "4d6b8b57-e08d-450d-9419-c6cb4cc0ab13"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.11780504,  0.37922971,  0.79020794],\n",
              "       [ 1.04945209,  0.72587247, -0.2042872 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ],
      "source": [
        "### let's assume learning rate is 1\n",
        "\n",
        "net_01.weights[1] - nabla_w2"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "net_01.biases[1] - nabla_b2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s6GMDCti6up6",
        "outputId": "e4ffb8d1-94aa-40c5-a70b-5e50bf726642"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.67771414],\n",
              "       [0.49301031]])"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 2.1 Calculate the error of hidden layer (layer 2) for sigmoid \n",
        "\n",
        "$$\n",
        "\\delta^l=((w^{l+1})^Tδ^{l+1})\\odot σ^\\prime(z^l) = ((w^{l+1})^Tδ^{l+1})\\odot(a_j^l(1-a_j^l))\n",
        "$$"
      ],
      "metadata": {
        "id": "zS-75jg0__yB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 2.1.1 Calculate: $(a_j^l(1-a_j^l))$"
      ],
      "metadata": {
        "id": "DRyRSfxAkMoQ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k5LEdW75k12e",
        "outputId": "330cd935-469f-4aaa-f210-9dda8b78a8ba"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[-2.98680281],\n",
              "       [ 3.37212708],\n",
              "       [ 5.68758514]])"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a1_bias"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "piXD4h8B3w8c",
        "outputId": "6a250168-9548-4dc5-b8c8-d663a5160907"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.09243417],\n",
              "       [0.23257552],\n",
              "       [0.21382479]])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "sp = sigmoid_prime(a1_bias)\n",
        "sp\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "clZYoLFkipHV",
        "outputId": "51d41ba2-9904-4de0-cff8-7d8a3cf261af"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "net_01.weights[1].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pyohz2OYivsm",
        "outputId": "5775686e-88c1-4176-cd2c-cf8193123fb8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "# from the output layer\n",
        "delta_L.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 2.1.2 get the error for hidden layer"
      ],
      "metadata": {
        "id": "q7XuWiXh55lh"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dRTpE9PG390p",
        "outputId": "97898923-5187-451e-fa8f-674ec70660c5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.01654216],\n",
              "       [-0.08771315],\n",
              "       [-0.00483954]])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "\n",
        "delta_1 = np.dot(net_01.weights[1].transpose(), delta_L) * sp\n",
        "delta_1\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 2.2 Update Weights and Bias for the hidden layer"
      ],
      "metadata": {
        "id": "l_vSd_re6LTg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 2.2.1 Calculate the $∇$ for bias ($b_2$) and weightes ($w_2$) for hidden layer\n",
        "\n",
        "$$\\frac{∂C}{\\partial w_{jk}^l}=a_k^{l-1}\\delta^l_j$$\n",
        "\n",
        "$$\\frac{∂C}{\\partial b_j^l}=\\delta^l_j$$"
      ],
      "metadata": {
        "id": "-AwADvdum_kG"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UeUE6Da8iUep",
        "outputId": "108e20eb-106f-429d-f48d-d3c359183e38"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.01654216,  0.03308432],\n",
              "       [-0.08771315, -0.17542629],\n",
              "       [-0.00483954, -0.00967908]])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "nabla_b1 = delta_1\n",
        "nabla_w1 = np.dot(delta_1, x.transpose())\n",
        "nabla_w1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "784qpsZkrSGS",
        "outputId": "19ac2ce8-d6db-44c2-f5a6-76559ffe1b44"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.12762149, -0.08329564],\n",
              "       [-1.43641504,  0.26172879],\n",
              "       [-0.41562306, -0.80466811]])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "### Change the weights\n",
        "### let's assume learning rate is 1\n",
        "\n",
        "net_01.weights[0] - nabla_w1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "BVyMgYECi6F8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2032ca9c-cfbc-4d91-da52-e3c7381645a5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.10345524],\n",
              "       [0.89842206],\n",
              "       [1.25295226]])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "net_01.biases[0] - nabla_b1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VA6s-lp6zbWV"
      },
      "source": [
        "### Backpropagation Algorithm\n",
        "1. Input x: the output/action of the input layer, $a^1$\n",
        "\n",
        "2. Feedforward: For each layer, $l = 2, 3, \\dots , L$, compute $z^l = w^la^{l-1} +b ^l$, and $a^l = σ(z_l)$\n",
        "\n",
        "3. Output error $δ^L$: $δ^L=(a^L-y)⊙σ^\\prime(z^L)$\n",
        "\n",
        "4. Backpropagate the error: for $l = L-1, L-2, \\dots, 2$, compute $\\delta^l=((w^{l+1})^Tδ^{l+1})\\odot σ^\\prime(z^l)$\n",
        "\n",
        "5. Output: The gradient of weight and bias: $\\frac{∂C}{\\partial w_{jk}^l}=a_k^{l-1}\\delta^l_j$ and $\\frac{∂C}{\\partial b_j^l}=\\delta^l_j$\n",
        "\n",
        "$$w^l \\rightarrow w^l - \\frac{\\eta}{m}\\sum_x \\delta^{x,l}(a^{x,l-1})^T$$\n",
        "\n",
        "$$b^l → b^l -  \\frac{\\eta}{m}\\sum_x \\delta^{x,l}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Digits classification (https://github.com/cumbalik/michael-nielsen_neural-networks_deep-learning/blob/master/network2.py)"
      ],
      "metadata": {
        "id": "k72yUHUdSdeh"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AMgzC_gonAGA"
      },
      "outputs": [],
      "source": [
        "\"\"\"\n",
        "mnist_loader\n",
        "~~~~~~~~~~~~\n",
        "\n",
        "A library to load the MNIST image data.  For details of the data\n",
        "structures that are returned, see the doc strings for ``load_data``\n",
        "and ``load_data_wrapper``.  In practice, ``load_data_wrapper`` is the\n",
        "function usually called by our neural network code.\n",
        "\"\"\"\n",
        "\n",
        "#### Libraries\n",
        "# Standard library\n",
        "import pickle\n",
        "import gzip\n",
        "\n",
        "# Third-party libraries\n",
        "#import numpy as np\n",
        "\n",
        "def load_data(mnist_data):\n",
        "    \"\"\"Return the MNIST data as a tuple containing the training data,\n",
        "    the validation data, and the test data.\n",
        "\n",
        "    The ``training_data`` is returned as a tuple with two entries.\n",
        "    The first entry contains the actual training images.  This is a\n",
        "    numpy ndarray with 50,000 entries.  Each entry is, in turn, a\n",
        "    numpy ndarray with 784 values, representing the 28 * 28 = 784\n",
        "    pixels in a single MNIST image.\n",
        "\n",
        "    The second entry in the ``training_data`` tuple is a numpy ndarray\n",
        "    containing 50,000 entries.  Those entries are just the digit\n",
        "    values (0...9) for the corresponding images contained in the first\n",
        "    entry of the tuple.\n",
        "\n",
        "    The ``validation_data`` and ``test_data`` are similar, except\n",
        "    each contains only 10,000 images.\n",
        "\n",
        "    This is a nice data format, but for use in neural networks it's\n",
        "    helpful to modify the format of the ``training_data`` a little.\n",
        "    That's done in the wrapper function ``load_data_wrapper()``, see\n",
        "    below.\n",
        "    \"\"\"\n",
        "    f = gzip.open(mnist_data, 'rb')\n",
        "    training_data, validation_data, test_data = pickle.load(f, encoding='bytes')\n",
        "    f.close()\n",
        "    return (training_data, validation_data, test_data)\n",
        "\n",
        "def load_data_wrapper(mnist_data):\n",
        "    \"\"\"Return a tuple containing ``(training_data, validation_data,\n",
        "    test_data)``. Based on ``load_data``, but the format is more\n",
        "    convenient for use in our implementation of neural networks.\n",
        "\n",
        "    In particular, ``training_data`` is a list containing 50,000\n",
        "    2-tuples ``(x, y)``.  ``x`` is a 784-dimensional numpy.ndarray\n",
        "    containing the input image.  ``y`` is a 10-dimensional\n",
        "    numpy.ndarray representing the unit vector corresponding to the\n",
        "    correct digit for ``x``.\n",
        "\n",
        "    ``validation_data`` and ``test_data`` are lists containing 10,000\n",
        "    2-tuples ``(x, y)``.  In each case, ``x`` is a 784-dimensional\n",
        "    numpy.ndarry containing the input image, and ``y`` is the\n",
        "    corresponding classification, i.e., the digit values (integers)\n",
        "    corresponding to ``x``.\n",
        "\n",
        "    Obviously, this means we're using slightly different formats for\n",
        "    the training data and the validation / test data.  These formats\n",
        "    turn out to be the most convenient for use in our neural network\n",
        "    code.\"\"\"\n",
        "    tr_d, va_d, te_d = load_data(mnist_data)\n",
        "    training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]\n",
        "    training_results = [vectorized_result(y) for y in tr_d[1]]\n",
        "    training_data = zip(training_inputs, training_results)\n",
        "    validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]\n",
        "    validation_data = zip(validation_inputs, va_d[1])\n",
        "    test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]\n",
        "    test_data = zip(test_inputs, te_d[1])\n",
        "    return (training_data, validation_data, test_data)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def vectorized_result(j):\n",
        "    \"\"\"Return a 10-dimensional unit vector with a 1.0 in the jth\n",
        "    position and zeroes elsewhere.  This is used to convert a digit\n",
        "    (0...9) into a corresponding desired output from the neural\n",
        "    network.\"\"\"\n",
        "    e = np.zeros((10, 1))\n",
        "    e[j] = 1.0\n",
        "    return e"
      ],
      "metadata": {
        "id": "K7m0nizWo6kc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ffrx_G4D9hTQ"
      },
      "outputs": [],
      "source": [
        "training_data, validation_data, test_data = load_data_wrapper('/content/drive/MyDrive/Colab Notebooks/mnist.pkl.gz')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b0au3dJmC48n",
        "outputId": "a83f40a4-553a-4ee0-fb39-a02a3ae30105"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(784, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "test_data = list(test_data)\n",
        "training_data = list(training_data)\n",
        "validation_data = list(validation_data)\n",
        "np.shape(training_data[0][0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "I0ngxQeY9zzg",
        "outputId": "9c79a727-e158-40f2-efa4-7aa6ae3647f1"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import matplotlib.cm as cm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "plt.imshow(training_data[0][0].reshape((28, 28)), cmap=cm.Greys_r)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Just another dataset of digits with lower resolution"
      ],
      "metadata": {
        "id": "y2IdFyRYpAIF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "digits = datasets.load_digits()"
      ],
      "metadata": {
        "id": "TGWA3zsk8e79"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "digits.data.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9BtcTj3L87M4",
        "outputId": "39988adb-53ce-4775-abc0-3db691c4f34e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(digits.data[1].reshape((8, 8)), cmap=cm.Greys_r)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "MK8a25jm9H34",
        "outputId": "cd9e1c7b-8159-45eb-fb4b-1ee989e0e8b2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPUAAAD4CAYAAAA0L6C7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAKf0lEQVR4nO3dX4hc9RnG8efpqqQ2VrG1RRKpudCABqoSgpIgNMFiqmgvepGAQqWQK0VpQLR4U/Ba7EURQjQVtEobFYJYrRDFKm2aP6at+VdssJhFG02RqBcN6tOLnZRoN92zs+ecmX37/cDi7uyw5x306zlzZub8nEQA6vjSqAcA0C6iBoohaqAYogaKIWqgmDO6+KO2OaXegssvv7y3bU1MTPS2rcnJyd62dezYsd621bcknu52d/GSFlG349ChQ71ta+HChb1t67777uttW1u2bOltW307XdQcfgPFEDVQDFEDxRA1UAxRA8UQNVAMUQPFEDVQDFEDxTSK2vb1tg/ZftP2PV0PBWB4M0Zte0LSzyWtlXSZpPW2L+t6MADDabKnXiHpzSSHk5yQ9KSkm7sdC8CwmkS9SNLbp/x8ZHDb59jeYHuX7V1tDQdg9lr76GWSTZI2SXxKCxilJnvqSUkXnfLz4sFtAMZQk6h3SrrE9hLbZ0laJ2lbt2MBGNaMh99JPrF9u6QXJE1IeiTJvs4nAzCURs+pkzwn6bmOZwHQAt5RBhRD1EAxRA0UQ9RAMUQNFEPUQDFEDRTTybI7aMfx48d729all17a27bWrl3b27Yqr9BxOuypgWKIGiiGqIFiiBoohqiBYogaKIaogWKIGiiGqIFiiBoopskKHY/YPmr7jT4GAjA3TfbUv5B0fcdzAGjJjFEneUXSP3uYBUALWvuUlu0Nkja09fcADIdld4BiOPsNFEPUQDFNXtJ6QtLvJS21fcT2j7ofC8Cwmqyltb6PQQC0g8NvoBiiBoohaqAYogaKIWqgGKIGiiFqoBiW3ZmFlStX9rq9ZcuW9bq9vuzYsWPUI5TGnhoohqiBYogaKIaogWKIGiiGqIFiiBoohqiBYogaKIaogWKaXKPsItsv2d5ve5/tO/sYDMBwmrz3+xNJG5PssX2OpN22X0yyv+PZAAyhybI77yTZM/j+Q0kHJC3qejAAw5nVp7RsXyzpSkn/9TEblt0BxkPjqG0vlPSUpLuSHP/i71l2BxgPjc5+2z5TU0E/nuTpbkcCMBdNzn5b0sOSDiR5oPuRAMxFkz31Skm3Slpte+/g63sdzwVgSE2W3XlVknuYBUALeEcZUAxRA8UQNVAMUQPFEDVQDFEDxRA1UAxRA8XM+7W07r///t62tXHjxt62JUkLFizodXt92bZt26hHKI09NVAMUQPFEDVQDFEDxRA1UAxRA8UQNVAMUQPFEDVQTJMLDy6w/Ufbfxosu/PTPgYDMJwmbxP9l6TVST4aXCr4Vdu/SfKHjmcDMIQmFx6MpI8GP545+OJi/cCYanox/wnbeyUdlfRikmmX3bG9y/autocE0FyjqJN8muQKSYslrbC9bJr7bEqyPMnytocE0Nyszn4n+UDSS5Ku72YcAHPV5Oz3BbbPG3z/ZUnXSTrY9WAAhtPk7PeFkh61PaGp/wn8Ksmz3Y4FYFhNzn7/WVNrUgOYB3hHGVAMUQPFEDVQDFEDxRA1UAxRA8UQNVAMUQPFeOqTlS3/UbvkRzPPP//8Xrd37NixXrfXl1WrVvW2rddee623bfUtiae7nT01UAxRA8UQNVAMUQPFEDVQDFEDxRA1UAxRA8UQNVAMUQPFNI56cEH/121z0UFgjM1mT32npANdDQKgHU2X3Vks6QZJm7sdB8BcNd1TPyjpbkmfne4OrKUFjIcmK3TcKOlokt3/636spQWMhyZ76pWSbrL9lqQnJa22/VinUwEY2oxRJ7k3yeIkF0taJ2l7kls6nwzAUHidGiimyQJ5/5HkZUkvdzIJgFawpwaKIWqgGKIGiiFqoBiiBoohaqAYogaKmdXr1EAbrr766t62VXnZndNhTw0UQ9RAMUQNFEPUQDFEDRRD1EAxRA0UQ9RAMUQNFEPUQDGN3iY6uJLoh5I+lfQJlwEGxtds3vv9nSTvdzYJgFZw+A0U0zTqSPqt7d22N0x3B5bdAcZD08PvVUkmbX9D0ou2DyZ55dQ7JNkkaZMk2U7LcwJoqNGeOsnk4J9HJT0jaUWXQwEYXpMF8r5i+5yT30v6rqQ3uh4MwHCaHH5/U9Iztk/e/5dJnu90KgBDmzHqJIclfbuHWQC0gJe0gGKIGiiGqIFiiBoohqiBYogaKIaogWKIGiiGqIFiiBoohqiBYogaKIaogWKIGiiGqIFiiBoohqiBYogaKKZR1LbPs73V9kHbB2xf0/VgAIbT9LrfP5P0fJIf2D5L0tkdzgRgDmaM2va5kq6V9ENJSnJC0oluxwIwrCaH30skvSdpi+3XbW8eXP/7c1h2BxgPTaI+Q9JVkh5KcqWkjyXd88U7JdmUZDnL3AKj1STqI5KOJNkx+HmrpiIHMIZmjDrJu5Letr10cNMaSfs7nQrA0Jqe/b5D0uODM9+HJd3W3UgA5qJR1En2SuK5MjAP8I4yoBiiBoohaqAYogaKIWqgGKIGiiFqoBiiBopxkvb/qN3+H/0/tHPnzt62tXx5f+8t2r59e2/bWrNmTW/b6lsST3c7e2qgGKIGiiFqoBiiBoohaqAYogaKIWqgGKIGiiFqoJgZo7a91PbeU76O276rj+EAzN6M1yhLckjSFZJke0LSpKRnOp4LwJBme/i9RtLfkvy9i2EAzF3TSwSftE7SE9P9wvYGSRvmPBGAOWm8px5c8/smSb+e7vcsuwOMh9kcfq+VtCfJP7oaBsDczSbq9TrNoTeA8dEo6sHStddJerrbcQDMVdNldz6W9LWOZwHQAt5RBhRD1EAxRA0UQ9RAMUQNFEPUQDFEDRRD1EAxXS27856k2X488+uS3m99mPFQ9bHxuEbnW0kumO4XnUQ9DNu7qn7Cq+pj43GNJw6/gWKIGihmnKLeNOoBOlT1sfG4xtDYPKcG0I5x2lMDaAFRA8WMRdS2r7d9yPabtu8Z9TxtsH2R7Zds77e9z/ado56pTbYnbL9u+9lRz9Im2+fZ3mr7oO0Dtq8Z9UyzNfLn1IMFAv6qqcslHZG0U9L6JPtHOtgc2b5Q0oVJ9tg+R9JuSd+f74/rJNs/lrRc0leT3Djqedpi+1FJv0uyeXAF3bOTfDDquWZjHPbUKyS9meRwkhOSnpR084hnmrMk7yTZM/j+Q0kHJC0a7VTtsL1Y0g2SNo96ljbZPlfStZIelqQkJ+Zb0NJ4RL1I0tun/HxERf7jP8n2xZKulLRjtJO05kFJd0v6bNSDtGyJpPckbRk8tdg8uOjmvDIOUZdme6GkpyTdleT4qOeZK9s3SjqaZPeoZ+nAGZKukvRQkislfSxp3p3jGYeoJyVddMrPiwe3zXu2z9RU0I8nqXJ55ZWSbrL9lqaeKq22/dhoR2rNEUlHkpw8otqqqcjnlXGIeqekS2wvGZyYWCdp24hnmjPb1tRzswNJHhj1PG1Jcm+SxUku1tS/q+1JbhnxWK1I8q6kt20vHdy0RtK8O7E52wXyWpfkE9u3S3pB0oSkR5LsG/FYbVgp6VZJf7G9d3DbT5I8N8KZMLM7JD0+2MEclnTbiOeZtZG/pAWgXeNw+A2gRUQNFEPUQDFEDRRD1EAxRA0UQ9RAMf8GBJp52NaYEG8AAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Check the ground truth (y)"
      ],
      "metadata": {
        "id": "DlJtFZ1CpLjv"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PSfrH7YUruOB",
        "outputId": "4d7295f0-b861-4565-f88a-5570c01793f1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [1.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "## Check y\n",
        "vectorized_result(5)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#### Miscellaneous functions\n",
        "\n",
        "\n",
        "def sigmoid(z):\n",
        "    \"\"\"The sigmoid function.\"\"\"\n",
        "    return 1.0/(1.0+np.exp(-z))\n",
        "\n",
        "def softmax(z):\n",
        "    \"\"\"Softmax function\"\"\"\n",
        "    return np.exp(z) / np.sum(np.exp(z), axis=1, keepdims=True)\n",
        "\n",
        "def sigmoid_prime(z):\n",
        "    \"\"\"Derivative of the sigmoid function.\"\"\"\n",
        "    return sigmoid(z)*(1-sigmoid(z))"
      ],
      "metadata": {
        "id": "fXuLUSe0nRZb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"network2.py\n",
        "~~~~~~~~~~~~~~\n",
        "\n",
        "An improved version of network.py, implementing the stochastic\n",
        "gradient descent learning algorithm for a feedforward neural network.\n",
        "Improvements include the addition of the cross-entropy cost function,\n",
        "regularization, and better initialization of network weights.  Note\n",
        "that I have focused on making the code simple, easily readable, and\n",
        "easily modifiable.  It is not optimized, and omits many desirable\n",
        "features.\n",
        "\n",
        "\"\"\"\n",
        "\n",
        "#### Libraries\n",
        "# Standard library\n",
        "import json\n",
        "import random\n",
        "import sys\n",
        "\n",
        "# Third-party libraries\n",
        "#import numpy as np\n",
        "\n",
        "\n",
        "#### Define the quadratic and cross-entropy cost functions\n",
        "\n",
        "class QuadraticCost:\n",
        "\n",
        "    @staticmethod\n",
        "    def fn(a, y):\n",
        "        \"\"\"Return the cost associated with an output ``a`` and desired output\n",
        "        ``y``.\n",
        "\n",
        "        \"\"\"\n",
        "        return 0.5*np.linalg.norm(a-y)**2\n",
        "\n",
        "    @staticmethod\n",
        "    def delta(z, a, y):\n",
        "        \"\"\"Return the error delta from the output layer.\"\"\"\n",
        "        return (a-y) * sigmoid_prime(z)\n",
        "\n",
        "\n",
        "class CrossEntropyCost:\n",
        "\n",
        "    @staticmethod\n",
        "    def fn(a, y):\n",
        "        \"\"\"Return the cost associated with an output ``a`` and desired output\n",
        "        ``y``.  Note that np.nan_to_num is used to ensure numerical\n",
        "        stability.  In particular, if both ``a`` and ``y`` have a 1.0\n",
        "        in the same slot, then the expression (1-y)*np.log(1-a)\n",
        "        returns nan.  The np.nan_to_num ensures that that is converted\n",
        "        to the correct value (0.0).\n",
        "\n",
        "        \"\"\"\n",
        "        return np.sum(np.nan_to_num(-y*np.log(a)-(1-y)*np.log(1-a)))\n",
        "\n",
        "    @staticmethod\n",
        "    def delta(z, a, y):\n",
        "        \"\"\"Return the error delta from the output layer.  Note that the\n",
        "        parameter ``z`` is not used by the method.  It is included in\n",
        "        the method's parameters in order to make the interface\n",
        "        consistent with the delta method for other cost classes.\n",
        "\n",
        "        \"\"\"\n",
        "        return (a-y)\n",
        "\n",
        "\n",
        "#### Main Network class\n",
        "class Network:\n",
        "    \n",
        "    def __init__(self, sizes, cost=CrossEntropyCost):\n",
        "        \"\"\"The list ``sizes`` contains the number of neurons in the respective\n",
        "        layers of the network.  For example, if the list was [2, 3, 1]\n",
        "        then it would be a three-layer network, with the first layer\n",
        "        containing 2 neurons, the second layer 3 neurons, and the\n",
        "        third layer 1 neuron.  The biases and weights for the network\n",
        "        are initialized randomly, using\n",
        "        ``self.default_weight_initializer`` (see docstring for that\n",
        "        method).\n",
        "\n",
        "        \"\"\"\n",
        "        self.num_layers = len(sizes)\n",
        "        self.sizes = sizes\n",
        "        self.default_weight_initializer()\n",
        "        self.cost=cost\n",
        "\n",
        "    def default_weight_initializer(self):\n",
        "        \"\"\"Initialize each weight using a Gaussian distribution with mean 0\n",
        "        and standard deviation 1 over the square root of the number of\n",
        "        weights connecting to the same neuron.  Initialize the biases\n",
        "        using a Gaussian distribution with mean 0 and standard\n",
        "        deviation 1.\n",
        "\n",
        "        Note that the first layer is assumed to be an input layer, and\n",
        "        by convention we won't set any biases for those neurons, since\n",
        "        biases are only ever used in computing the outputs from later\n",
        "        layers.\n",
        "\n",
        "        \"\"\"\n",
        "        self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]\n",
        "        self.weights = [np.random.randn(y, x)/np.sqrt(x)\n",
        "                        for x, y in zip(self.sizes[:-1], self.sizes[1:])]\n",
        "\n",
        "    def large_weight_initializer(self):\n",
        "        \"\"\"Initialize the weights using a Gaussian distribution with mean 0\n",
        "        and standard deviation 1.  Initialize the biases using a\n",
        "        Gaussian distribution with mean 0 and standard deviation 1.\n",
        "\n",
        "        Note that the first layer is assumed to be an input layer, and\n",
        "        by convention we won't set any biases for those neurons, since\n",
        "        biases are only ever used in computing the outputs from later\n",
        "        layers.\n",
        "\n",
        "        This weight and bias initializer uses the same approach as in\n",
        "        Chapter 1, and is included for purposes of comparison.  It\n",
        "        will usually be better to use the default weight initializer\n",
        "        instead.\n",
        "\n",
        "        \"\"\"\n",
        "        self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]\n",
        "        self.weights = [np.random.randn(y, x)\n",
        "                        for x, y in zip(self.sizes[:-1], self.sizes[1:])]\n",
        "\n",
        "    def feedforward(self, a):\n",
        "        \"\"\"Return the output of the network if ``a`` is input.\"\"\"\n",
        "        for b, w in zip(self.biases, self.weights):\n",
        "            a = sigmoid(np.dot(w, a)+b)\n",
        "        return a\n",
        "\n",
        "    def SGD(self, training_data, epochs, mini_batch_size, eta,\n",
        "            lmbda = 0.0,\n",
        "            evaluation_data=None,\n",
        "            monitor_evaluation_cost=False,\n",
        "            monitor_evaluation_accuracy=False,\n",
        "            monitor_training_cost=False,\n",
        "            monitor_training_accuracy=False):\n",
        "        \"\"\"Train the neural network using mini-batch stochastic gradient\n",
        "        descent.  The ``training_data`` is a list of tuples ``(x, y)``\n",
        "        representing the training inputs and the desired outputs.  The\n",
        "        other non-optional parameters are self-explanatory, as is the\n",
        "        regularization parameter ``lmbda``.  The method also accepts\n",
        "        ``evaluation_data``, usually either the validation or test\n",
        "        data.  We can monitor the cost and accuracy on either the\n",
        "        evaluation data or the training data, by setting the\n",
        "        appropriate flags.  The method returns a tuple containing four\n",
        "        lists: the (per-epoch) costs on the evaluation data, the\n",
        "        accuracies on the evaluation data, the costs on the training\n",
        "        data, and the accuracies on the training data.  All values are\n",
        "        evaluated at the end of each training epoch.  So, for example,\n",
        "        if we train for 30 epochs, then the first element of the tuple\n",
        "        will be a 30-element list containing the cost on the\n",
        "        evaluation data at the end of each epoch. Note that the lists\n",
        "        are empty if the corresponding flag is not set.\n",
        "\n",
        "        \"\"\"\n",
        "        if evaluation_data: n_data = len(evaluation_data)\n",
        "        n = len(training_data)\n",
        "        evaluation_cost, evaluation_accuracy = [], []\n",
        "        training_cost, training_accuracy = [], []\n",
        "        for j in range(epochs):\n",
        "            random.shuffle(training_data)\n",
        "            mini_batches = [\n",
        "                training_data[k:k+mini_batch_size]\n",
        "                for k in range(0, n, mini_batch_size)]\n",
        "            for mini_batch in mini_batches:\n",
        "                self.update_mini_batch(\n",
        "                    mini_batch, eta, lmbda, len(training_data))\n",
        "            print(\"Epoch %s training complete\" % j)\n",
        "            if monitor_training_cost:\n",
        "                cost = self.total_cost(training_data, lmbda)\n",
        "                training_cost.append(cost)\n",
        "                print(\"Cost on training data: {}\".format(cost))\n",
        "            if monitor_training_accuracy:\n",
        "                accuracy = self.accuracy(training_data, convert=True)\n",
        "                training_accuracy.append(accuracy)\n",
        "                print(\"Accuracy on training data: {} / {}\".format(\n",
        "                    accuracy, n))\n",
        "            if monitor_evaluation_cost:\n",
        "                cost = self.total_cost(evaluation_data, lmbda, convert=True)\n",
        "                evaluation_cost.append(cost)\n",
        "                print(\"Cost on evaluation data: {}\".format(cost))\n",
        "            if monitor_evaluation_accuracy:\n",
        "                accuracy = self.accuracy(evaluation_data)\n",
        "                evaluation_accuracy.append(accuracy)\n",
        "                print(\"Accuracy on evaluation data: {} / {}\".format(\n",
        "                    self.accuracy(evaluation_data), n_data))\n",
        "        return evaluation_cost, evaluation_accuracy, \\\n",
        "            training_cost, training_accuracy\n",
        "\n",
        "    def update_mini_batch(self, mini_batch, eta, lmbda, n):\n",
        "        \"\"\"Update the network's weights and biases by applying gradient\n",
        "        descent using backpropagation to a single mini batch.  The\n",
        "        ``mini_batch`` is a list of tuples ``(x, y)``, ``eta`` is the\n",
        "        learning rate, ``lmbda`` is the regularization parameter, and\n",
        "        ``n`` is the total size of the training data set.\n",
        "\n",
        "        \"\"\"\n",
        "        nabla_b = [np.zeros(b.shape) for b in self.biases]\n",
        "        nabla_w = [np.zeros(w.shape) for w in self.weights]\n",
        "        for x, y in mini_batch:\n",
        "            delta_nabla_b, delta_nabla_w = self.backprop(x, y)\n",
        "            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]\n",
        "            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]\n",
        "        self.weights = [(1-eta*(lmbda/n))*w-(eta/len(mini_batch))*nw\n",
        "                        for w, nw in zip(self.weights, nabla_w)]\n",
        "        #print(self.weights)\n",
        "        self.biases = [b-(eta/len(mini_batch))*nb\n",
        "                       for b, nb in zip(self.biases, nabla_b)]\n",
        "\n",
        "    def backprop(self, x, y):\n",
        "        \"\"\"Return a tuple ``(nabla_b, nabla_w)`` representing the\n",
        "        gradient for the cost function C_x.  ``nabla_b`` and\n",
        "        ``nabla_w`` are layer-by-layer lists of numpy arrays, similar\n",
        "        to ``self.biases`` and ``self.weights``.\"\"\"\n",
        "        nabla_b = [np.zeros(b.shape) for b in self.biases]\n",
        "        nabla_w = [np.zeros(w.shape) for w in self.weights]\n",
        "        # feedforward\n",
        "        activation = x\n",
        "        activations = [x] # list to store all the activations, layer by layer\n",
        "        zs = [] # list to store all the z vectors, layer by layer\n",
        "        for b, w in zip(self.biases, self.weights):\n",
        "            z = np.dot(w, activation)+b\n",
        "            zs.append(z)\n",
        "            activation = sigmoid(z)\n",
        "            activations.append(activation)\n",
        "        # backward pass\n",
        "        delta = (self.cost).delta(zs[-1], activations[-1], y)\n",
        "        nabla_b[-1] = delta\n",
        "        nabla_w[-1] = np.dot(delta, activations[-2].transpose())\n",
        "        # Note that the variable l in the loop below is used a little\n",
        "        # differently to the notation in Chapter 2 of the book.  Here,\n",
        "        # l = 1 means the last layer of neurons, l = 2 is the\n",
        "        # second-last layer, and so on.  It's a renumbering of the\n",
        "        # scheme in the book, used here to take advantage of the fact\n",
        "        # that Python can use negative indices in lists.\n",
        "        for l in range(2, self.num_layers):\n",
        "            z = zs[-l]\n",
        "            sp = sigmoid_prime(z)\n",
        "            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp\n",
        "            nabla_b[-l] = delta\n",
        "            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())\n",
        "        return (nabla_b, nabla_w)\n",
        "\n",
        "    def accuracy(self, data, convert=False):\n",
        "        \"\"\"Return the number of inputs in ``data`` for which the neural\n",
        "        network outputs the correct result. The neural network's\n",
        "        output is assumed to be the index of whichever neuron in the\n",
        "        final layer has the highest activation.\n",
        "\n",
        "        The flag ``convert`` should be set to False if the data set is\n",
        "        validation or test data (the usual case), and to True if the\n",
        "        data set is the training data. The need for this flag arises\n",
        "        due to differences in the way the results ``y`` are\n",
        "        represented in the different data sets.  In particular, it\n",
        "        flags whether we need to convert between the different\n",
        "        representations.  It may seem strange to use different\n",
        "        representations for the different data sets.  Why not use the\n",
        "        same representation for all three data sets?  It's done for\n",
        "        efficiency reasons -- the program usually evaluates the cost\n",
        "        on the training data and the accuracy on other data sets.\n",
        "        These are different types of computations, and using different\n",
        "        representations speeds things up.  More details on the\n",
        "        representations can be found in\n",
        "        mnist_loader.load_data_wrapper.\n",
        "\n",
        "        \"\"\"\n",
        "        if convert:\n",
        "            results = [(np.argmax(self.feedforward(x)), np.argmax(y))\n",
        "                       for (x, y) in data]\n",
        "        else:\n",
        "            results = [(np.argmax(self.feedforward(x)), y)\n",
        "                        for (x, y) in data]\n",
        "        return sum(int(x == y) for (x, y) in results)\n",
        "\n",
        "    def total_cost(self, data, lmbda, convert=False):\n",
        "        \"\"\"Return the total cost for the data set ``data``.  The flag\n",
        "        ``convert`` should be set to False if the data set is the\n",
        "        training data (the usual case), and to True if the data set is\n",
        "        the validation or test data.  See comments on the similar (but\n",
        "        reversed) convention for the ``accuracy`` method, above.\n",
        "        \"\"\"\n",
        "        cost = 0.0\n",
        "        for x, y in data:\n",
        "            a = self.feedforward(x)\n",
        "            if convert: y = vectorized_result(y)\n",
        "            cost += self.cost.fn(a, y)/len(data)\n",
        "        cost += 0.5*(lmbda/len(data))*sum(\n",
        "            np.linalg.norm(w)**2 for w in self.weights)\n",
        "        return cost\n",
        "\n",
        "    def save(self, filename):\n",
        "        \"\"\"Save the neural network to the file ``filename``.\"\"\"\n",
        "        data = {\"sizes\": self.sizes,\n",
        "                \"weights\": [w.tolist() for w in self.weights],\n",
        "                \"biases\": [b.tolist() for b in self.biases],\n",
        "                \"cost\": str(self.cost.__name__)}\n",
        "        f = open(filename, \"w\")\n",
        "        json.dump(data, f)\n",
        "        f.close()"
      ],
      "metadata": {
        "id": "bwT-g6vJrzai"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wctulKD48iOD"
      },
      "source": [
        "### Model training"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "txMD0XBUD5wJ",
        "outputId": "2bb2745a-7652-414c-c897-2f0ce8bc18f9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 training complete\n",
            "Accuracy on evaluation data: 9520 / 10000\n",
            "Epoch 1 training complete\n",
            "Accuracy on evaluation data: 9649 / 10000\n",
            "Epoch 2 training complete\n",
            "Accuracy on evaluation data: 9696 / 10000\n",
            "Epoch 3 training complete\n",
            "Accuracy on evaluation data: 9701 / 10000\n",
            "Epoch 4 training complete\n",
            "Accuracy on evaluation data: 9697 / 10000\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([], [9520, 9649, 9696, 9701, 9697], [], [])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "net = Network([784, 100, 10])\n",
        "#start = time.time()\n",
        "net.SGD(training_data, 5,10,0.3, \n",
        "        lmbda = 5,\n",
        "        evaluation_data = validation_data,\n",
        "        monitor_evaluation_accuracy = True\n",
        "        )"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "gpuClass": "standard"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}