04. Learning Rate Decay Methods/02. Step Decay - MXNet.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Step Decay - MXNet.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "L3KIZndDdgt4",
        "colab_type": "code",
        "outputId": "d59f1f49-4bd4-48ec-f88d-59c4b19ba6ec",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 171
        }
      },
      "source": [
        "!pip install mxnet-cu100"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: mxnet-cu100 in /usr/local/lib/python3.6/dist-packages (1.4.1)\n",
            "Requirement already satisfied: graphviz<0.9.0,>=0.8.1 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (0.8.4)\n",
            "Requirement already satisfied: requests>=2.20.0 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (2.21.0)\n",
            "Requirement already satisfied: numpy<1.15.0,>=1.8.2 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (1.14.6)\n",
            "Requirement already satisfied: idna<2.9,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2.8)\n",
            "Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (3.0.4)\n",
            "Requirement already satisfied: urllib3<1.25,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (1.24.3)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2019.6.16)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1YN4PT_Idstj",
        "colab_type": "text"
      },
      "source": [
        "#MXNet (From Scratch)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CLGHa8i6WEaA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import mxnet as mx\n",
        "from mxnet import nd, autograd, gluon\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "mx.random.seed(1)\n",
        "\n",
        "model_ctx = mx.gpu()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "huuK9vLaWEcO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def transform(data, label):\n",
        "    return data.astype('float32')/255.0, label.astype('float32')\n",
        "\n",
        "train_mnist = gluon.data.vision.FashionMNIST(train = True, transform = transform)\n",
        "test_mnist = gluon.data.vision.FashionMNIST(train = False, transform = transform)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sAXcT8nSWEYo",
        "colab_type": "code",
        "outputId": "0b286bb0-9b41-41a1-91cc-c24ddcb6c7cc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "image, label = train_mnist[0]\n",
        "print(image.shape, label.shape)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(28, 28, 1) ()\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SIQSLxiFWEXg",
        "colab_type": "code",
        "outputId": "6a1bb4ba-c57f-4248-c8db-c410b4f48dad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "plt.imshow(image.reshape((28, 28)).asnumpy())\n",
        "plt.title(label)\n",
        "plt.show()\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oF-WKS-xX73T",
        "colab_type": "text"
      },
      "source": [
        "##Creating data loader for training and testing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IVmMwE94WEWY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "batch_size = 64\n",
        "training_data = gluon.data.DataLoader(train_mnist, batch_size = batch_size, shuffle = True)\n",
        "testing_data = gluon.data.DataLoader(test_mnist, batch_size = batch_size, shuffle = False)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5HUXvMyHYKoM",
        "colab_type": "text"
      },
      "source": [
        "##Building the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u7Vdh54QWESq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "weight_scale = .01\n",
        "\n",
        "#  Allocate parameters for the first hidden layer\n",
        "W1 = nd.random_normal(shape = (784, 256), scale=weight_scale, ctx=model_ctx)\n",
        "b1 = nd.random_normal(shape = 256, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "#  Allocate parameters for the second hidden layer\n",
        "W2 = nd.random_normal(shape = (256, 128), scale=weight_scale, ctx=model_ctx)\n",
        "b2 = nd.random_normal(shape = 128, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "#  Allocate parameters for the output layer\n",
        "W3 = nd.random_normal(shape=(128, 10), scale=weight_scale, ctx=model_ctx)\n",
        "b3 = nd.random_normal(shape=10, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "params = [W1, b1, W2, b2, W3, b3]\n",
        "\n",
        "for param in params:\n",
        "    param.attach_grad()\n",
        "    \n",
        "def neuralnetworks(inputs):\n",
        "    layer1 = nd.relu(nd.dot(inputs, W1) + b1)\n",
        "    layer2 = nd.relu(nd.dot(layer1, W2) + b2)\n",
        "    return nd.softmax(nd.dot(layer2, W3) + b3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HW4Jzb46EyyD",
        "colab_type": "text"
      },
      "source": [
        "##Defining our objective function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "avO1uf5fItMV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def categoricalcrossentropy(predictions, labels):\n",
        "    return -nd.sum(labels * nd.log(predictions))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3qr1NTDkE7Kh",
        "colab_type": "text"
      },
      "source": [
        "##Defining our parameters optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hvFKa4WuI9c-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sgd(params, lr):\n",
        "    for param in params:\n",
        "        param[:] = param - lr * param.grad"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lbHoiGM3ZrQY",
        "colab_type": "text"
      },
      "source": [
        "##Defining our accuracy function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-3osTW97ZuHR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def accuracy(predictions, labels):\n",
        "    return nd.mean(predictions.argmax(1) == labels.argmax(1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6GHgqNdMK7y_",
        "colab_type": "text"
      },
      "source": [
        "##Defining Step Based Decay"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eRG13WS5OSAQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def step_decay(lr, drop, epochs_drop, epoch):\n",
        "    return lr * nd.power(drop, nd.floor(nd.array([epoch / epochs_drop], ctx = model_ctx)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lr2eiTs8OTHd",
        "colab_type": "text"
      },
      "source": [
        "##Doing a quick visualization for different drop values for epoch_drop 10"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJ7dmGxrLNRB",
        "colab_type": "code",
        "outputId": "109e63b5-0a24-4aab-d0ba-309a8ea53e26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "epochs_drop = 10.0\n",
        "\n",
        "drop1 = 0.2\n",
        "drop2 = 0.4\n",
        "drop3 = 0.6\n",
        "\n",
        "# smaller the drop smaller the learning rate for upcomming epochs\n",
        "\n",
        "epochs = 50\n",
        "\n",
        "initial_lr = nd.array([0.01], ctx = model_ctx)\n",
        "\n",
        "lrs1 = []\n",
        "for epoch in range(epochs):\n",
        "    lr_ = step_decay(initial_lr, drop1, epochs_drop, epoch)\n",
        "    lrs1.append(lr_.asscalar())\n",
        "\n",
        "lrs2 = []\n",
        "for epoch in range(epochs):\n",
        "    lr_ = step_decay(initial_lr, drop2, epochs_drop, epoch)\n",
        "    lrs2.append(lr_.asscalar())\n",
        "\n",
        "lrs3 = []\n",
        "for epoch in range(epochs):\n",
        "    lr_ = step_decay(initial_lr, drop3, epochs_drop, epoch)\n",
        "    lrs3.append(lr_.asscalar())\n",
        "\n",
        "plt.plot(list(range(epochs)), lrs1, label = f'Drop = {drop1}')\n",
        "plt.plot(list(range(epochs)), lrs2, label = f'Drop = {drop2}')\n",
        "plt.plot(list(range(epochs)), lrs3, label = f'Drop = {drop3}')\n",
        "plt.title('Learning rate for 100 epochs')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Learning rate')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HkbKlS5fys5/9jOeee87rUNrU1s9ZRFap6pRkjrcaiY9FxWnb3Vm70+NIjDG9WcbekGg6\nFpVcAHbX7vI4EmMy2ymnnMIpp5zidRhpYzUSH8sO5gOwa99WjyMxxvRmlkh8LCerEIDdNZ97HIkx\npjezROJj0ZDTwW41EmNMKiyR+Fgwkk9eLM6u/Yea3swYYw7NEomPSTiXwniMHftt1JYx7QkGg833\nkUyePJmf//znKU+42F1++tOfMmrUKI466iiWLFlyyH2vvfZacnNz0xKHjdryMYnmUxSLs6uuyutQ\njDls9fZp5AFWrlzJrl3pG51pNRIfC0TyKIzH2V3fvTOqGpOpeuM08rFYjOuvv5677747pfc7FKuR\n+FgwUkBhLMaGRluTxPQCf7sJPnu3e885eCKc/V+dOqS3TSN///33M2vWLIYMGdKp6+wMSyQ+Form\nURSPUxXb73UoxvRah/M08pWVlfz5z39m6dKl3Xre1iyR+Fg4J4/CWJw6Yuxv3E80K+p1SMa0r5M1\nh3TpTdPIv/3225SVlTFq1CgA9u3bx6hRoygrK0sq5mRZIvGxSDhENOZ0zFXVVVkiMaYDyUwj/+CD\nD3L55Zezc+dOXnvtNf77v/+bDRs2NE8jP3z4cBYtWsS8efMOOr4zNZJZs2Zx8cUXc91111FZWdnm\nNPIzZszgs88+a36dm5vb7UkELJH4WjQUJBJzPgI7a3cyuM9gjyMy5vDTNI18Q0MDWVlZXHrppVx3\n3XVt7nv++efz+uuvM3nyZESkeRr5DRs2NE8jX1ZWxqmnntqt08hnZWUdNI38ggULGDp0aErvkSyb\nRt7HNm3fy7vzp/Cj4iwePP1BvlT8Ja9DMqYFm0a+Z9g08qbLoqEgWbFsAHbV2QzAxpiusaYtH4uG\ngwQbI8Bedtft9jocYzKWTSNvMlY0FCQezyGgsMvWJDHGdJElEh8LBYVacsiPq9VIjDFdZonEx0SE\n2kCUwnjcaiTGmC6zROJztYE+FMUarUZijOkySyQ+15CVQ1Esxq5am0remLb09mnkVZUf/ehHjBkz\nhrFjx3Lfffd1exw2asvn6oN9KIrHedeatoxpU2+fRv6RRx5hy5YtbNiwgUAg0DzZZHeyGonPNWb1\noTAWY1ddFX64OdWYVPTGaeR//etfc8sttxAIBJqvobtZjcTnYll96B+L06iN7G3YS244PSuoGZOq\nu5bfxYadG7r1nEf3PZobp97YqWN62zTyH330EYsWLeLpp59mwIAB3HfffYwePbpT19wRSyQ+Fwvn\nUbjP+ctoV90uSyTGdNLhPI08QF1dHZFIhJUrV/LUU0/xrW99i3/+85/d+h6WSHxOw7kUVccA56bE\nI/KO8DgiY9rW2ZpDuvSmaeTBqal87WtfA5xJJa+44oqk4u0M6yPxOQ3nUui21doQYGMOLZlp5Bct\nWkQsFmPbtm289tprzVO7N00jH4/HWbRoESeddNJBx99zzz2sXr36oEfrJALONPILFy6krq6OTZs2\ntTmNPMB5553XnJxeffVVxowZk+qP4SBpTSQiMl1E3heRMhE56CchItkissjd/qaIlCZsu9ktf19E\nzkoo/4GIrBORtSLymIhE0nkNGS87j6KY27RlI7eMOUjTNPLjx4/n9NNP58wzz+TWW29tc9/zzz+f\nSZMmMXnyZKZNm9Y8jTzQPI382LFjGTFiRLdOIz99+vSDppGvrKwE4KabbuLJJ59k4sSJ3HzzzSxY\nsCCl922TqqblAQSBj4CRQBh4BxjXap/vAP/XfT4XWOQ+H+funw2McM8TBIqBTUDU3e9x4N86iuXY\nY49V07a7nn5T99xWoBMemaCPrH3E63CMaWH9+vVeh9AtXnnlFZ0xY4bXYbSrrZ8zsFKT/L5PZ41k\nKlCmqhtVtR5YCMxutc9s4Hfu8yeA08SpL84GFqpqnapuAsrc84HTrxMVkSwgB6hM4zVkvGAkl1xV\nsghYjcQY0yXpTCTFwJaE1+VuWZv7qGojUAX0a+9YVa0AfgZ8AnwKVKnq39t6cxGZJyIrRWTltm3b\nuuFyMlMkO8w+zaYoELI+EmPS5JRTTjlsF7XqDr2qs11EinBqKyOAoUAfEflmW/uq6nxVnaKqUwYM\nGNCTYfYqkVCQGqIUkGU1EnNYUrtRNq264+ebzkRSASSOJS1xy9rcx22qKgB2HOLY04FNqrpNVRuA\npwBbHzYF0VCQGo1SqGI1EnPYiUQi7Nixw5JJmqgqO3bsIBJJbcxSOu8jWQGMFpEROElgLnBxq30W\nA5cDrwNzgJdVVUVkMfAnEfkFTs1jNLAciAMniEgOsB84DbDF2FMQDQfYS4SCOGy05XbNYaakpITy\n8nKseTp9IpEIJSUlKZ0jbYlEVRtF5BpgCc6Iq4dVdZ2I3IEzGmAx8BDwqIiUATtxkg3ufo8D64FG\n4LuqGgPeFJEngLfc8reB+em6Bj9orpHEYuyutRqJObyEQiFGjBjhdRimA2m9s11Vnweeb1V2S8Lz\nWuAb7Rx7J3BnG+W3Am0P4jadFgkF2UuUgsbdVNVXEYvHCAaCHR9ojDGuXtXZbrpfNBSkhghFjfXE\nNU51fbXXIRljehlLJD4XDTtNW0UNtYAzcaMxxnSGJRKfi7pNW33r9wM2TYoxpvMskfhcJBSkWqP0\na6wDrEZijOk8SyQ+lxMOspdI88SNNnLLGNNZlkh8Luomkqap5K1GYozpLEskPhfJClKtOURViQTC\nViMxxnSaJRKfCwSE+mAUgKJQrtVIjDGdZonE0JDlrNNemJVj820ZYzrNEokhluWsOV0UzLamLWNM\np1kiMcRDbo1Ewta0ZYzpNEskhpibSIokaDUSY0ynWSIxkO3WSDRAdUM1DfEGjwMyxvQmlkgM2eEw\ntWRT5C4eVFVX5XFExpjexBKJIRIKsk+iFMadRGLzbRljOsMSiSEaDrKPKEWNjQA2BNgY0ymWSAzR\nUIAaohQ2OBM37qzd6XFExpjexBKJcZfbjVDkJhIbuWWM6QxLJIZIOMieeITCuhrAJm40xnSOJRJD\nNBRkj0bIqttLbijX+kiMMZ1iicQ4qyRqFOpqKMwutFFbxphOsURiiIaDVBOF+mr6RvpajcQY0ykd\nJhIRyRGRH4vIb9zXo0Xk3PSHZnpKJBRkr0aQxloKs/OtRmKM6ZRkaiS/BeqAE93XFcBP0haR6XHR\nUJC9OGuSFGZZH4kxpnOSSSRHqurdQAOAqu4DJK1RmR4VDblNW0BRVtQSiTGmU5JJJPUiEgUUQESO\nxKmhmAwRDTtNWwCFwQj7G/ezv3G/x1EZY3qLrCT2uQ14AThCRP4IfBm4Ip1BmZ4VCQWpaaqRSAhw\nJm6MZkW9DMsY00t0mEhU9e8isgo4AadJ6/uquj3tkZke49zZ7vaRiPOR2FW7i8F9BnsZljGml0hm\n1NZLqrpDVf+qqs+p6nYReakngjM9IxoOshenaatIne4vu7vdGJOsdmskIhIBcoD+IlLEgQ72fKC4\nB2IzPSQnnFAjiTtlNgTYGJOsQ9VI/iewCjja/bfp8QxwfzInF5HpIvK+iJSJyE1tbM8WkUXu9jdF\npDRh281u+fsiclZCeaGIPCEiG0TkPRE5sfV5Tee06COJO5nERm4ZY5LVbo1EVe8F7hWR76nqrzp7\nYhEJAg8AZwDlwAoRWayq6xN2uxLYpaqjRGQucBdwoYiMA+YC44GhwD9EZIyqxoB7gRdUdY6IhHFq\nTSYFzn0kTtNWfmM9gliNxBiTtGQ6238lIhOAceB+2zjlv+/g0KlAmapuBBCRhcBsIDGRzMYZFQbw\nBHC/iIhbvlBV64BNIlIGTBWR9cDJwL+5MdQD9R1dgzm0UFDQQIiGQDah+r0UZBewbsc6XvokM7vC\nBGHK4Cnkh/O9DsWYjNBhIhGRW4FTcBLJ88DZwDKgo0RSDGxJeF0OHN/ePqraKCJVQD+3/I1WxxYD\n+4FtwG9FZDJOU9v3VXVvG3HPA+YBDBs2rKPL9DURIRoKUh/IIVRfQ3FuMcsqlrGsYpnXoaXNZeMu\n4/rjrvc6DGMyQjL3kcwBJgNvq+oVIjII+EN6w2pXFvBF4Huq+qaI3AvcBPy49Y6qOh+YDzBlyhTt\n0Sh7oUgoSG0ghz511cyfOZ/KmkqvQ0qbG1+7kc17NnsdhjEZI5lEsl9V4yLSKCL5wFbgiCSOq2i1\nX4lb1tY+5SKSBRQAOw5xbDlQrqpvuuVP4CQSk6JoOMD+mDOVfH44n/y+mdvsM6JgBJuqNnkdhjEZ\nI5kpUlaKSCHwG5ympLeA15M4bgUwWkRGuJ3ic4HFrfZZDFzuPp8DvKyq6pbPdUd1jQBGA8tV9TNg\ni4gc5R5zGi37XEwXRUNB9ksU6qq9DiXtSnJLqKipwPmoGWNSdcgaidvx/VNV3Q38XxF5AchX1TUd\nndjt87gGWAIEgYdVdZ2I3AGsVNXFwEPAo25n+k6cZIO73+M4SaIR+K47Ygvge8Af3eS0EZuupVtE\nQ0H21udAfeYnkuK8YupidWzfv50BOQO8DseYXu+QiURVVUSeBya6rzd35uSq+jxOB31i2S0Jz2uB\nb7Rz7J3AnW2UrwamdCYO07GmNUmoy/zZb0pySwCoqKmwRGJMN0imaestETku7ZEYTzWvkuiDpq3i\nPGdihi3VWzrY0xiTjGQ6248HLhGRj4G9OFOlqKpOSmtkpkdFQ0Gq4xGI1XgdStoV5zqJpKKm9dgP\nY0xXJJNIzup4F9PbRUNB9mgEGvZBrBGCyXw0eqfsYDYDowMpry73OhRjMkIyd7Z/3BOBGG9FwkGq\nYu7EBfU1EC30NqA0K8krsRqJMd0kmT4S4wPRUJCqWLbzot4fzVvlNVYjMaY7WCIxgJNIdjYlEp90\nuH++93MaYg1eh2JMr2eJxADuqK2427RVl/k1kpLcEhSlcm/mTgVjTE9JZoXEahHZ0+qxRUSeFpGR\nPRGkSb9IKEiNNiWSPd4G0wOaR25VWz+JMalKZmjOL3HmuPoTztDfucCROFOlPIwzM7Dp5aKhIDVN\nS7v4oI+kJM+5KdH6SYxJXTJNW7NU9UFVrVbVPe6sumep6iKgKM3xmR4SDQeowT9NWwNzBhIKhCyR\nGNMNkkkk+0TkAhEJuI8LgFp3m816lyGioQPrtvuhsz0gAYpzi61py5hukEwiuQS4FGf6+M/d598U\nkShwTRpjMz0oEgqy11233Q8TN4INATamuyRzQ+JGYGY7mzN3CT2fiYaCNJBFPBAm4IOmLXD6Sdbu\nWOt1GMb0eskstTsA+DZQmri/qn4rfWGZnhYNBwFoDPUh7IOmLXBqJFV1VVTXV5MXzvM6HGN6rWRG\nbT0D/BP4BxDrYF/TS0VDTiJpCPYh7INRW3Bg5FZFTQVH9z3a42iM6b2SSSQ5qnpj2iMxnmqqkTQE\nc3zR2Q4H7iUpry63RGJMCpLpbH9ORM5JeyTGU001krpgH98kksQaiTGm65JJJN/HSSb73bvaq0Uk\n82999pmmGkldMMcXNyQC5IfzyQvn2QJXxqQomVFb1gvpA5EsJ5Hslxyo+9zjaHpOSa5NJ29MqtpN\nJCJytKpuEJEvtrVdVd9KX1impwUCQnZWgP0ShVp/1EjAad4q213mdRjG9GqHqpFcB8wDft7GNgWm\npSUi45loOMg+n6zb3qQkt4RXt7xKXOMExCbDNqYr2k0kqjrP/ffUngvHeCnadHd7w16IxyGQ+V+s\nxbnF1Mfr2b5/OwNzBnodjjG9UlILc4vIlzj4hsTfpykm4xFnBuCmaVJqIJLvbUA9oHkW4OpySyTG\ndFEyd7Y/ijNt/GoO3JCogCWSDBMJBdkTT5i40QeJpHldkpoKvjioze5AY0wHkqmRTAHGqarN9Jvh\nouEg1Q3+WbcdYGjuUAShvNombzSmq5JpBF8LDE53IMZ70VCQqubldv3R4R4OhhmYM9BmATYmBcnU\nSPoD60VkOVDXVKiqs9IWlfFEJBRkd6NbI/FJIgGnn8RqJMZ0XTKJ5LZ0B2EOD9FwkN0xfzVtgdNP\n8uanb3odhjG91iETiYgEgdtsCLA/REMBKmM+rJHklvDsvmepj9UTDoa9DseYXueQfSSqGgPiIlLQ\nQ/EYD0VDQXY2uF+kPlncCpymLUWprKn0OhRjeqVkmrZqgHdF5EVgb1Ohql6btqiMJyLhINsbws6n\nwifL7ULCdPI15ZQWlHobjDG9UDKjtp4Cfgy8BqxKeHRIRKaLyPsiUiYiN7WxPVtEFrnb3xSR0oRt\nN7vl74vIWa2OC4rI2yLyXDLpI5eiAAAW7UlEQVRxmOREQ0GqG4NoIOSvpq2m6eSrbfJGY7oimdl/\nf9eVE7v9Kw8AZwDlwAoRWayq6xN2uxLYpaqjRGQucBdwoYiMA+YC44GhwD9EZIzb1AbO1PbvAZl/\nx1wPctYkEcjO9VXTVv9of8KBsM0CbEwXJXNn+2jgp8A4INJUrqojOzh0KlCmqhvd8ywEZgOJiWQ2\nB0aFPQHcLyLili9U1Tpgk4iUued7XURKgBnAnTgTS5pu0rQmSTyUS3DDX2HXZm8DShcR+NL3YMTJ\nAAQkQHFesd1LYkwXJdNH8lvgVuAe4FTgCpJrEisGElcMKgeOb28fVW0UkSqgn1v+Rqtji93nvwRu\nAA65ToqIzMOZvZhhw4YlEa6JuKsk7j36G+SXL4V9O7wNKF0+Xwc5/ZsTCTj9JHYviTFdk0wiiarq\nSyIiqvoxcJuIrAJuSXNsBxGRc4GtqrpKRE451L6qOh+YDzBlyhSb3iUJTcvtbp1yHfnn3OpxNGn0\n8NkH1bZKckt4Z9s73sRjTC+XTM2iTkQCwIcico2InA/kJnFcBXBEwusSt6zNfUQkCygAdhzi2C8D\ns0RkM7AQmCYif0giFpOEpkSyvz7ucSRpVlQKuz9uUVSSV0J1fTVVdVXexGRML5bsmu05wLXAscA3\ngcuTOG4FMFpERohIGKfzfHGrfRYnnGsO8LI7OeRiYK47qmsEMBpYrqo3q2qJqpa653tZVb+ZRCwm\nCU19JPsbYh3s2csVDYc9ldDYPOMPJbnuyC3rcDem05IZtbUCQETiqnpFsid2+zyuAZYAQeBhVV0n\nIncAK1V1MfAQ8Kjbmb4TJzng7vc4Tsd8I/DdhBFbJk2a+kgyPpEUDgcUdm+B/qMAKM47MJ38uH7j\nPAzOmN4nmVFbJ+J84ecCw0RkMvA/VfU7HR2rqs8Dz7cquyXheS3wjXaOvRNnZFZ7514KLO0oBpO8\nA01bGZ5Iikqdf3dtPpBImm5KtA53YzotmaatXwJn4fRdoKrvACcf8gjTK+W4TVu1mV4jKRru/Lt7\nc3NRXjiPguwCa9oypguSWmpXVbc4t3c0y/BvGn/yTR9J7mAIZrc5cuv5Tc+zdvtab+LqAXPGzGHO\nmDleh2EyTDKJZIu7ZruKSIgDd5WbDBPxS9NWIACFw2BXy5Fbl4y9hL9t+ptHQaXfhp0bWLhhoSUS\n0+2SSSRXAffi3BBYAfwd6LB/xPQ+Ub90toPTT9KqRjLzyJnMPHKmJ+H0hAdWP8D8NfPZ17CPnFCO\n1+GYDNJhH4mqblfVS1R1kKoOdIfbXtYDsZkeFgoKwYBkfo0EnH6SVveSZLqJ/ScS1zjrdqzzOhST\nYZLpbG+LzXGVgUSEaCjonxpJbRXs3+V1JD1mUv9JAKzZtsbjSEym6WoikY53Mb1RxC+JpNAdubXL\nP7WSwkghw/OHWyIx3a6ricTmrspQ0XCAWl80bZU6//qseWtS/0ms2b4GZwIJY7pHu4lERKpFZE8b\nj2qcNUJMBvJP01ZTjWSzp2H0tIkDJrJ9/3Y+2/uZ16GYDNLuqC1VPeQ07SYz+SaRRAogWuSrpi2A\nSQOcfpJ3tr/DkNwhHkdjMkVXm7ZMhoqEgv4YtQVOP4nPaiRjisaQHcy2fhLTrSyRmBai4WDmT5HS\npI3p5DNdKBBifL/xlkhMt7JEYlrwTdMWuPeSfALxDF9/pZWJ/Sfy3o73aIg1eB2KyRCWSEwL/kok\npRCrh+pPvY6kR00aMIn6eD3v73rf61BMhrBEYlqIhIOZv0Jik0J/jtxq7nC3pYVNN7FEYlqIhnzW\nRwK+6ycZ3GcwA3MGWj+J6TaWSEwLTU1bvrhhreAIQHxXIwGYPGCyJRLTbSyRmBai4SCxuNIQ80Ei\nyQpDQYnv7iUBp8O9vKacnbU7vQ7FZABLJKYF36zb3qTQf7MAw4F+kne3vetxJCYTWCIxLTStSeKr\nfhIfNm2N6zeOoAStw910C0skpoVo2PlI+Obu9qLhzvDfhlqvI+lR0awoY4rGsGa79ZOY1FkiMS34\napVESBi59YmnYXhh0oBJrN2+lljcJ79rkzaWSEwLvuwjAd/2k+xt2Mumqk1eh2J6OUskpoXmPhI/\nNW2BL/tJmldMtOYtkyJLJKaFaNhnNZLcQZAV8WUiGZ4/nPxwvt1PYlJmicS0kOO3RCLiy+nkAUSE\niQMmWo3EpMwSiWmhuY/EL01b4Mvp5JtM7j+Zsl1l7G3Y63UophezRGJa8N19JOD0k+z6GPwwLUwr\nkwZMQlHWbl/rdSimF7NEYlrwXR8JODWSuj2wf5fXkfS4Cf0nAFg/iUlJu2u2G3+KZDmJZJ+fmrYS\np5PP6etpKD2tILuA0vxSllUsY2y/sV6HkzajCkcxuM9gr8PIWGlNJCIyHbgXCAILVPW/Wm3PBn4P\nHAvsAC5U1c3utpuBK4EYcK2qLhGRI9z9BwEKzFfVe9N5DX4TCAjZWQH/1UjA6Scp/qKnoXhhyuAp\nPPHBE1z9j6u9DiVtSvNLWXzeYkTE61AyUtoSiYgEgQeAM4ByYIWILFbV9Qm7XQnsUtVRIjIXuAu4\nUETGAXOB8cBQ4B8iMgZoBH6oqm+JSB6wSkRebHVOk6JoOOif+0gg4V4Sf3a433DcDZw36jyvw0ib\n1ytf54HVD/Du9nebJ6s03SudNZKpQJmqbgQQkYXAbCDxS382cJv7/AngfnH+ZJgNLFTVOmCTiJQB\nU1X1deBTAFWtFpH3gOJW5zQpioaC7NhbT+Xu/V6HkhYiMDg/cuCv0+w8yOnnyyHA4My7NXnAZK/D\nSJuRBSNZ8O4Cnv3oWUskaZLORFIMbEl4XQ4c394+qtooIlVAP7f8jVbHFiceKCKlwBeAN7szaAP5\nkRDPrfmU59Zk7lrm3z9tND84Y8yBAp9OJ+8HeeE8TjniFF7Y/AI3HHcDoWDI65AyTq/sbBeRXOBJ\n4N9VdU87+8wD5gEMGzasB6Pr/X5+wWTWVVZ5HUbaPPjqRpZvarWgU1EpfLrak3hM+s0cOZMlm5ew\nrGIZpw471etwMk46E0kFcETC6xK3rK19ykUkCyjA6XRv91gRCeEkkT+q6lPtvbmqzgfmA0yZMsV/\nNwikYEJxAROKC7wOI23WlFex+J1KVPVA81bRcHjvWYjHIBD0NkDT7b5U/CX6Rvry7MZnLZGkQTrv\nI1kBjBaRESISxuk8X9xqn8XA5e7zOcDL6iwWvhiYKyLZIjICGA0sd/tPHgLeU9VfpDF2k8EmFhdQ\nXdvIJzv3HSgsKoV4A+yp9Cwukz6hQIjppdN5dcur7KlvsxHDpCBtiURVG4FrgCXAe8DjqrpORO4Q\nkVnubg8B/dzO9OuAm9xj1wGP43SivwB8V1VjwJeBS4FpIrLafZyTrmswmamptrW2IuELxcfTyfvF\nzCNnUh+v58XNL3odSsZJax+Jqj4PPN+q7JaE57XAN9o59k7gzlZlywAbCG5SMnpQLqGgsLayihmT\nhjiFTfeS7NoMpSd5FZpJo/H9xlOaX8qzG5/l62O+7nU4GcWmSDG+k50VZMygPNZWJAwoKCgBCfj2\nXhI/EBFmHjmTVZ+voqKmdXetSUWvHLVlTKomDC3gxfc+P9DhHgw5yeTTd6Ayg0dv9R8N4T5eR+GZ\nGSNn8Ku3f8VfN/6VeZPmeR1OxrBEYnxpQkkBi1ZuobKqluLCqFPYbzR8uMR5ZKqjz4W5f/Q6Cs8U\n5xZz7KBjefajZ/n2xG/blCndxBKJ8aUJQ/MBWFtRdSCRzH4AKt/2MKo0e/fPsOE5qN0DkXyvo/HM\nzJEzue3121i3Y13z7McmNZZIjC+NHZJPMCCsq6jirPHurLD5Q5xHpsrpC+uegg+WwKQ2x7j4whml\nZ/B/3vw/PPvRs5ZIuol1thtfioSCjBqQy9pKH91TUDIVcgfD+r94HYmn8sP5zVOmNMQbvA4nI1gi\nMb41vjifdysydyqYgwQCMG4WlP0D6mq8jsZTM4+cyc7anfyr4l9eh5IRrGnL+NbE4gKeequCrXtq\nGZgf8TqcnjF2FiyfD2UvwvjzvY7GM18u/jJF2UU88cETDMnN3ObMLMliZOHI9L9P2t/BmMNU8x3u\nlVVM80siGf4lyOkP65/xdSIJBUKcPeJs/rThTywtX+p1OGnTL9KPpRcuTfv7WCIxvjV2SD4izlQp\n044e5HU4PSMQhLEzYc3j0LAfQlGvI/LM977wPaYOnkqcuNehpE04EO6R97FEYnwrNzuLEf37tLzD\n3Q/GzYJVv4Wyl2DsuV5H45nccC6nDT/N6zAygnW2G1+bMLTAf4mk9CsQLXKat4zpBpZIjK9NLC6g\nsqqWHTV1XofSc4IhOHoGfPACNProuk3aWCIxvja+2LnDe52f7icBGDsb6vbAxqVeR2IygCUS42vj\nhx4YueUrI78K2QXWvGW6hSUS42sF0RDD+uawrsJnNZKsbDjqbNjwV4jZ3d0mNZZIjO9N8Nsd7k3G\nzYLa3bDpNa8jMb2cJRLjexOKC/hk5z6q9vnsL/Mjp0E415q3TMoskRjfm+D2k6z71Ge1klAUxpzl\nNm81eh2N6cUskRjfG++uTeK7fhJw5t7atx0+sckLTdfZne3G9/rlZjO0IOK/kVsAo8+ArCi8/QeI\nFHodTfr0HQnZuV5HkbEskRiD00/iyw73cB+neWvNIueRqQqGwbdfhtwBXkeSkSyRGIOTSF5873Nq\n6hrJzfbZf4sZv4CJGbxiYm0V/PU6ePwyuOwZyOqZiQz9xGf/Y4xp24TifFThvU/3cFxpX6/D6Vl9\n+mX+5I1Z2fDklfC3G2DmL72OJuNYZ7sxHBi55bsJHP1i4hz48r87sx6vWOB1NBnHaiTGAAPzIwzI\ny+a5NZ8SV6+jSZ+TR/dn9KA8r8Pwxmm3wNb34G83woCjofQkryPKGJZIjHF9ZVR/nnq7glUf7/I6\nlLTJzc7i0Sun8oVhRV6H0vMCQfj6b2DB6bDoUpj3ChSVeh1VRhDVDP7zyzVlyhRduXKl12GYw1w8\nrlTXZe6Nebv21nP5b5ezs6aeP377eCaVZPBw30PZXgYLpkF+CVz5dxsW3A4RWaWqU5La1xKJMf5R\nuXs/F85/nap9Dfzp2yc0r1vvO2UvwR/nQMlxMGiC19GkT3YenHF7lw61RNKKJRJjDtiycx9z57/B\n3vpGHvv2CYwdku91SN5Y8RC8ehfEY15Hkj59+sN33+zSoZZIWrFEYkxLH+/Yy4UPvkF9LM7CeScw\nxq8d8KZdh00iEZHpwL1AEFigqv/Vans28HvgWGAHcKGqbna33QxcCcSAa1V1STLnbIslEmMOtmn7\nXi588HXiqjx0+XEMLoh4HVLa5EdCRMNBr8PoVQ6LRCIiQeAD4AygHFgBXKSq6xP2+Q4wSVWvEpG5\nwPmqeqGIjAMeA6YCQ4F/AGPcww55zrZYIjGmbWVba5g7/3W219R7HUpaBQTGDMpjYnEBk44oZFJx\nAUcPySM7y5JLezqTSNI5/HcqUKaqG92gFgKzgcQv/dnAbe7zJ4D7RUTc8oWqWgdsEpEy93wkcU5j\nTJJGDczlL9/9Mv/8cDuZ2sqtKJ9X1bKmooqXNmzlz6vKAQgFhSP65hAU8TjC9CnKCfP4VSem/X3S\nmUiKgS0Jr8uB49vbR1UbRaQK6OeWv9Hq2GL3eUfnBEBE5gHzAIYNG9a1KzDGB0qKcrhoqj/+j6gq\nFbv38255FWsqqvhkxz6UDM2gOE16PSFjb0hU1fnAfHCatjwOxxhzGBARSopyKCnK4eyJQ7wOJ2Ok\nc66tCuCIhNclblmb+4hIFlCA0+ne3rHJnNMYY0wPSmciWQGMFpERIhIG5gKLW+2zGLjcfT4HeFmd\n3v/FwFwRyRaREcBoYHmS5zTGGNOD0ta05fZ5XAMswRmq+7CqrhORO4CVqroYeAh41O1M34mTGHD3\nexynE70R+K6qxgDaOme6rsEYY0zH7IZEY4wxB+nM8F9bj8QYY0xKLJEYY4xJiSUSY4wxKbFEYowx\nJiW+6GwXkW3Ax108vD+wvRvD6S3suv3Frttfkrnu4ao6IJmT+SKRpEJEViY7ciGT2HX7i123v3T3\ndVvTljHGmJRYIjHGGJMSSyQdm+91AB6x6/YXu25/6dbrtj4SY4wxKbEaiTHGmJRYIjHGGJMSSyTt\nEJHpIvK+iJSJyE1ex5NOIvKwiGwVkbUJZX1F5EUR+dD9t8jLGLubiBwhIq+IyHoRWSci33fLM/q6\nAUQkIiLLReQd99pvd8tHiMib7md+kbtUQ0YRkaCIvC0iz7mvM/6aAURks4i8KyKrRWSlW9Ztn3VL\nJG0QkSDwAHA2MA64SETGeRtVWj0CTG9VdhPwkqqOBl5yX2eSRuCHqjoOOAH4rvs7zvTrBqgDpqnq\nZOAYYLqInADcBdyjqqOAXcCVHsaYLt8H3kt47YdrbnKqqh6TcP9It33WLZG0bSpQpqobVbUeWAjM\n9jimtFHV13DWg0k0G/id+/x3wHk9GlSaqeqnqvqW+7wa58ulmAy/bgB11LgvQ+5DgWnAE255xl27\niJQAM4AF7mshw6+5A932WbdE0rZiYEvC63K3zE8Gqeqn7vPPgEFeBpNOIlIKfAF4E59ct9vEsxrY\nCrwIfATsVtVGd5dM/Mz/ErgBiLuv+5H519xEgb+LyCoRmeeWddtnPW0rJJrMoaoqIhk5TlxEcoEn\ngX9X1T3OH6mOTL5ud8XRY0SkEHgaONrjkNJKRM4FtqrqKhE5xet4PHCSqlaIyEDgRRHZkLgx1c+6\n1UjaVgEckfC6xC3zk89FZAiA++9Wj+PpdiISwkkif1TVp9zijL/uRKq6G3gFOBEoFJGmPy4z7TP/\nZWCWiGzGaaqeBtxLZl9zM1WtcP/divOHw1S68bNuiaRtK4DR7oiOMM5a8os9jqmnLQYud59fDjzj\nYSzdzm0ffwh4T1V/kbApo68bQEQGuDURRCQKnIHTR/QKMMfdLaOuXVVvVtUSVS3F+f/8sqpeQgZf\ncxMR6SMieU3PgTOBtXTjZ93ubG+HiJyD06YaBB5W1Ts9DiltROQx4BScqaU/B24F/gI8DgzDmYL/\nAlVt3SHfa4nIScA/gXc50Gb+nzj9JBl73QAiMgmnczWI88fk46p6h4iMxPlrvS/wNvBNVa3zLtL0\ncJu2/kNVz/XDNbvX+LT7Mgv4k6reKSL96KbPuiUSY4wxKbGmLWOMMSmxRGKMMSYllkiMMcakxBKJ\nMcaYlFgiMcYYkxJLJMZ0kYjE3NlUmx7dNsGjiJQmzsZszOHMpkgxpuv2q+oxXgdhjNesRmJMN3PX\nfrjbXf9huYiMcstLReRlEVkjIi+JyDC3fJCIPO2uD/KOiHzJPVVQRH7jrhnyd/cudETkWncdlTUi\nstCjyzSmmSUSY7ou2qpp68KEbVWqOhG4H2eGBIBfAb9T1UnAH4H73PL7gFfd9UG+CKxzy0cDD6jq\neGA38HW3/CbgC+55rkrXxRmTLLuz3ZguEpEaVc1to3wzzsJRG92JIT9T1X4ish0YoqoNbvmnqtpf\nRLYBJYlTc7hT27/oLjqEiNwIhFT1JyLyAlCDM43NXxLWFjHGE1YjMSY9tJ3nnZE451OMA32aM3BW\n8PwisCJh9lpjPGGJxJj0uDDh39fd5//CmXkW4BKcSSPBWeb0amhecKqgvZOKSAA4QlVfAW4ECoCD\nakXG9CT7S8aYrou6qww2eUFVm4YAF4nIGpxaxUVu2feA34rI9cA24Aq3/PvAfBG5EqfmcTXwKW0L\nAn9wk40A97lrihjjGesjMaabuX0kU1R1u9exGNMTrGnLGGNMSqxGYowxJiVWIzHGGJMSSyTGGGNS\nYonEGGNMSiyRGGOMSYklEmOMMSn5/wE2E9+0luLFUwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UlkEn5XxFPkd",
        "colab_type": "text"
      },
      "source": [
        "##Training the  model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kVao6lbWCizF",
        "colab_type": "code",
        "outputId": "26f79b69-6f63-4c39-d5c9-ef12564d04ef",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 185
        }
      },
      "source": [
        "epochs = 10\n",
        "num_batches = 60000//batch_size\n",
        "\n",
        "initial_learning_rate = nd.array([.001], ctx = model_ctx)\n",
        "drop = 0.6\n",
        "epochs_drop = 2\n",
        "\n",
        "losses = []\n",
        "accs = []\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    cumulative_loss = 0\n",
        "    cumulative_acc = 0\n",
        "    \n",
        "    learning_rate = step_decay(initial_learning_rate, drop, epochs_drop, epoch)\n",
        "    \n",
        "    for features, labels in training_data:\n",
        "        features = features.as_in_context(model_ctx).reshape((-1, 784))\n",
        "        labels = labels.as_in_context(model_ctx).one_hot(10)\n",
        "        with autograd.record():\n",
        "            output = neuralnetworks(features)\n",
        "            loss = categoricalcrossentropy(output, labels)\n",
        "        loss.backward()\n",
        "        \n",
        "        sgd(params, learning_rate)\n",
        "        \n",
        "        cumulative_loss += loss\n",
        "        acc = accuracy(output, labels)\n",
        "        cumulative_acc += acc\n",
        "        losses.append(loss.asscalar())\n",
        "        accs.append(acc.asscalar())\n",
        "    print(f'Epoch: {epoch} | Loss: {cumulative_loss.asscalar()/num_batches:.5f} | Accuracy: {cumulative_acc.asscalar()/num_batches:.5f} | Learning Rate: {learning_rate.asscalar():.10f}')"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch: 0 | Loss: 78.37689 | Accuracy: 0.54024 | Learning Rate: 0.0010000000\n",
            "Epoch: 1 | Loss: 37.99153 | Accuracy: 0.78772 | Learning Rate: 0.0010000000\n",
            "Epoch: 2 | Loss: 30.33730 | Accuracy: 0.83274 | Learning Rate: 0.0006000000\n",
            "Epoch: 3 | Loss: 28.11451 | Accuracy: 0.84250 | Learning Rate: 0.0006000000\n",
            "Epoch: 4 | Loss: 25.74679 | Accuracy: 0.85754 | Learning Rate: 0.0003600001\n",
            "Epoch: 5 | Loss: 24.83582 | Accuracy: 0.86161 | Learning Rate: 0.0003600001\n",
            "Epoch: 6 | Loss: 23.75982 | Accuracy: 0.86813 | Learning Rate: 0.0002160000\n",
            "Epoch: 7 | Loss: 23.25912 | Accuracy: 0.87173 | Learning Rate: 0.0002160000\n",
            "Epoch: 8 | Loss: 22.63730 | Accuracy: 0.87475 | Learning Rate: 0.0001296000\n",
            "Epoch: 9 | Loss: 22.37795 | Accuracy: 0.87667 | Learning Rate: 0.0001296000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JJOc7DOepwEE",
        "colab_type": "text"
      },
      "source": [
        "##Lets see test accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dvvQC3oQYu5A",
        "colab_type": "code",
        "outputId": "45a6dc18-98b8-4f10-ec25-9f6dc07ca98b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "acc = 0.0\n",
        "batches = 0\n",
        "for features, labels in testing_data:\n",
        "    features = features.as_in_context(model_ctx).reshape((-1, 784))\n",
        "    labels = labels.as_in_context(model_ctx).one_hot(10)\n",
        "    predictions = neuralnetworks(features)\n",
        "    acc += accuracy(predictions, labels)\n",
        "    batches += 1\n",
        "print(f'Test Accuracy: {acc.asscalar()/batches}')"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Test Accuracy: 0.8699243630573248\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hIBgjWVBYu3t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot(losses = losses, accs = accs, model = neuralnetworks, samples = 5):\n",
        "    plt.plot(losses, 'r')\n",
        "    plt.title('Loss during Training')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Loss')\n",
        "    plt.show()\n",
        "    \n",
        "    plt.plot(accs, 'g')\n",
        "    plt.title('Accuracy during Training')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Accuracy')\n",
        "    plt.show()\n",
        "    \n",
        "    for i, batch in enumerate(test_mnist):\n",
        "        features = batch[0].as_in_context(model_ctx).reshape((1, 784))\n",
        "        labels = batch[1]\n",
        "        predictions = model(features).argmax(1).asscalar()\n",
        "        plt.imshow(features.reshape((28, 28)).asnumpy())\n",
        "        plt.title(f'Predicted Class: {predictions}, Target Class: {labels}')\n",
        "        plt.show()\n",
        "        if i == samples:\n",
        "            break"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mkorWu1EYu2b",
        "colab_type": "code",
        "outputId": "562e4f03-47d4-4064-d1cf-87c4df764507",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "plot(samples = 10)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KMM7TAw/k97344srTaAY33lg8CH70URgqJOm57mmDTLFWZIUqqYNYtKj1iABp\nLV/euoFHhpXfWYzF9HngQDPbD1gTWB+4COhjZt2jXMQgoMI2j01g+PCsUyDllLthHHNM6SKbaooR\n0uQaIPTUT9OGPr7Pb34Tpu7Jx95wQ764Ja5YfUG83iLtDanwBjZmTCgiSxsYx43LdzrMFZv95jet\nz5t7DzfeGAJQvHHI+eeHDo3rrJPueknGjw+BuVu38Mx3CPVEffrATjsV/964h9Z0SUVzffvCzjsX\n74xazvz5YaSDDANEw3MQ7n6muw9y98HAaOAhdz8ceBg4JNrtSCBFA/Qm1LN5G18JoYiolDTl+ZUG\niVIdBgulqZTOVQrHnXlmfrywuNGj0/XlqEThr+L2Vp4ec0y+biCXC3j66fz2+I3x0ENDh77Pfja/\nLtc4IOlJe4VpK1W3sfbaoXgnZ999ww0+rvCYFStCX4o990zep1iuJ/eY3VKPTN15Z/jSl1oHiA02\naOhT9JqpH8TpwClmNoNQJ9ExHzZbycBy0njVZPnjZs5s26u6lupRETl6dG3Pl+tBDqHIKFdv055f\nuEOGhEEf054j7ei2pYJXvNK+VOX8TjvlA9duu+VHDIbk4sCkoq5CuQEuc0VuSdd/9dXWy2ZhCJwG\nPoc70+G+3f0R4JFofiawY5bpqYn4LxuRSp1zTu3P2Z7WNeWcdFJ+fuXK1s1TS40InKTweRelbu5m\n+e2V5mCGD4dPfKL0PvFhdJ56Kow7lhPv3JeUOxs4sHWaPvoI1lwzv3zLLWGolrj4iMjQuld7hj20\n9TwIEamNX/86jKWVU8kzRSDcCONDWeRG302qgI/nNHKDDqZ5sBSENMbTWeiuu9o+1zs+eGX8hp3m\n5j1iROs6n1y9EeTfR+EzWeLDzuSKKONPglyxoiHP71CAEJHaKHXTTSPX47xQ0uCH8QBRSR+kNK29\nCodEKSVe3FbsHIXnSypGK9UR9LzzwjReL9MgzVQHISLSVlIHvzR1FSec0LYF0cknlz/u9NNLb0+T\na9hmm9bL5YY9KTcOWUYUIOop16ok3jJCRNovTYC45JLKRwiul3HjwvAiK1a07aBXzSi5F1xQu7SV\noABRT4cdlnUKRDqnNC2F6mXvvas7br31Qh+R+Jhdzz0XesJX6vTTk4cwrzHVQYiI1FtujKW//a12\n52xvk+0UlIOohzvuCMNu5LKSnegRhCLSJMoNgVIDChD1cOCBoa31/vuH5d13L39MvJ20iEg5xx1X\n90soQNTTHnuESqg02cpqx2sREakTBYhGGDCg/D6FYzhV2gtVRKTGFCAa5amnWneY+b//C8VKL78c\nnmg2bFjr/Xv3zs8/+mh4XoGWhGbRAAAQaUlEQVSISAOZZzjOR3uNGDHCJ5V66Hkzij8Qpdi2u++G\nrbcOz06O79uJnnUrIjVQ5f3bzCa7e8ID3ltTDqIZlXscpYhIAyhANKtcbmHQoGzTISJdlgJEs8r1\nrkx6CIyISAMoQDSTBx/MN3fdeOPwGMQ778xv/9WvskmXiHRJGmqjmeyxR+vl+POBITwSUUSkQZSD\n6Ei+/e2sUyAiXYgCRKPdcw/MmFHdsWut1Xr5G98Iw3qIiNRBw4uYzGwz4GpgAODAWHe/yMz6ATcA\ng4FZwKHu/m6j01d3I0fW5jy59s+TJ8OECcn7fPzj0Ldv2EdEpEJZ5CBWAKe6+zBgJ+B4MxsGnAE8\n6O5DgQejZSm0+eatl3PNYYcPb9tpZv31M33guYh0bA0PEO4+192fiebfB14CBgKjgPHRbuOBgxqd\ntg5h2jR47738cmHP7H/9KzxIZM89YezY4ucZUbYTpYh0cZm2YjKzwcB2wFPAAHefG22aRyiCSjrm\nWOBYgM0Lf013BWuu2Xpo8MIA8YUvhOkDD5Q+z223wWabld7nwgthnXVUOS7SRWVWSW1m6wK3AN93\n9/fi2zwMEJVYNuLuY919hLuP6N+/fwNS2uSGDAnTU09N3r7BBsnr0/TQ/tKX4JhjQlGViHQ5mQQI\nM+tBCA7XuPut0er5ZrZJtH0TYEEWaetwevcOuYfCPhM511wD554bhhy/5JJ05zz0UFi8GLbdNiwX\nGyTwyisrT6+IdBgNDxBmZsA44CV3vyC2aQJwZDR/JHBHo9PWKfXvD2eeCfPmwfHHh4emF5Mrcrri\ninS5hqOOgk02ab0uNwJtORdcAP/9L9x7b7r90+rbF669trbnFOmisshBfB74BrCHmU2JXvsBvwa+\nbGbTgb2iZam1yy6DJUtar7v11vCAosceg+uvD/UOcY88EqbPPlv+/GPGwE9+Un6/o46CoUNh773z\n6x5/HJ55pvyxxbz8Mrz2Gqyh7j0iNeHuHfa1ww47uLTD/fe7/+AHlR0TCrTCy919441br1u5Mqx/\n5hn3E09svS33mjq19TmnTHGfNi2/vGqV+09+0vqY889PPldhetzdb7ghefuYMeXP0Zlfxx2XfRr0\nqu2rSsAk9/L3WP3U6sr22gt++9v2neOqq+Czn80v5369b7cdXHQRvPlm6/0/9anwivvMZ+CTn8wv\nJ9V5FPYiL6VYxXw8nbUwf37oGd8Mbrwxef27sb6maeugpGP4+tfrfgkFCKnM88+Heo2cffaBp59O\nd+wvfxmKsdL47ndbL3fr1nafvn3h7bfbrt9zT7jpprbrCwPP+ecXv/5hhyWvd8/Pb7RR7XrGl5NU\nbPe73+XnDzkk+bg+ffLz9Xoi4Xnn1ee8Sc49t3HXanbx72KdKEBIZbbZBmbPhqVLKz92773DTT2N\ngQPDP8Axx4TleL2CO/ztbzBpEvTrl3x8/Ia59dbJ+5S6ubuHyu7ddw/L/fuH4deTTJwIJ51U/Fw5\no0eX/6eOP7c8rjBgApxySvlrNsKqVeX3+elP4eijW6/bdNPKr1XqbzZxYvrvV7M6+OAw3WGH8vsq\nQEhT6tmzuqHHq/lC5wJAYauqww8PY02lscsuYVr4C3rrrUMz4KROhUOHhlzEl74Ulr/3veJNiUeM\nCE2Dk6yxRijaOvNMuO661tviz/rIGTYsOaCV+/Vfbvs++5TeXszEiaW3X3ghtLSUP8/Pf972eSZz\n5pQ/rm9fOPbY8vtB+D6cc06Y32mn0vuOGlW+MUNhQGuEbbYJ0wMOaPy1EyhASO0k3djWXbd95/z5\nz+HSS+FrXyu+z/vvh1cxucBkFupc1lgDnnwyrPvf/w1FUjnbbAP33Rd+8UL41R+fApx4Ipx2WvI1\nAP785/z8KaeEIrikopEDDgjngtBy7KOP8unM2XdfmD69fcVD7vCPf4T5Slp4nX9+8pAsQ4fm5zfc\nEJYtK36O00/Pfzb9+uV7+lfikkugV68wX+pziOcmS/0Y2XJLuP324sWIEL4Dl19evOiu1Pf6jHYM\nI7fXXmH65S8X32ePPcLoBhdfXP110kpTk92sL7ViaiLLlrm3tCRvu+ii0OLi3Xfbd43ttqus5Uau\npcfNN4fp5Mnl963Wo4+G47/wBffp0/Pne/nltvuedZb7pElhfulS9wMOcJ85M7/905/OH3/yyWHd\nm2+G5QEDWqc1aT732mCDttduaSndIiz3PiC0Jks67+mnux9xRJgfP979oYfa7vPAA+7//nfyZxVP\n85VXtj7uq191v+++/HKfPmG/WbPczzgjpKlUi54//CHMjxzZett55+Xnc9/Tt992P/vs0PKuVOug\nSy5pvW3zzd0vvbR4OiZPzs9fe23yPmPGuM+e7f63v7l/6lPhPY8bF66X+9zPPjvse8IJYXrMMe7b\nbuv+7LPJn2sFSNmKKfObfHteChBdTEuL+0cfpd8//s++ZEn5fbt3rz5tjzwSzrHrrtWfI2fbbfNp\nP/XUsG7u3LC80UZhusYaYf1117nfcUeYv/de9wsucL/ssnBTiQedQn/8Y/4aW22Vv6m6h+C1fHl+\n3623bn1z+/Wvw83t4IPzn+urr7p///vJN9hCl13mfuCBrdfl3t/DD4flwgARVypAXHxxmD/+ePcn\nn8xvmzvXfb31ygetpPSvWOH+ta+F9fvtF9bdcktyGl54IV1607j66rDvxRen278CChAilfwzTpvm\nPm9e9ddauDBc66abqj9HzvDh+bRPnx7WzZsXlvv3d//gA/cPP2z/deIBYsWKfB+WQrNmhaCQ23/i\nxOT9PvggbP/Yx9qfth49wrkOOqh4usH9s59t/Xe+6qowf9ZZrc9T7odFuRv4jBlh/V/+EpZvvTW/\n78Ybhz5FS5cmn/uee0JQzPUZWn/9dJ/BqlXut91W/O/SDmkDhIV9O6YRI0b4pEmTsk6GNKvCkW47\niu23D73WJ03Kt2ZZsCCMp7XhhrBwYW2uk/t8Hnkk31orzf6lPs9x40I5etohV4rZYgt45RV46SXY\naqvW27bcMgzTMnNmaF02ZUro7/GVr8DKlaHO6thjQ71F376waBF8+GHrUZALvflmGH9s+XJ45518\n44S4pUtD4wyzcM3ttgvrN9mkbX+fYpYuDfVAlfTrqQMzm+zuZcf8z3S4bxFJkHQj7tsXevRof8fG\nJGmCQ1q1bvmT1P9l4sTQ/yU3knG84rtbNzjhhPzyY4+FCulSwQFCk9tyzW7jQ9AMH56fr6QBQeEw\nNk1OAUI6r8cfh6lTs05F5T7zmTAmVe/e+XU9eoRft1lrVNPPXXcNOYikQSPXXz/9EPTDhoVXPTz7\nbGgBd9999Tl/E1ARk0iz+eij0DR2t93qe51Ki+BaWsIv9EYMhrhsWWjem+sXIDWlIiaRjmrNNesf\nHAD+/vfSfRgK9ehRv7QU6tVLwaEJKECIdFX77591CqTJqSe1iIgkUoAQEZFEChAiIpJIAUJERBIp\nQIiISKKmCxBmNtLMppnZDDNrx7i5IiLSHk0VIMysG/BHYF9gGHCYmdWpG6SIiJTSVAEC2BGY4e4z\n3X05cD0wKuM0iYh0Sc3WUW4g8EZseTbwufgOZnYskHsG4RIzm1bltTYE3qry2M5Cn4E+A9BnAF3v\nM0g13G6zBYiy3H0sMLa95zGzSWnGIunM9BnoMwB9BqDPoJhmK2KaA2wWWx4UrRMRkQZrtgAxERhq\nZkPMrCcwGpiQcZpERLqkpipicvcVZvZ/wL1AN+AKd3+xTpdrdzFVJ6DPQJ8B6DMAfQaJOvTzIERE\npH6arYhJRESahAKEiIgk6pIBojMP52Fmm5nZw2Y21cxeNLOTovX9zOx+M5seTftG683MLo4+i+fM\nbPvYuY6M9p9uZkdm9Z6qYWbdzOxZM/t7tDzEzJ6K3ucNUSMIzKxXtDwj2j44do4zo/XTzGyfbN5J\ndcysj5ndbGYvm9lLZrZzF/wOnBz9D7xgZteZ2Zpd7XvQbu7epV6Eyu9XgI8DPYH/AMOyTlcN398m\nwPbR/HrAfwnDlvwGOCNafwZwXjS/H3APYMBOwFPR+n7AzGjaN5rvm/X7q+BzOAW4Fvh7tHwjMDqa\n/zPwvWj+OODP0fxo4IZoflj03egFDIm+M92yfl8VvP/xwDHRfE+gT1f6DhA63b4KrBX7+x/V1b4H\n7X11xRxEpx7Ow93nuvsz0fz7wEuEf5ZRhJsG0fSgaH4UcLUHTwJ9zGwTYB/gfnd/x93fBe4HRjbw\nrVTNzAYB+wOXR8sG7AHcHO1S+P5zn8vNwJ7R/qOA6919mbu/CswgfHeanpn1BnYDxgG4+3J3X0QX\n+g5EugNrmVl3YG1gLl3oe1ALXTFAJA3nMTCjtNRVlE3eDngKGODuc6NN84AB0Xyxz6Mjf04XAqcB\nq6LlDYBF7r4iWo6/l9XvM9q+ONq/I7//IcBC4MqomO1yM1uHLvQdcPc5wPnA64TAsBiYTNf6HrRb\nVwwQXYKZrQvcAnzf3d+Lb/OQd+6U7ZvN7ABggbtPzjotGeoObA/8yd23A5YSipRW68zfAYCofmUU\nIVhuCqxDx8r9NIWuGCA6/XAeZtaDEByucfdbo9Xzo2IDoumCaH2xz6Ojfk6fBw40s1mE4sM9gIsI\nxSa5jqHx97L6fUbbewNv03HfP4RfubPd/alo+WZCwOgq3wGAvYBX3X2hu7cAtxK+G13pe9BuXTFA\ndOrhPKJy03HAS+5+QWzTBCDXCuVI4I7Y+m9GLVl2AhZHxRD3AnubWd/o19je0bqm5u5nuvsgdx9M\n+Ns+5O6HAw8Dh0S7Fb7/3OdySLS/R+tHR61bhgBDgacb9Dbaxd3nAW+Y2ZbRqj2BqXSR70DkdWAn\nM1s7+p/IfQZd5ntQE1nXkmfxIrTa+C+hRcKPs05Pjd/bFwhFB88BU6LXfoTy1AeB6cADQL9ofyM8\npOkV4HlgROxc3yJUys0AxmT93qr4LL5IvhXTxwn/2DOAm4Be0fo1o+UZ0faPx47/cfS5TAP2zfr9\nVPjehwOTou/B7YRWSF3qOwD8HHgZeAH4K6ElUpf6HrT3paE2REQkUVcsYhIRkRQUIEREJJEChIiI\nJFKAEBGRRAoQIiKSSAFCpAQzW2lmU2Kvmo3+a2aDzeyFWp1PpNaa6pGjIk3oQ3cfnnUiRLKgHIRI\nFcxslpn9xsyeN7OnzWyLaP1gM3soeq7Cg2a2ebR+gJndZmb/iV67RKfqZmaXRc8tuM/M1srsTYkU\nUIAQKW2tgiKmr8e2LXb3TwOXEEaQBfgDMN7dtwWuAS6O1l8M/NPdP0MYF+nFaP1Q4I/uvjWwCDi4\nzu9HJDX1pBYpwcyWuPu6CetnAXu4+8xocMR57r6Bmb0FbOLuLdH6ue6+oZktBAa5+7LYOQYTnrcw\nNFo+Hejh7v+v/u9MpDzlIESq50XmK7EsNr8S1QtKE1GAEKne12PTJ6L5xwmjyAIcDvwrmn8Q+B6s\nfl5270YlUqRa+rUiUtpaZjYltvwPd881de1rZs8RcgGHRetOIDzJ7YeEp7qNidafBIw1s6MJOYXv\nEZ50JtK0VAchUoWoDmKEu7+VdVpE6kVFTCIikkg5CBERSaQchIiIJFKAEBGRRAoQIiKSSAFCREQS\nKUCIiEii/w/g6pW8PG/wCAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TL57IgI4DOKnpSdzaNb6qsLF/G8vZbc7mvEPOY0LfCYBztfHeBe/5j0foifzB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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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L8YQQY89oLD7yp+6+eRSOI4RoAGoTEKLk1CoCDtxmZg+Y2bLBdjCzZWa20sxW9hC/2woh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\nAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3IblqgbZdifLu3vL258cvWhldduc350TT+w6K92HftT7etr0SKW9PfS5PnAEWLy5P6tge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\nQUAkcwoCIplTEBDJ3P8HjZ4t/tV48JEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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j8E3go3jVyar6Z+u3OklXHScNn8081SlcebvqklFm2u5v2+PElw6x68t7/25J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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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33P17Y+LVKOibMTlqH9gT17veg+OR29gS22ni5x6Id2GgdU8qJl1+/oGE34MpeyTWDlX0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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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o9wD4S4iaQBAkTphAECROmEAQJE6YQBAkTphAECROmEAQJE6YQBAkTt/PJ9ANqidOKNQe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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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trwMLgFutGHfdBtzk7t8bF6+akH3zI28ybfGAtrfE34Ja9saLoWXggFaaHpF53JzsR5AY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\nArw4k5MrAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KRHx7QryaBLYfnde7nSfkB5j33V0fF1Z+SD592/JvQbsOzfv2y0s+m7Wf+/NX1tqOnb0x\nm3b97tlZ+4I/2ZW1r9o5L2t/1rtX1dqGIx+LX3TW1qz9xre9MGvfcnx954+9s/N5R757BTsX5a9Z\nEf0EIuI3wLMm0BdjTAdwiNCYwrEIGFM4FgFjCsciYEzhWASMKZxihhL37MzbtSevh3vn1ttmNgyf\nGs6POmXWuvyQ2pN/+Pqsfe4h9cOBf/HA07Npn/GUh7P2W+46OWs/45m/ztq/8Z3n1tpOPfuX2bQ3\nfqk+LcDRDz+atffPX1Rr2zM/f+sfsiYf1t1xZD7E2H344Vn70Pr1WftU4pqAMYVjETCmcCwCxhSO\nRcCYwrEIGFM4FgFjCsciYEzhHDT9BLoX18eEAfbmR7xyyCMNS3A/t35I7uzl+YGjG9+cX+f6iAX5\n4b67t2c6KQBPml/fUWHLjpnZtJcs+WHWftltx+fTH/HPWfvdxx1Va3toa34a+IXn1Q9DBtj9yoZp\nw79ef023nZTvm9H74/zzsWn4+PCxi/M7uJ+AMWa6YBEwpnAsAsYUjkXAmMKxCBhTOBYBYwrHImBM\n4Rw0/QS2viAfzx6akY8p9z+WP/6O3fVLbD/lsvyY+gfvPTFrH16wKWvfvPWQrP21J91Va/vZl56W\nTfs3816UtS/54WDW/t4nX5C185tZtaYjz16dTbpjYEbW/m+OzvdR+E8nv67WFt35+6Erf9qNbD+2\n/rwBZq1o7/gTiWsCxhSORcCYwrEIGFM4FgFjCsciYEzhWASMKRyLgDGFc9D0E+jenY/79u7IzxM/\nkA/rsndT/TLXF5yWD/r+5NGnZu2/2JDv47DkR/mx75/+2kW1tr7Z+XJZ86Mjs/befDcD+m/NL6ow\nZ1V9wP3R+/L9J/o35s/740vqzxugJ3P44cV7s2l3H5rvmxEH0eOz8VQkXS5pnaR7W7YtlHSTpF+l\n//nZIYwx05bx6NkXgHNHbXs/cHNEnATcnL4bYw5AGkUgIr4PjJ7/6nzgivT5CuA1E+yXMWaK2N82\ngcURMdLxew1QO6GapEuBSwH6yb9nGWOmnrabNyIigNrWp4hYHhHLImJZL/kBIcaYqWd/RWCtpCUA\n6f+6iXPJGDOV7K8IXA9ckj5fAlw3Me4YY6YaVbX5zA7SV4FzgMOAtcCHgGuBq4BjgAeBCyMiP3k+\nMFcL4yy9uE2XO4POeEatbc+h9X0IAFY/L9/0MnNNvg/DnoYA7IzMdARdQ/nr270nf+yugXz6wZl5\n33PH3zsvn7Zvaz7vPQ3pF925o9bW+2h+DofYvCVrH2qwd4rb42a2xsZ8wYyisWEwIi6uMR2Yv2Zj\nzBM4iPo9GWP2B4uAMYVjETCmcCwCxhSORcCYwjlohhJPNnHHPbW2/ln5cch7L35K1t63OR9i7M6P\neqVrsD6UNtybjxYN51dkpys/mrfx+NkQYz4CyFB+lDIDs/P2nvXbam2DKx/KJy4I1wSMKRyLgDGF\nYxEwpnAsAsYUjkXAmMKxCBhTOBYBYwrH/QRG6GoImA/XB8zjycdlk8bu/LGjIeum6a01nDPm0+b6\nGDQeG5pj/ZnJpJqGKQ/XrwYPjMO3noaCzdF0P0RD5g1D9KcTrgkYUzgWAWMKxyJgTOFYBIwpHIuA\nMYVjETCmcCwCxhSO+wmM0BT3zdC1fVfW3r96XtY+ODN//N76mbMrMn0BoqGfwFBffgc1hLubYv3Z\nYzcU+eCsfZo5+/fpauMZdxD1A2jCNQFjCsciYEzhWASMKRyLgDGFYxEwpnAsAsYUjkXAmMJxP4ER\n2on7bsgvc62BI7L2dsfND81oM57eBk1zHUR3vW89OxvKvME83HD35vI2j9NYE5B0uaR1ku5t2fZh\nSask3Z3+zptcN40xk8V4Xge+AJw7xvZPRsSp6e+GiXXLGDNVNIpARHwf2DgFvhhjOkA7DYNvl/TT\n9LqwoG4nSZdKWiFpxQB72sjOGDMZ7K8IfBY4ETgVWA18vG7HiFgeEcsiYlkvmVknjTEdYb9EICLW\nRsRQRAwD/wCcObFuGWOmiv0SAUlLWr6+Fri3bl9jzPSmsZ+ApK8C5wCHSXoE+BBwjqRTqSK5K4G3\nTKKP056hTQ39BBri3b3b23Qg14+gMZbecOz65Raq9F35WHzu+E1zHfRuzxfcnoX59F3b6ud52P/Z\nIw4+GkUgIi4eY/PnJ8EXY0wHcLdhYwrHImBM4VgEjCkci4AxhWMRMKZwPJR4BDXEqzJDjbtmzcom\n3XNoPiA1Y0Nei9UUpsuE4ZqG27a79HgTGqy3NQ2h7tvatGx6wzNst7upjwfXBIwpHIuAMYVjETCm\ncCwCxhSORcCYwrEIGFM4FgFjCsf9BCYAdefH42pgcqe+boz1t5O2yfWmfgSZ9MM9DcOQGx5RXU3d\nANpZmrwgXErGFI5FwJjCsQgYUzgWAWMKxyJgTOFYBIwpHIuAMYXjfgITQDQsa940rXfTuPqugf1P\n33Tspn4ATdOCdzVOSZ4zNqRtmg69gaFFtavjwapH2zv4QYRrAsYUjkXAmMKxCBhTOBYBYwrHImBM\n4VgEjCkci4AxhTOepcmXAl8EFlNFdpdHxKclLQS+DhxHtTz5hRGRX6P7IKVr3tz8Dg1rk3fvzgfj\nh3vzh8/1BejZmU/bOF9Am4+Jrr2ZrNtc86Apfdfe+kUPGro3FMV4LvEg8J6IOBl4DvA2SScD7wdu\njoiTgJvTd2PMAUajCETE6oi4K33eBtwPHAWcD1yRdrsCeM1kOWmMmTz2qbIn6TjgNOB2YHFErE6m\nNVSvC8aYA4xxi4Ck2cDVwLsiYmurLarO82O+wUm6VNIKSSsG8Npwxkw3xiUCknqpBODKiLgmbV4r\naUmyLwHWjZU2IpZHxLKIWNbLjInw2RgzgTSKgCQBnwfuj4hPtJiuBy5Jny8Brpt494wxk814hhI/\nH3gDcI+ku9O2y4CPAVdJ+nfAg8CFk+PiFKEGPYz6oNLQ4fOzSfs254/dnQmjAeydl7crN9S4IQQ4\n3DRct93Z0nPLpjeEPpuGUDfZc8vJm8dpFIGIuI36W+HFE+uOMWaqcY9BYwrHImBM4VgEjCkci4Ax\nhWMRMKZwLALGFI6nHJ8IevJaOtyXj1cPNM3r3RDu7s0MF27qB9AUq28YBd3IcOYOy9kANNywdHnT\nuR3SNN+6AdcEjCkei4AxhWMRMKZwLALGFI5FwJjCsQgYUzgWAWMKx/0ERoim+a/rGe5rCFg39APo\n2Z1P3t0wK9tgfybrNpf3bnfa75y9q35G8HHZB2fm7UMz6ztB+On3OC4LYwrHImBM4VgEjCkci4Ax\nhWMRMKZwLALGFI5FwJjCcT+BEdqYo37nEQ0rKzUMyh/uyfcjGGoYFp/rC6A21+COhsdEk285mtYN\naMq7sf/EIfUF0+h2QWsWuCZgTOFYBIwpHIuAMYVjETCmcCwCxhSORcCYwrEIGFM4jf0EJC0Fvggs\nphpdvjwiPi3pw8CbgfVp18si4obJcnQ6M9ifj/NrqGH+/AYpHm4Ianft3f9jN80H0BTLr120fiT/\nTB+GaLj7htuYqwBguM/PuPEwns5Cg8B7IuIuSXOAOyXdlGyfjIi/njz3jDGTTaMIRMRqYHX6vE3S\n/cBRk+2YMWZq2Kf6kqTjgNOA29Omt0v6qaTLJS2oSXOppBWSVgzQ0M/TGDPljFsEJM0GrgbeFRFb\ngc8CJwKnUtUUPj5WuohYHhHLImJZLw197I0xU864REBSL5UAXBkR1wBExNqIGIqIYeAfgDMnz01j\nzGTRKAKSBHweuD8iPtGyfUnLbq8F7p1494wxk814ogPPB94A3CPp7rTtMuBiSadShQ1XAm+ZFA8P\nADY/Oa+lQzPyw1J7G0KIA7MbhrV21ds12BDDa2ISR9R2NQxz7tme971pWfXBmZMYIlRTbPTAGYo8\nnujAbYwdDS6yT4AxBxvuTWFM4VgEjCkci4AxhWMRMKZwLALGFI5FwJjC8ZTjE8DR38uvLb53fr6Y\ne7flA+ZNU5JH1/73BdBwPp6tofbi3dFd71vTUF8N5vPeOze/7vq8u9fX2hpnYu9qWNN9uM253KcR\nrgkYUzgWAWMKxyJgTOFYBIwpHIuAMYVjETCmcCwCxhSOYgrHPUtaDzzYsukwYMOUObBvTFffpqtf\nYN/2l4n07diIOHxfEkypCPxe5tKKiFjWMQcyTFffpqtfYN/2l0775tcBYwrHImBM4XRaBJZ3OP8c\n09W36eoX2Lf9paO+dbRNwBjTeTpdEzDGdBiLgDGF0xERkHSupF9IekDS+zvhQx2SVkq6R9LdklZ0\n2JfLJa2TdG/LtoWSbpL0q/R/zDUgO+TbhyWtSmV3t6TzOuTbUknfk/QzSfdJemfa3tGyy/jV0XKb\n8jYBSd3AL4GXAo8AdwAXR8TPptSRGiStBJZFRMc7lkh6IbAd+GJEPD1t+ytgY0R8LAnogoh43zTx\n7cPA9k4vV59Wx1oSEXdJmgPcCbwGeCMdLLuMXxfSwXLrRE3gTOCBiPhNROwFvgac3wE/pj0R8X1g\n46jN5wNXpM9XUN1EU06Nb9OCiFgdEXelz9uA+4Gj6HDZZfzqKJ0QgaOAh1u+P8I0KIgWArhR0p2S\nLu20M2OwOCJWp89rgMWddGYMGpern0okHQecBtzONCq7UX5BB8vNDYO/z9kR8WzgFcDbUrV3WhLV\nu9x0ivGOa7n6qULSbKrVtN8VEVtbbZ0suzH86mi5dUIEVgFLW74fnbZNCyJiVfq/DvgG02/J9bUj\nK0Kn/+s67M/vmE7L1UvqpfqhXRkR16TNHS+7sfzqdLl1QgTuAE6SdLykPuAi4PoO+PF7SJqVGmyQ\nNAt4GdNvyfXrgUvS50uA6zroyxOYLsvVSxLweeD+iPhEi6mjZVfnV6fLrSM9BlMI5FNAN3B5RHx0\nyp0YA0knUD39oZqO/Sud9E3SV4FzqIaargU+BFwLXAUcQzUs+8KImPIGuhrfzqGq0v5uufqWd/Cp\n9O1s4AfAPcBw2nwZ1ft3x8ou49fFdLDc3G3YmMJxw6AxhWMRMKZwLALGFI5FwJjCsQgYUzgWAWMK\nxyJgTOH8f64Tuwcuc1XlAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Fy/OWwTRdvZnVkn3R7nD3e8PTFd93PZWr0vutEklgCXCsmU03szrgI8ADFSjH\nO5hZQ7hgg5k1ABcw+KZcfwCYHx7PB+6vYFkOMFimqzczA24GVrr7dQWhiu67vHJVer9VpMdgaAK5\nHqgGbnH3r5S9ED0wsxlkv/6Qzdj8/UqWzczuBM4ju9V0E3AN8CPgbuBIstuyL3P3sl+gyynbeWRV\n2remqy84By9n2eYATwLLga55368mO/+u2L6LlOtyKrjf1G1YJHG6MCiSOCUBkcQpCYgkTklAJHFK\nAiKJUxIQSZySgEji/j+z1tGa2Ik53QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}