04. Learning Rate Decay Methods/03. Exponential Decay - MXNet.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Exponential 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": "46e39607-7d8f-4c48-e8c8-14c54bde8da3",
        "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: 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: 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: 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: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2019.6.16)\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: 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"
          ],
          "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": "8c60b41e-e062-42ed-f8cb-2e30bbc10066",
        "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": "39d3c7a5-2052-40a1-fd0e-51d890f6aade",
        "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 Exponential Based Decay"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eRG13WS5OSAQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def exponential_decay(lr, k, epoch):\n",
        "    return lr * nd.exp(-k * epoch)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lr2eiTs8OTHd",
        "colab_type": "text"
      },
      "source": [
        "##Doing a quick visualization for different k values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJ7dmGxrLNRB",
        "colab_type": "code",
        "outputId": "bbcd08c9-33cc-495a-ef9e-b518670f2c4f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "k1 = nd.array([0.001], ctx = model_ctx)\n",
        "k2 = nd.array([0.01], ctx = model_ctx)\n",
        "k3 = nd.array([0.1], ctx = model_ctx)\n",
        "\n",
        "# smaller the k greater 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_ = exponential_decay(initial_lr, k1, epoch)\n",
        "    lrs1.append(lr_.asscalar())\n",
        "\n",
        "lrs2 = []\n",
        "for epoch in range(epochs):\n",
        "    lr_ = exponential_decay(initial_lr, k2, epoch)\n",
        "    lrs2.append(lr_.asscalar())\n",
        "\n",
        "lrs3 = []\n",
        "for epoch in range(epochs):\n",
        "    lr_ = exponential_decay(initial_lr, k3, epoch)\n",
        "    lrs3.append(lr_.asscalar())\n",
        "\n",
        "plt.plot(list(range(epochs)), lrs1, label = f'k = {k1.asscalar():.3f}')\n",
        "plt.plot(list(range(epochs)), lrs2, label = f'k = {k2.asscalar():.3f}')\n",
        "plt.plot(list(range(epochs)), lrs3, label = f'k = {k3.asscalar():.3f}')\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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hJc5YrPoTVVSVvAI9JrSOOcxY6uzEsoKs9KFG30OIRSd8lAy5yjlzEaBxQiTz7hlUCT+R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\niYiIWhJIIiKilgSSiIio5W8jRzEMY2/z8gAAAABJRU5ErkJggg==\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": "54691302-d831-47b2-9eef-0243d05d6cb8",
        "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",
        "k = nd.array([0.01], ctx = model_ctx)\n",
        "\n",
        "losses = []\n",
        "accs = []\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    cumulative_loss = 0\n",
        "    cumulative_acc = 0\n",
        "    \n",
        "    learning_rate = exponential_decay(initial_learning_rate, k, 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: 78.12442 | Accuracy: 0.53895 | Learning Rate: 0.0010000000\n",
            "Epoch: 1 | Loss: 38.24226 | Accuracy: 0.78547 | Learning Rate: 0.0009900498\n",
            "Epoch: 2 | Loss: 31.10512 | Accuracy: 0.82701 | Learning Rate: 0.0009801986\n",
            "Epoch: 3 | Loss: 27.69624 | Accuracy: 0.84367 | Learning Rate: 0.0009704455\n",
            "Epoch: 4 | Loss: 25.50676 | Accuracy: 0.85686 | Learning Rate: 0.0009607894\n",
            "Epoch: 5 | Loss: 23.81247 | Accuracy: 0.86591 | Learning Rate: 0.0009512294\n",
            "Epoch: 6 | Loss: 22.63584 | Accuracy: 0.87148 | Learning Rate: 0.0009417646\n",
            "Epoch: 7 | Loss: 21.68581 | Accuracy: 0.87810 | Learning Rate: 0.0009323938\n",
            "Epoch: 8 | Loss: 20.84017 | Accuracy: 0.88209 | Learning Rate: 0.0009231163\n",
            "Epoch: 9 | Loss: 20.08772 | Accuracy: 0.88676 | Learning Rate: 0.0009139312\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": "a13849dd-58c4-4997-d6ba-1578cb417a9b",
        "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: 0.8796775477707006\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": "31a38079-757b-4b21-a9c9-6296f7441c14",
        "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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2TzMekVQ88kh4TXTx4lCDvJY2qSZNKtwETP6dQqGTTLyHwHhN92LbQIh76VJY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\n/gLDAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6x/P+0veDysJdnTSg/QBP2wz8VhwY94VHXejp9TfmhL6jtmqFqv6Tx9mtzva0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\n6+vSqfEAAAAASUVORK5CYII=\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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xBspPsttfrPhK/JxdfU98TgKA/A6mTOuV9jgLrdU+btom3m6lOU5N7jjOAYyb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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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p74b8Yph799hPt97W5FLgZgYj/9ma3Q79yL6ptbGem/OXWB80KX/48o6tM7JxGx23BMwK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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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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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j1sOLUYuAu68F4is4CCGaHoUIhcgciYAQmSMRECJzJAJCZI5EQIjM0VDiKjkwq3xacYsM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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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            "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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\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": []
          }
        }
      ]
    }
  ]
}