Gradient_Descent_finds_Global_Minima_Conv2D_Network.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Gradient_Descent_finds_Global_Minima_Conv2D_Network.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "N8_ShSe14tA5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6d20bc70-4a15-45c4-c0d9-1304540b20d2"
      },
      "source": [
        "from keras.datasets import mnist\n",
        "from keras.utils import to_categorical\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
        "\n",
        "train_images = train_images.reshape((60000, 28, 28, 1))\n",
        "train_images = train_images.astype('float32') / 255\n",
        "test_images = test_images.reshape((10000, 28, 28, 1))\n",
        "test_images = test_images.astype('float32') / 255\n",
        "train_labels = to_categorical(train_labels)\n",
        "test_labels = to_categorical(test_labels)\n",
        "\n",
        "x_val = train_images[:10000]\n",
        "x_train = train_images[10000:]\n",
        "\n",
        "y_val = train_labels[:10000]\n",
        "y_train = train_labels[10000:]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WN0ZpC-e4vau",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras import layers\n",
        "from keras import models\n",
        "\n",
        "model = models.Sequential()\n",
        "model.add(layers.Conv2D(16, (3,3), activation='relu', input_shape=(28,28,1)))\n",
        "model.add(layers.MaxPooling2D((2,2)))\n",
        "model.add(layers.Conv2D(8,(3,3), activation='relu'))\n",
        "model.add(layers.MaxPooling2D((2,2)))\n",
        "model.add(layers.Conv2D(8,(3,3), activation='relu'))\n",
        "model.add(layers.Flatten())\n",
        "model.add(layers.Dense(10, activation='softmax'))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PtwwPtK_6Egq",
        "colab_type": "text"
      },
      "source": [
        "# **Under parameterized Conv2D**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RGGrymNS4ydM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "outputId": "bad4be01-4c09-4aae-ddce-fb3377b5938e"
      },
      "source": [
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"sequential_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "conv2d_1 (Conv2D)            (None, 26, 26, 16)        160       \n",
            "_________________________________________________________________\n",
            "max_pooling2d_1 (MaxPooling2 (None, 13, 13, 16)        0         \n",
            "_________________________________________________________________\n",
            "conv2d_2 (Conv2D)            (None, 11, 11, 8)         1160      \n",
            "_________________________________________________________________\n",
            "max_pooling2d_2 (MaxPooling2 (None, 5, 5, 8)           0         \n",
            "_________________________________________________________________\n",
            "conv2d_3 (Conv2D)            (None, 3, 3, 8)           584       \n",
            "_________________________________________________________________\n",
            "flatten_1 (Flatten)          (None, 72)                0         \n",
            "_________________________________________________________________\n",
            "dense_1 (Dense)              (None, 10)                730       \n",
            "=================================================================\n",
            "Total params: 2,634\n",
            "Trainable params: 2,634\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XaTrkyPR418x",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras import optimizers\n",
        "model.compile(optimizer=optimizers.RMSprop(lr=0.001), loss='categorical_crossentropy', metrics=['acc'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fjOExhg742av",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "5192b161-6c5f-4666-bf1f-b2720a60d9f5"
      },
      "source": [
        "history = model.fit(x_train, y_train,\n",
        "                    epochs=5,\n",
        "                    batch_size=128,\n",
        "                    validation_data=(x_val, y_val))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 50000 samples, validate on 10000 samples\n",
            "Epoch 1/5\n",
            "50000/50000 [==============================] - 5s 92us/step - loss: 0.7591 - acc: 0.7703 - val_loss: 0.3416 - val_acc: 0.8960\n",
            "Epoch 2/5\n",
            "50000/50000 [==============================] - 3s 64us/step - loss: 0.2733 - acc: 0.9170 - val_loss: 0.2128 - val_acc: 0.9354\n",
            "Epoch 3/5\n",
            "50000/50000 [==============================] - 3s 63us/step - loss: 0.1881 - acc: 0.9433 - val_loss: 0.1624 - val_acc: 0.9533\n",
            "Epoch 4/5\n",
            "50000/50000 [==============================] - 3s 64us/step - loss: 0.1486 - acc: 0.9554 - val_loss: 0.1376 - val_acc: 0.9617\n",
            "Epoch 5/5\n",
            "50000/50000 [==============================] - 3s 65us/step - loss: 0.1249 - acc: 0.9621 - val_loss: 0.1202 - val_acc: 0.9666\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5CmfVW_T44oP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "7fa820a3-d6dc-445d-f44a-33ca05021264"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "acc = history.history['acc']\n",
        "val_acc = history.history['val_acc']\n",
        "\n",
        "loss= history.history['loss']\n",
        "val_loss = history.history['val_loss']\n",
        "\n",
        "epochs = range(1, len(acc)+1)\n",
        "\n",
        "\n",
        "plt.plot(epochs, acc, 'bo', label='Training acc')\n",
        "plt.plot(epochs, val_acc, 'b', label='Validation acc')\n",
        "plt.plot(epochs, loss, 'bo', label='Training loss', color='red')\n",
        "plt.plot(epochs, val_loss, 'b', label='Validation loss', color='red')\n",
        "plt.title('Training and validation accuracy')\n",
        "plt.legend()\n",
        "plt.figure()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jDEcTOh_51mg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras import layers\n",
        "from keras import models\n",
        "\n",
        "model = models.Sequential()\n",
        "model.add(layers.Conv2D(128, (3,3), activation='relu', input_shape=(28,28,1)))\n",
        "model.add(layers.MaxPooling2D((2,2)))\n",
        "model.add(layers.Conv2D(128,(3,3), activation='relu'))\n",
        "model.add(layers.MaxPooling2D((2,2)))\n",
        "model.add(layers.Conv2D(32,(3,3), activation='relu'))\n",
        "model.add(layers.Flatten())\n",
        "model.add(layers.Dense(10, activation='softmax'))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mgx1jpOT6vbU",
        "colab_type": "text"
      },
      "source": [
        "# **Over-parameterization**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MuIY27DT8CaW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "outputId": "e70a52bf-0591-488f-fc64-c0f1e9afce5a"
      },
      "source": [
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"sequential_2\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "conv2d_4 (Conv2D)            (None, 26, 26, 128)       1280      \n",
            "_________________________________________________________________\n",
            "max_pooling2d_3 (MaxPooling2 (None, 13, 13, 128)       0         \n",
            "_________________________________________________________________\n",
            "conv2d_5 (Conv2D)            (None, 11, 11, 128)       147584    \n",
            "_________________________________________________________________\n",
            "max_pooling2d_4 (MaxPooling2 (None, 5, 5, 128)         0         \n",
            "_________________________________________________________________\n",
            "conv2d_6 (Conv2D)            (None, 3, 3, 32)          36896     \n",
            "_________________________________________________________________\n",
            "flatten_2 (Flatten)          (None, 288)               0         \n",
            "_________________________________________________________________\n",
            "dense_2 (Dense)              (None, 10)                2890      \n",
            "=================================================================\n",
            "Total params: 188,650\n",
            "Trainable params: 188,650\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oWj4B73l8HsP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras import optimizers\n",
        "model.compile(optimizer=optimizers.RMSprop(lr=0.001), loss='categorical_crossentropy', metrics=['acc'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jmEQo7DJ8sr_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "125a68f2-f6b5-4178-ea4c-e6111c4a4fc4"
      },
      "source": [
        "history = model.fit(x_train, y_train,\n",
        "                    epochs=5,\n",
        "                    batch_size=128,\n",
        "                    validation_data=(x_val, y_val))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 50000 samples, validate on 10000 samples\n",
            "Epoch 1/5\n",
            "50000/50000 [==============================] - 9s 174us/step - loss: 0.2527 - acc: 0.9189 - val_loss: 0.0868 - val_acc: 0.9734\n",
            "Epoch 2/5\n",
            "50000/50000 [==============================] - 8s 161us/step - loss: 0.0612 - acc: 0.9807 - val_loss: 0.0605 - val_acc: 0.9814\n",
            "Epoch 3/5\n",
            "50000/50000 [==============================] - 8s 164us/step - loss: 0.0397 - acc: 0.9870 - val_loss: 0.0916 - val_acc: 0.9767\n",
            "Epoch 4/5\n",
            "50000/50000 [==============================] - 8s 163us/step - loss: 0.0293 - acc: 0.9907 - val_loss: 0.0472 - val_acc: 0.9886\n",
            "Epoch 5/5\n",
            "50000/50000 [==============================] - 8s 161us/step - loss: 0.0231 - acc: 0.9924 - val_loss: 0.0411 - val_acc: 0.9891\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Fqfs8Do8vGt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "b3c275b9-3a9f-48a0-996c-ddd5b308b080"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "acc = history.history['acc']\n",
        "val_acc = history.history['val_acc']\n",
        "\n",
        "loss= history.history['loss']\n",
        "val_loss = history.history['val_loss']\n",
        "\n",
        "epochs = range(1, len(acc)+1)\n",
        "\n",
        "\n",
        "plt.plot(epochs, acc, 'bo', label='Training acc')\n",
        "plt.plot(epochs, val_acc, 'b', label='Validation acc')\n",
        "plt.plot(epochs, loss, 'bo', label='Training loss', color='red')\n",
        "plt.plot(epochs, val_loss, 'b', label='Validation loss', color='red')\n",
        "plt.title('Training and validation accuracy')\n",
        "plt.legend()\n",
        "plt.figure()\n",
        "plt.show()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uX1zkA89_kmh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FnxEZoJV7O9k",
        "colab_type": "text"
      },
      "source": [
        "no. of paramter = number of smaples"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SsTvwJXk7Spd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras import layers\n",
        "from keras import models\n",
        "\n",
        "model = models.Sequential()\n",
        "model.add(layers.Conv2D(64, (3,3), activation='relu', input_shape=(28,28,1)))\n",
        "model.add(layers.MaxPooling2D((2,2)))\n",
        "model.add(layers.Conv2D(64,(3,3), activation='relu'))\n",
        "model.add(layers.MaxPooling2D((2,2)))\n",
        "model.add(layers.Conv2D(19,(3,3), activation='relu'))\n",
        "model.add(layers.Flatten())\n",
        "model.add(layers.Dense(10, activation='softmax'))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-GciOPA7A7y",
        "colab_type": "text"
      },
      "source": [
        "# **Practicle Degree of parameterization**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DuPRtzs_8E2Y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "outputId": "5e74d8be-a1fc-40a2-f181-278c6e9e2b7d"
      },
      "source": [
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"sequential_3\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "conv2d_7 (Conv2D)            (None, 26, 26, 64)        640       \n",
            "_________________________________________________________________\n",
            "max_pooling2d_5 (MaxPooling2 (None, 13, 13, 64)        0         \n",
            "_________________________________________________________________\n",
            "conv2d_8 (Conv2D)            (None, 11, 11, 64)        36928     \n",
            "_________________________________________________________________\n",
            "max_pooling2d_6 (MaxPooling2 (None, 5, 5, 64)          0         \n",
            "_________________________________________________________________\n",
            "conv2d_9 (Conv2D)            (None, 3, 3, 19)          10963     \n",
            "_________________________________________________________________\n",
            "flatten_3 (Flatten)          (None, 171)               0         \n",
            "_________________________________________________________________\n",
            "dense_3 (Dense)              (None, 10)                1720      \n",
            "=================================================================\n",
            "Total params: 50,251\n",
            "Trainable params: 50,251\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZTZg4LeA7Tz1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from keras import optimizers\n",
        "model.compile(optimizer=optimizers.RMSprop(lr=0.001), loss='categorical_crossentropy', metrics=['acc'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1wQCfF0W7Wv9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "84f0b7d0-02b2-4c9c-b531-2d5fc7096e0e"
      },
      "source": [
        "history = model.fit(x_train, y_train,\n",
        "                    epochs=5,\n",
        "                    batch_size=256,\n",
        "                    validation_data=(x_val, y_val))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 50000 samples, validate on 10000 samples\n",
            "Epoch 1/5\n",
            "50000/50000 [==============================] - 4s 85us/step - loss: 0.4421 - acc: 0.8639 - val_loss: 0.1555 - val_acc: 0.9531\n",
            "Epoch 2/5\n",
            "50000/50000 [==============================] - 4s 76us/step - loss: 0.1154 - acc: 0.9651 - val_loss: 0.1067 - val_acc: 0.9672\n",
            "Epoch 3/5\n",
            "50000/50000 [==============================] - 4s 76us/step - loss: 0.0798 - acc: 0.9745 - val_loss: 0.1047 - val_acc: 0.9689\n",
            "Epoch 4/5\n",
            "50000/50000 [==============================] - 4s 76us/step - loss: 0.0610 - acc: 0.9807 - val_loss: 0.0878 - val_acc: 0.9740\n",
            "Epoch 5/5\n",
            "50000/50000 [==============================] - 4s 76us/step - loss: 0.0496 - acc: 0.9848 - val_loss: 0.0606 - val_acc: 0.9816\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fvWP_7Fc7Y1U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "a30b30f1-7578-497b-d4b3-a84290e7caff"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "acc = history.history['acc']\n",
        "val_acc = history.history['val_acc']\n",
        "\n",
        "loss= history.history['loss']\n",
        "val_loss = history.history['val_loss']\n",
        "\n",
        "epochs = range(1, len(acc)+1)\n",
        "\n",
        "plt.plot(epochs, acc, 'bo', label='Training acc')\n",
        "plt.plot(epochs, val_acc, 'b', label='Validation acc')\n",
        "plt.title('Training and validation accuracy')\n",
        "plt.legend()\n",
        "plt.figure()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dbNvioO8A1qxJjtZnzoS7704u0unUKQn0n/wkCff99y/8+bbV+6ubbasc9O3U++8n/ewzZ8KDDyb96eXlMHp00iVz/PHQq9eWPXcW769uZo1z0LcTEfDSS3WjZJ5+OpnXrx+cfXZy1D5yZHE+ELmj3V/dzLaOT8aW0Lp1yZj2mnB/441k/qGHJkftY8fCwQf7Skwza95Wn4yVNBr4L6AM+FVE/ChveX/gRqA3sAw4IyKq02X9gF8BfYEAjo+IRVv2Ujq+ZcuSq1JnzUq+r1iRXGB07LFwySXJaJm99ip1lWaWJc0GvaQy4Drg80A1MFvSzIiYn9PsKuCWiLhZ0jHAD4Ez02W3AFMj4kFJ5cCmor6CDuC11+pGyfz5z8nFTLvvDqeemhy1H3ts0kduZtYaCjmiHw4sjIjXASTNAE4CcoN+EPAv6fSjwF1p20FA54h4ECAiVhWp7nZt40Z46qm6cH/llWR+zVWpX/xi0j3j29SaWVsoJOj7AG/nPK4GDstrMxc4maR7ZxzQQ1JPYD/gI0m/BwYCDwEXR0S9W2VJmgRMAujXQcf41VyVOnMm3Htv/atSzzuv7qpUM7O2VqxRN1OAayVNBB4HFgMb0+c/EjgEeAu4HZgI3JC7ckRMA6ZBcjK2SDW1upqrUmfOhEcfLeyqVDOztlZI0C8mOZFaoyKdVysi3iE5oifth/9yRHwkqRqYk9PtcxfwGfKCvqOouSq1ZpTMllyVambW1gqJpNnAvpIGkgT8acDpuQ0k9QKWRcQm4BKSETg16+4sqXdELAGOATrU2Mk1a+Dhh+vuJ/Puu0nf+hFHbNlVqWZmba3ZoI+IDZIuAO4nGV55Y0S8JOkKoCoiZgKjgB9KCpKum/PTdTdKmgI8LEnAs8AvW+elFM/77ye3Gpg1K+l3X7Om7qrUsWNhzJgtvyrVzKyt+YIpkitQX3yxrr/9mWfqrkqtuXCpWFelmpm1Bt+9sgHr1sHjj9f1t9fcnvfQQ+H73/dVqWaWHdtU0NdclTpzZvJ5qblXpX77274q1cyyKfNB/9prdUftuVelfuUrSbeMr0o1s6zLXNDXXJU6c2bytWBBMt9XpZrZtiozQf/ee/Dv/57cw33p0rqrUs8/31elmtm2LTNBv+OOyXj3MWN8VaqZWa7MBH337sktCTxKxsysvkz1VDvkzcw2l6mgNzOzzTnozcwyzkFvZpZxDnozs4xz0JuZZZyD3sws4xz0ZmYZ56A3M8s4B72ZWcY56M3MMs5Bb2aWcQ56M7OMc9CbmWWcg97MLOMc9GZmGVdQ0EsaLWmBpIWSLm5geX9JD0uaJ+kxSRV5y3eUVC3p2mIVbmZmhWk26CWVAdcBY4BBwHhJg/KaXQXcEhEHA1cAP8xbfiXw+NaXa2ZmLVXIEf1wYGFEvB4R64AZwEl5bQYBj6TTj+YulzQM2B14YOvLNTOzliok6PsAb+c8rk7n5ZoLnJxOjwN6SOopqRPwH8CUrS3UzMy2TLFOxk4BRkp6HhgJLAY2AucB90ZEdVMrS5okqUpS1ZIlS4pUkpmZAXQuoM1ioG/O44p0Xq2IeIf0iF5SOfDliPhI0uHAkZLOA8qB7SStioiL89afBkwDqKysjC19MWZmtrlCgn42sK+kgSQBfxpwem4DSb2AZRGxCbgEuBEgIibktJkIVOaHvJmZta5mu24iYgNwAXA/8DJwR0S8JOkKSWPTZqOABZJeJTnxOrWV6jUzsxZSRPvqKamsrIyqqqpSl2Fm1qFIejYiKhta5itjzcwyzkFvZpZxDnozs4xz0JuZZZyD3sws4xz0ZmYZ56A3M8s4B72ZWcY56M3MMs5Bb2aWcQ56M7OMc9CbmWWcg97MLOMc9GZmGeegNzPLOAe9mVnGOejNzDLOQW9mlnEOejOzjHPQm5llnIPezCzjHPRmZhnnoDczyzgHvZlZxhUU9JJGS1ogaaGkixtY3l/Sw5LmSXpMUkU6f4ikpyS9lC77arFfgJmZNa3ZoJdUBlwHjAEGAeMlDcprdhVwS0QcDFwB/DCdvxr4h4j4NDAauFrSzsUq3szMmlfIEf1wYGFEvB4R64AZwEl5bQYBj6TTj9Ysj4hXI+K1dPod4AOgdzEKNzOzwhQS9H2At3MeV6fzcs0FTk6nxwE9JPXMbSBpOLAd8Lf8DUiaJKlKUtWSJUsKrd3MzApQrJOxU4CRkp4HRgKLgY01CyXtCdwKnB0Rm/JXjohpEVEZEZW9e/uA38ysmDoX0GYx0DfncUU6r1baLXMygKRy4MsR8VH6eEfgHuDSiPhrMYo2M7PCFXJEPxvYV9JASdsBpwEzcxtI6iWp5rkuAW5M528H/IHkRO1vi1e2mZkVqtmgj4gNwAXA/cDLwB0R8ZKkKySNTZuNAhZIehXYHZiazv8KcBQwUdKc9GtIsV+EmZk1ThFR6hrqqaysjKqqqlKXYWbWoUh6NiIqG1rmK2PNzDLOQW9mlnEOejOzjHPQm5llnIPezCzjHPRmZhnnoDczyzgHvZlZxjnozcwyzkFvZpZxDnozs4xz0JuZZZyD3sws4xz0ZmYZ56A3M8s4B72ZWcY56M3MMs5Bb2aWcQ56M7OMc9CbmWWcg97MLOMc9GZmGeegNzPLOAe9mVnGFRT0kkZLWiBpoaSLG1jeX9LDkuZJekxSRc6ysyS9ln6dVczizcysec0GvaQy4DpgDDAIGC9pUF6zq4BbIuJg4Argh+m6uwLfAw4DhgPfk7RL8co3M7PmFHJEPxxYGBGvR8Q6YAZwUl6bQcAj6fSjOcuPAx6MiGUR8SHwIDB668s2M7NCFRL0fYC3cx5Xp/NyzQVOTqfHAT0k9SxwXSRNklQlqWrJkiWF1m5mZgUo1snYKcBISc8DI4HFwMZCV46IaRFRGRGVvXv3LlJJZmYG0LmANouBvjmPK9J5tSLiHdIjeknlwJcj4iNJi4FRees+thX1mplZCxVyRD8b2FfSQEnbAacBM3MbSOolqea5LgFuTKfvB74gaZf0JOwX0nlmZtZGmg36iNgAXEAS0C8Dd0TES5KukDQ2bTYKWCDpVWB3YGq67jLgSpJ/FrOBK9J5ZmbWRhQRpa6hnsrKyqiqqip1GWZmHYqkZyOisqFlvjLWzCzjHPRmZhnnoDczyzgHvZlZxjnozcwyzkFvZpZxDnozs4xz0JuZZZyD3sws4xz0ZmYZ56A3M8s4B72ZWcY56M3MMs5Bb2aWcQ56M7OMc9CbmWWcg97MLOMc9GZmGeegNzPLOAe9mVnGOejNzDLOQW9mlnEOejOzjCso6CWNlrRA0kJJFzewvJ+kRyU9L2mepOPT+V0k3SzpBUkvS7qk2C/AzMya1mzQSyoDrgPGAIOA8ZIG5TW7DLgjIg4BTgN+ns4/FegaEQcBw4BzJA0oTulmZlaIzgW0GQ4sjIjXASTNAE4C5ue0CWDHdHon4J2c+TtI6gxsD6wDVhShbjNrBevXr6e6upq1a9eWuhRrRLdu3aioqKBLly4Fr1NI0PcB3s55XA0cltfmcuABSd8AdgCOTef/luSfwrtAd+DCiFhWcHVm1qaqq6vp0aMHAwYMQFKpy7E8EcHSpUuprq5m4MCBBa9XrJOx44FfR0QFcDxwq6ROJO8GNgJ7AQOBf5W0d/7KkiZJqpJUtWTJkiKVZGYttXbtWnr27OmQb6ck0bNnzxa/4yok6BcDfXMeV6Tzcv0jcAdARDwFdAN6AacDf4yI9RHxAfAXoDJ/AxExLSIqI6Kyd+/eLXoBZlZcDvn2bUt+PoUE/WxgX0kDJW1HcrJ1Zl6bt4DPpUUcSBL0S9L5x6TzdwA+A7zS4irNzGyLNRv0EbEBuAC4H3iZZHTNS5KukDQ2bfavwNclzQX+B5gYEUEyWqdc0ksk/zBuioh5rfFCzKztTZ8OAwZAp07J9+nTt+75li5dypAhQxgyZAh77LEHffr0qX28bt26Jtetqqrim9/8ZrPbGDFixNYV2QEpyeP2o7KyMqqqqkpdhtk26eWXX+bAAw8sqO306TBpEqxeXTeve3eYNg0mTNj6Wi6//HLKy8uZMmVK7bwNGzbQuXMhY0iyraGfk6RnI2KzrnHwlbFmtoUuvbR+yEPy+NJLi7udiRMncu6553LYYYdx0UUX8cwzz3D44YdzyCGHMGLECBYsWADAY489xoknnggk/yS+9rWvMWrUKPbee2+uueaa2ucrLy+vbT9q1ChOOeUUDjjgACZMmEDNge+9997LAQccwLBhw/jmN79Z+7y5Fi1axJFHHsnQoUMZOnQoTz75ZO2yH//4xxx00EEMHjyYiy9OrjFduHAhxx57LIMHD2bo0KH87W9/K+6OaoL/NZrZFnnrrZbN3xrV1dU8+eSTlJWVsWLFCp544gk6d+7MQw89xLe//W1+97vfbbbOK6+8wqOPPsrKlSvZf//9mTx58mZjz59//nleeukl9tprL4444gj+8pe/UFlZyTnnnMPjjz/OwIEDGT9+fIM17bbbbjz44IN069aN1157jfHjx1NVVcV9993H//7v//L000/TvXt3li1LRpRPmDCBiy++mHHjxrF27Vo2bdpU/B3VCAe9mW2Rfv3gzTcbnl9sp556KmVlZQAsX76cs846i9deew1JrF+/vsF1TjjhBLp27UrXrl3ZbbfdeP/996moqKjXZvjw4bXzhgwZwqJFiygvL2fvvfeuHac+fvx4pk2bttnzr1+/ngsuuIA5c+ZQVlbGq6++CsBDDz3E2WefTffu3QHYddddWblyJYsXL2bcuHFActFTW3LXjZltkalTkz75XN27J/OLbYcddqid/s53vsPRRx/Niy++yKxZsxodU961a9fa6bKyMjZs2LBFbRrzs5/9jN133525c+dSVVXV7MniUnLQm9kWmTAhOfHavz9IyfdinYhtyvLly+nTpw8Av/71r4v+/Pvvvz+vv/46ixYtAuD2229vtI4999yTTp06ceutt7Jx40YAPv/5z3PTTTexOj2BsWzZMnr06EFFRQV33XUXAJ988knt8rbgoDezLTZhAixaBJs2Jd9bO+QBLrroIi655BIOOeSQFh2BF2r77bfn5z//OaNHj2bYsGH06NGDnXbaabN25513HjfffDODBw/mlVdeqX3XMXr0aMaOHUtlZSVDhgzhqquuAuDWW2/lmmuu4eCDD2bEiBG89957Ra+9MR5eaWa1WjK8MstWrVpFeXk5EcH555/Pvvvuy4UXXljqsmp5eKWZ2Vb65S9/yZAhQ/j0pz/N8uXLOeecc0pd0lbxqBszszwXXnhhuzqC31o+ojczyzgHvZlZxjnozcwyzkFvZpZxDnozazeOPvpo7r///nrzrr76aiZPntzoOqNGjaJmSPbxxx/PRx99tFmbyy+/vHY8e2Puuusu5s+v+yjs7373uzz00EMtKb/dctCbWbsxfvx4ZsyYUW/ejBkzGr2xWL57772XnXfeeYu2nR/0V1xxBccee2wTa3QcHl5pZg361rdgzpziPueQIXD11Y0vP+WUU7jssstYt24d2223HYsWLeKdd97hyCOPZPLkycyePZs1a9Zwyimn8P3vf3+z9QcMGEBVVRW9evVi6tSp3Hzzzey222707duXYcOGAckY+WnTprFu3Tr22Wcfbr31VubMmcPMmTP505/+xA9+8AN+97vfceWVV3LiiSdyyimn8PDDDzNlyhQ2bNjAoYceyvXXX0/Xrl0ZMGAAZ511FrNmzWL9+vXceeedHHDAAfVqWrRoEWeeeSYff/wxANdee23th5/8+Mc/5rbbbqNTp06MGTOGH/3oRyxcuJBzzz2XJUuWUFZWxp133smnPvWprdrvPqI3s3Zj1113Zfjw4dx3331AcjT/la98BUlMnTqVqqoq5s2bx5/+9CfmzWv8w+qeffZZZsyYwZw5c7j33nuZPXt27bKTTz6Z2bNnM3fuXA488EBuuOEGRowYwdixY/npT3/KnDlz6gXr2rVrmThxIrfffjsvvPACGzZs4Prrr69d3qtXL5577jkmT57cYPdQze2Mn3vuOW6//fbaT8HKvZ3x3Llzueiii4Dkdsbnn38+c+fO5cknn2TPPffcup2Kj+jNrBFNHXm3pprum5NOOokZM2Zww1NeLWcAAAfpSURBVA03AHDHHXcwbdo0NmzYwLvvvsv8+fM5+OCDG3yOJ554gnHjxtXeKnjs2LG1y1588UUuu+wyPvroI1atWsVxxx3XZD0LFixg4MCB7LfffgCcddZZXHfddXzrW98Ckn8cAMOGDeP3v//9Zuu3h9sZZ+aIvtifXWlmpXHSSSfx8MMP89xzz7F69WqGDRvGG2+8wVVXXcXDDz/MvHnzOOGEExq9PXFzJk6cyLXXXssLL7zA9773vS1+nho1tzpu7DbH7eF2xpkI+prPrnzzTYhIvk+a5LA364jKy8s5+uij+drXvlZ7EnbFihXssMMO7LTTTrz//vu1XTuNOeqoo7jrrrtYs2YNK1euZNasWbXLVq5cyZ577sn69euZnhMSPXr0YOXKlZs91/7778+iRYtYuHAhkNyFcuTIkQW/nvZwO+NMBH1bfXalmbWN8ePHM3fu3NqgHzx4MIcccggHHHAAp59+OkcccUST6w8dOpSvfvWrDB48mDFjxnDooYfWLrvyyis57LDDOOKII+qdOD3ttNP46U9/yiGHHFLv81y7devGTTfdxKmnnspBBx1Ep06dOPfccwt+Le3hdsaZuE1xp07JkXw+KblPtpkVxrcp7hi2ydsUN/YZla3x2ZVmZh1NJoK+LT+70sysoyko6CWNlrRA0kJJFzewvJ+kRyU9L2mepONzlh0s6SlJL0l6QVLRP/68VJ9daZZF7a071+rbkp9Ps+PoJZUB1wGfB6qB2ZJmRsT8nGaXAXdExPWSBgH3AgMkdQZuA86MiLmSegLrW1xlASZMcLCbba1u3bqxdOlSevbsiaRSl2N5IoKlS5e2eHx9IRdMDQcWRsTrAJJmACcBuUEfwI7p9E7AO+n0F4B5ETE3LXJpi6ozszZVUVFBdXU1S5YsKXUp1ohu3bpRUVHRonUKCfo+wNs5j6uBw/LaXA48IOkbwA5AzZ2A9gNC0v1Ab2BGRPwkfwOSJgGTAPr5DKpZyXTp0oWBAweWugwrsmKdjB0P/DoiKoDjgVsldSL5R/JZYEL6fZykz+WvHBHTIqIyIip79+5dpJLMzAwKC/rFQN+cxxXpvFz/CNwBEBFPAd2AXiRH/49HxN8jYjVJ3/3QrS3azMwKV0jQzwb2lTRQ0nbAacDMvDZvAZ8DkHQgSdAvAe4HDpLUPT0xO5L6fftmZtbKCroyNh0ueTVQBtwYEVMlXQFURcTMdKTNL4FykhOzF0XEA+m6ZwCXpPPvjYiLmtnWEuDNrXhNvYC/b8X6rcV1tYzrahnX1TJZrKt/RDTY993uboGwtSRVNXYZcCm5rpZxXS3julpmW6srE1fGmplZ4xz0ZmYZl8Wgn1bqAhrhulrGdbWM62qZbaquzPXRm5lZfVk8ojczsxwOejOzjOuQQS/pRkkfSHqxkeWSdE16W+V5ktrkatwC6holabmkOenXd9uorr7pbaTnp7eL/ucG2rT5PiuwrjbfZ5K6SXpG0ty0ru830KarpNvT/fW0pAHtpK6Jkpbk7K9/au26crZdlt6q/O4GlrX5/iqgplLuq0XpbdvnSNrsI/WK/vcYER3uCziK5FYKLzay/HjgPkDAZ4Cn20ldo4C7S7C/9gSGptM9gFeBQaXeZwXW1eb7LN0H5el0F+Bp4DN5bc4DfpFOnwbc3k7qmghc29a/Y+m2/wX4TUM/r1LsrwJqKuW+WgT0amJ5Uf8eO+QRfUQ8DixroslJwC2R+Cuws6Q920FdJRER70bEc+n0SuBlkruS5mrzfVZgXW0u3Qer0odd0q/8UQsnATen078FPqdWvoF7gXWVhKQK4ATgV400afP9VUBN7VlR/x47ZNAXoKFbK5c8QFKHp2+975P06bbeePqW+RCSo8FcJd1nTdQFJdhn6Vv+OcAHwIMR0ej+iogNwHKgZzuoC+DL6dv930rq28Dy1nA1cBGwqZHlpdhfzdUEpdlXkPyDfkDSs0pu056vqH+PWQ369uo5kvtRDAb+H3BXW25cUjnwO+BbEbGiLbfdlGbqKsk+i4iNETGE5G6twyX9n7bYbnMKqGsWMCAiDgYepO4outVIOhH4ICKebe1tFarAmtp8X+X4bEQMBcYA50s6qjU3ltWgL+TWym0uIlbUvPWOiHuBLpJ6tcW2JXUhCdPpEfH7BpqUZJ81V1cp91m6zY+AR4HReYtq95eSO7PuBLTZJ6g1VldELI2IT9KHvwKGtUE5RwBjJS0CZgDHSLotr01b769mayrRvqrZ9uL0+wfAH0g+yS9XUf8esxr0M4F/SM9cfwZYHhHvlrooSXvU9EtKGk6y/1s9HNJt3gC8HBH/2UizNt9nhdRVin0mqbekndPp7Uk+L/mVvGYzgbPS6VOARyI9i1bKuvL6cceSnPdoVRFxSURURMQAkhOtj0TEGXnN2nR/FVJTKfZVut0dJPWomSb5yNX8kXpF/Xss5KME2x1J/0MyGqOXpGrgeyQnpoiIX5B8wMnxwEJgNXB2O6nrFGCypA3AGuC01g6H1BHAmcALaf8uwLeBfjm1lWKfFVJXKfbZnsDNkspI/rHcERF3K+fW3CT/oG6VtJDkBPxprVxToXV9U9JYYENa18Q2qKtB7WB/NVdTqfbV7sAf0uOXzsBvIuKPks6F1vl79C0QzMwyLqtdN2ZmlnLQm5llnIPezCzjHPRmZhnnoDczyzgHvZlZxjnozcwy7v8D/N4R/8pmpWAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "viQiLCYXDEzY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "f05b9159-2f15-4c36-bde9-619df99821f6"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "acc = history.history['acc']\n",
        "val_acc = history.history['val_acc']\n",
        "\n",
        "loss= history.history['loss']\n",
        "val_loss = history.history['val_loss']\n",
        "\n",
        "epochs = range(1, len(acc)+1)\n",
        "\n",
        "\n",
        "plt.plot(epochs, acc, 'bo', label='Training acc')\n",
        "plt.plot(epochs, val_acc, 'b', label='Validation acc')\n",
        "plt.plot(epochs, loss, 'bo', label='Training loss', color='red')\n",
        "plt.plot(epochs, val_loss, 'b', label='Validation loss', color='red')\n",
        "plt.title('Training and validation accuracy')\n",
        "plt.legend()\n",
        "plt.figure()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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oUdx+++289tprnH/++eTm5jJ69GjeffddADZu3MjkyZMB78Ng9uzZjB8/nkGDBrFs2bLa/aWlpdWWHz9+PDNmzGDo0KEUFhbinANg3bp1DB06lPz8fG666aba/QYqKytj7Nix5OXlkZeXV+eD4he/+AVZWVlkZ2ezYMECAHbv3s3FF19MdnY2eXl57NmzJ7IVFQa10EUkqIULoaqq7rqqKm/9qbTSgykvL+fll18mOTmZQ4cOsXnzZtq1a8eGDRu48847eeqppxo8Z9euXbzwwgtUVlYyZMgQ5s2b1+AWvzfeeIMdO3Zw1llnMWbMGF566SUKCgq45ppr2LRpEwMHDmTWrFlBY+rduzd/+MMfSElJ4b333mPWrFls2bKF9evX81//9V+8+uqrpKam8sUXXwBQWFjIggULmDZtGkeOHOHEiRORraQwKKGLSFD79jVv/amYOXMmycnJABw8eJCrr76a9957DzPj2LFjQZ9z2WWX0bFjRzp27Ejv3r357LPPyMjIqFNm5MiRtetycnIoKysjLS2NQYMG1d4OOGvWLFasWNFg/8eOHeOGG25g+/btJCcn85e//AWADRs28OMf/5jU1FQAunfvTmVlJR999BHTpk0DvHvIY0FdLiISVP/+zVt/Kjp37lw7//Of/5wJEybw9ttv8/TTT4e8da9jx46188nJyVRXV7eoTCj3338/3/jGN3jzzTfZsmVLkxdt24KwErqZTTSzd81st5ktCFHm+2a208x2mNnjkQ1TRKKtuBj8Rmit1FRvfWs6ePAgffv2BWDlypUR3/+QIUN4//33KSsrA+CJJ54IGUefPn1ISkriscce4/jx4wBccsklPPLII1T5/VFffPEF6enpZGRksGbNGgCOHj1auz2amkzoZpYMPABMAs4BZpnZOfXKnA3cAYxxzg0Dbm6FWEUkigoLYcUKGDAAzLzHFSsi339e3+23384dd9xBbm5us1rU4erUqRPLly9n4sSJ5Ofnk56eTteuXRuUu+6661i1ahXZ2dns2rWr9ixi4sSJTJkyhYKCAnJycliyZAkAjz32GMuWLWP48OGMHj2aTz/9NOKxN8VqrvqGLGB2PrDYOfddf/kOAOfc/w0o88/AX5xzD4V74IKCArdly5YWBS0iLfPOO+/w7W9/O9ZhxNzhw4dJS0vDOcf111/P2Wefzfz582MdVgPB/l5mttU5F/T+zXC6XPoCHwYsl/vrAg0GBpvZS2b2iplNbEbMIiJR9atf/YqcnByGDRvGwYMHueaaa2IdUkRE6i6XdsDZwHggA9hkZlnOuQOBhcxsLjAXoH9rXFkREQnD/Pnz22SL/FSF00L/COgXsJzhrwtUDqx1zh1zzn0A/AUvwdfhnFvhnCtwzhX06tWrpTGLiEgQ4ST014GzzWygmXUArgDW1iuzBq91jpn1xOuCeT+CcYqISBOaTOjOuWrgBuBZ4B1gtXNuh5ndY2ZT/GLPAhVmthN4AbjNOVfRWkGLiEhDYfWhO+fWAevqrbs7YN4Bt/iTiIjEgL4pKiJRM2HCBJ599tk665YuXcq8efNCPmf8+PHU3OJ86aWXcuDAgQZlFi9eXHs/eChr1qxh586dtct33303GzZsaE74bZ4SuohEzaxZsygtLa2zrrS0NOQAWfWtW7eObt26tejY9RP6Pffcw8UXX9yifbVVSugiEjUzZszgmWeeqR0XpaysjI8//pixY8cyb948CgoKGDZsGIsWLQr6/MzMTD7//HMAiouLGTx4MBdccEHtELvg3WM+YsQIsrOzufzyy6mqquLll19m7dq13HbbbeTk5LBnzx6Kiop48sknAXjuuefIzc0lKyuL2bNnc/To0drjLVq0iLy8PLKysti1a1eDmNrSMLsabVHkNHXzzeD/1kTE5OTA0qWht3fv3p2RI0eyfv16pk6dSmlpKd///vcxM4qLi+nevTvHjx/noosu4q233mL48OFB97N161ZKS0vZvn071dXV5OXlkZ+fD8D06dOZM2cOAHfddRcPP/wwN954I1OmTGHy5MnMmDGjzr6OHDlCUVERzz33HIMHD+aqq67iwQcf5OabvRFMevbsybZt21i+fDlLlizhoYfqfiG+LQ2zqxa6iERVYLdLYHfL6tWrycvLIzc3lx07dtTpHqlv8+bNTJs2jdTUVLp06cKUKVNqt7399tuMHTuWrKwsSkpK2LFjR6PxvPvuuwwcOJDBgwcDcPXVV7Np06ba7dOnTwcgPz+/dkCvQMeOHWPOnDlkZWUxc+bM2rjDHWY3tf4IaKdALXSR01RjLenWNHXqVObPn8+2bduoqqoiPz+fDz74gCVLlvD6669zxhlnUFRU1OxfvK9RVFTEmjVryM7OZuXKlWzcuPGU4q0ZgjfU8LuBw+yeOHEiZmOhg1roIhJlaWlpTJgwgdmzZ9e2zg8dOkTnzp3p2rUrn332GevXr290H+PGjWPNmjV89dVXVFZW8vTTT9duq6yspE+fPhw7doySgN/LS09Pp7KyssG+hgwZQllZGbt37wa8URMvvPDCsF9PWxpmVwldRKJu1qxZvPnmm7UJPTs7m9zcXIYOHcoPf/hDxowZ0+jz8/Ly+MEPfkB2djaTJk1ixIgRtdvuvfdeRo0axZgxYxg6dGjt+iuuuIL77ruP3NzcOhciU1JSeOSRR5g5cyZZWVkkJSVx7bXXhv1a2tIwu00On9taNHyuSPRp+Nz40hrD54qISBxQQhcRSRBK6CIiCUIJXUQkQSihi4gkCCV0EZEEoYQuIlFTUVFBTk4OOTk5nHnmmfTt27d2uWbArlC2bNnCTTfd1OQxRo8eHZFYN27cyOTJkyOyr2jRV/9FJLSSEli4EPbtg/79obgYCgtbvLsePXqw3R8RbPHixaSlpXHrrbfWbq+urqZdu+BpqaCggIKCoLdf1xE42uHpRi10EQmupATmzoW9e8E573HuXG99BBUVFXHttdcyatQobr/9dl577TXOP/98cnNzGT16dO3QuIEt5sWLFzN79mzGjx/PoEGDWLZsWe3+0tLSasuPHz+eGTNmMHToUAoLC6n5IuW6desYOnQo+fn53HTTTU22xL/44gu+973vMXz4cM477zzeeustAP74xz/WnmHk5uZSWVnJJ598wrhx48jJyeHcc89l8+bNEa2vxqiFLiLBLVwI9ccZqary1p9CKz2Y8vJyXn75ZZKTkzl06BCbN2+mXbt2bNiwgTvvvJOnnnqqwXN27drFCy+8QGVlJUOGDGHevHm0b9++Tpk33niDHTt2cNZZZzFmzBheeuklCgoKuOaaa9i0aRMDBw4M68c1Fi1aRG5uLmvWrOH555/nqquuYvv27SxZsoQHHniAMWPGcPjwYVJSUlixYgXf/e53WbhwIcePH4/oWC1NUUIXkeD27Wve+lMwc+ZMkpOTAW+wq6uvvpr33nsPM+PYsWNBn3PZZZfRsWNHOnbsSO/evfnss8/IyMioU2bkyJG163JycigrKyMtLY1BgwYxcOBAwBtXZsWKFY3G9+KLL9Z+qHznO9+hoqKCQ4cOMWbMGG655RYKCwuZPn06GRkZjBgxgtmzZ3Ps2DG+973vkZOTc0p10xzqchGR4Pr3b976U1AzoBXAz3/+cyZMmMDbb7/N008/HXIY3ZphbSH00LbhlDkVCxYs4KGHHuKrr75izJgx7Nq1i3HjxrFp0yb69u1LUVERjz76aESP2RgldBEJrrgY6v/4Qmqqt74VHTx4kL59+wKwcuXKiO9/yJAhvP/++7U/VvHEE080+ZyxY8fWDsW7ceNGevbsSZcuXdizZw9ZWVn87Gc/Y8SIEezatYu9e/fyjW98gzlz5vCTn/yEbdu2Rfw1hKKELiLBFRbCihUwYACYeY8rVkS8/7y+22+/nTvuuIPc3NyIt6gBOnXqxPLly5k4cSL5+fmkp6fTtWvXRp+zePFitm7dyvDhw1mwYAGrVq0CYOnSpZx77rkMHz6c9u3bM2nSJDZu3Fg7HPATTzzBT3/604i/hlA0fK7IaUTD53oOHz5MWloazjmuv/56zj77bObPnx/rsBrQ8LkiIk341a9+RU5ODsOGDePgwYNcc801sQ4pIuIroZeUQGYmJCV5jxG+H1ZETg/z589n+/bt7Ny5k5KSkoj+UHMsxc9tizVfcqi5p7PmSw7Q6n16IiLxIH5a6I19yUFEROIooUfxSw4iIvEofhJ6FL/kICISj+InocfoSw4iEjkTJkzg2WefrbNu6dKlzJs3L+Rzxo8fT80tzpdeeikHDhxoUGbx4sUsWbKk0WOvWbOGnTt31i7ffffdbNiwoTnhB9WWhtmNn4Qeoy85iEjkzJo1i9LS0jrrSktLwxogC7xRErt169aiY9dP6Pfccw8XX3xxi/bVVsVPQgcveZeVwYkT3qOSuUhcmTFjBs8880ztj1mUlZXx8ccfM3bsWObNm0dBQQHDhg1j0aJFQZ+fmZnJ559/DkBxcTGDBw/mggsuqB1iF7x7zEeMGEF2djaXX345VVVVvPzyy6xdu5bbbruNnJwc9uzZQ1FREU8++SQAzz33HLm5uWRlZTF79myOHj1ae7xFixaRl5dHVlYWu3btavT1xXqY3fi5bVFEIuvmm8H/sYmIycmBpUtDbu7evTsjR45k/fr1TJ06ldLSUr7//e9jZhQXF9O9e3eOHz/ORRddxFtvvcXw4cOD7mfr1q2Ulpayfft2qqurycvLIz8/H4Dp06czZ84cAO666y4efvhhbrzxRqZMmcLkyZOZMWNGnX0dOXKEoqIinnvuOQYPHsxVV13Fgw8+yM033wxAz5492bZtG8uXL2fJkiU89NBDIV9frIfZDauFbmYTzexdM9ttZgsaKXe5mTkza/pnRUTktBTY7RLY3bJ69Wry8vLIzc1lx44ddbpH6tu8eTPTpk0jNTWVLl26MGXKlNptb7/9NmPHjiUrK4uSkhJ27NjRaDzvvvsuAwcOZPDgwQBcffXVbNq0qXb79OnTAcjPz68d0CuUF198kSuvvBIIPszusmXLOHDgAO3atWPEiBE88sgjLF68mD//+c+kp6c3uu9wNNlCN7Nk4AHgEqAceN3M1jrndtYrlw78FHj1lKMSkdbXSEu6NU2dOpX58+ezbds2qqqqyM/P54MPPmDJkiW8/vrrnHHGGRQVFYUcNrcpRUVFrFmzhuzsbFauXMnGjRtPKd6aIXhPZfjdBQsWcNlll7Fu3TrGjBnDs88+WzvM7jPPPENRURG33HILV1111SnFGk4LfSSw2zn3vnPua6AUmBqk3L3AL4CW/RVE5LSQlpbGhAkTmD17dm3r/NChQ3Tu3JmuXbvy2WefsX79+kb3MW7cONasWcNXX31FZWUlTz/9dO22yspK+vTpw7Fjx2qHvAVIT0+nsrKywb6GDBlCWVkZu3fvBuCxxx7jwgsvbNFri/Uwu+H0ofcFPgxYLgdGBRYwszygn3PuGTO7LdSOzGwuMBegv+4fFzltzZo1i2nTptV2vdQMNzt06FD69evHmDFjGn1+Xl4eP/jBD8jOzqZ3796MGDGidtu9997LqFGj6NWrF6NGjapN4ldccQVz5sxh2bJltRdDAVJSUnjkkUeYOXMm1dXVjBgxgmuvvbZFr6vmt06HDx9OampqnWF2X3jhBZKSkhg2bBiTJk2itLSU++67j/bt25OWlhaRH8JocvhcM5sBTHTO/cRfvhIY5Zy7wV9OAp4HipxzZWa2EbjVOdfo2LgaPlck+jR8bnxpjeFzPwL6BSxn+OtqpAPnAhvNrAw4D1irC6MiItEVTkJ/HTjbzAaaWQfgCmBtzUbn3EHnXE/nXKZzLhN4BZjSVAtdREQiq8mE7pyrBm4AngXeAVY753aY2T1mNqXxZ4uISLSE9cUi59w6YF29dXeHKDv+1MMSkdbinMPMYh2GNKElPw8aX1/9F5FTkpKSQkVFRYuShUSPc46KigpSUlKa9Tx99V/kNJKRkUF5eTn79++PdSjShJSUFDIyMpr1HCV0kdNI+/btGThwYKzDkFaiLhcRkQShhC4ikiCU0EVEEoQSuohIglBCFxFJEEroIiIJQgldRCRBKKGLiCQIJXQRkQShhC4ikiCU0EVEEqfQhDoAAAr+SURBVIQSuohIglBCFxFJEEroIiIJQgldRCRBKKGLiCQIJXQRkQShhC4ikiCU0EVEEoQSuohIglBCFxFJEEroIiIJQgldRCRBKKGLiCQIJXQRkQShhC4ikiCU0EVEEoQSuohIglBCFxFJEEroIiIJIqyEbmYTzexdM9ttZguCbL/FzHaa2Vtm9pyZDYh8qCIi0pgmE7qZJQMPAJOAc4BZZnZOvWJvAAXOueHAk8A/RzpQERFpXDgt9JHAbufc+865r4FSYGpgAefcC865Kn/xFSAjsmGKiEhTwknofYEPA5bL/XWh/B2wPtgGM5trZlvMbMv+/fvDj1JERJoU0YuiZvYjoAC4L9h259wK51yBc66gV69ekTy0iMhpr10YZT4C+gUsZ/jr6jCzi4GFwIXOuaORCU9ERMIVTgv9deBsMxtoZh2AK4C1gQXMLBf4d2CKc+6vkQ9TRESa0mRCd85VAzcAzwLvAKudczvM7B4zm+IXuw9IA35nZtvNbG2I3YmISCsJp8sF59w6YF29dXcHzF8c4bhERKSZ9E1REZEEoYQuIpIg4i+hl5fDli3wxRexjkREpE0Jqw+9TXn8cfjZz7z5bt3gm9/0pkGDTs5/85vQty8kJ8c2VhGRKIq/hD5rFgweDHv2nJy2bYP/+A+orj5ZrkMHyMwMnvAHDYJOnWL2EkREWkP8JfR+/bypvupq+PBDL8G///7JZP/++/DSS3DoUN3yffrUbdEHJvyePcEsOq9HRCRC4i+hh9KuHQwc6E31OQcVFQ2T/Z49sGEDrFpVt3x6esMunJrl/v29Y4mItDGnR2Yy81rdPXvCqFENt3/1FXzwQcOEv2MH/P738PXXJ8u2awcDBjTswqmZT0uL3usSEQlweiT0pnTqBOec4031nTgBH30UvHW/enXDu2169w7duj/zTHXliEirUUJvSlLSyX778eMbbj9woG5/fc385s3eHTnOnSybmuol92AJPzPTu5AbSSUlsHAh7NvndRUVF0NhYWSPISJthhL6qerWDfLzvam+o0dh797gCf8Pf/C6emrUfHAEuwVz0CDvOM1RUgJz50KV/7sje/d6y6CkLpKgzAW2IKOooKDAbdmyJSbHbhOcg08/DZ7s9+yB+j8A0r176HvuzzrL+0AIlJnpJfH6BgyAsrLWelUi0srMbKtzriDYNrXQY8XMu3WyTx+44IKG2ysrG95+uWcPvPYa/O53cPz4ybIdO3p39wQm/GDJHLzuFxFJSErobVV6OmRne1N9x46dvOe+fsL/4x/h8OHQ+01K8lrvZt584GM01sXDsZKToXNn746lmsdgU+fOuoVV2hT9N8aj9u1PXly95JK625yDzz+H5cvhH/+x7i2XyckwerTXmnfOm06cqPsY7rrGtlVXt3y/kTh+c9edipSU0Am/pVOHDrobSlpECT3RmEGvXrBoEXzrW7rLJRw1yb1mqq72LiYfPtzy6bPP6i4HXgBvSrt2kf+Q6NSp4XUWSTi6KCoSDcePw9/+dmofEsGmcN+/Zg27jxrrTgp3UpdT1OmiqEg4WvO+/eRk6NLFmyLFOa/l35wPgPofKl9+6V2PCVwX2E3XlI4dvcTevbv3TewePbypZj7Yuh49vG5DiTgldBGIz/v2zbwvq6Wmet9QjpSvv27e2cShQ943pisqvA+H7du96zhHjoQ+Rpcu4Sf/mnmNkNokdbmIgO7bbw1VVV6Sr6jwEnw485WVoffXqVP4yb9mPi0t4S4wq8tFpCmh7s/XffstV3P2EGy461C+/tpr7YfzAbB3r/f45ZehryW0bx9+8q957No1bi8gK6GLgNdnHqyF3r9/9GOJJ5G+7tChgzeI3Zlnhv+c48e9pN7YB0DN4zvvnJwP/HJeoKSk0NcEQnURde/eJi4Qxz4CkbaguLhuHzp4rcvi4tjF1Na1lesOycknh8cOl3Ne3384ZwJlZbB1q7fu6NHQ++zWLfyzgAEDInuB3Kc+dJEaGp2yeU636w7Otey6QKhvbg8Y0KL/scb60JXQRaRlkpKC912bnfo3cBPJ0aPedYFVq2Dx4rqt/NRUWLGiWUm9sYQenz3/IhJ7oa4v6LpDXR07eoPw/fKXDbtsqqq8s8IIUUIXkZYpLvZamIF03SG0KNxJpYQuIi1TWOh1FwwY4HWzDBjQ7O6D00oUzmiU0EWk5QoLvQugJ054j0rmoUXhjEYJXUQkGqJwRqP70EVEoqWwsFXPYtRCFxFJEEroIiIJQgldRCRBKKGLiCQIJXQRkQQRs7FczGw/EGRkn7D0BD6PYDiRoriaR3E1X1uNTXE1z6nENcA51yvYhpgl9FNhZltCDU4TS4qreRRX87XV2BRX87RWXOpyERFJEEroIiIJIl4T+opYBxCC4moexdV8bTU2xdU8rRJXXPahi4hIQ/HaQhcRkXqU0EVEEkSbTehm9msz+6uZvR1iu5nZMjPbbWZvmVleG4lrvJkdNLPt/nR3lOLqZ2YvmNlOM9thZj8NUibqdRZmXFGvMzNLMbPXzOxNP66/D1Kmo5k94dfXq2aW2UbiKjKz/QH19ZPWjivg2Mlm9oaZ/T7ItqjXV5hxxbK+yszsz/5xG/yIcsTfk865NjkB44A84O0Q2y8F1gMGnAe82kbiGg/8Pgb11QfI8+fTgb8A58S6zsKMK+p15tdBmj/fHngVOK9emeuAX/rzVwBPtJG4ioB/i/b/mH/sW4DHg/29YlFfYcYVy/oqA3o2sj2i78k220J3zm0CvmikyFTgUed5BehmZn3aQFwx4Zz7xDm3zZ+vBN4B+tYrFvU6CzOuqPPr4LC/2N6f6t8hMBVY5c8/CVxkZtYG4ooJM8sALgMeClEk6vUVZlxtWUTfk202oYehL/BhwHI5bSBR+M73T5nXm9mwaB/cP9XNxWvdBYppnTUSF8SgzvzT9O3AX4E/OOdC1pdzrho4CPRoA3EBXO6foj9pZv1aOybfUuB24ESI7TGprzDigtjUF3gfxv9jZlvNbG6Q7RF9T8ZzQm+rtuGNtZAN/D9gTTQPbmZpwFPAzc65Q9E8dmOaiCsmdeacO+6cywEygJFmdm40jtuUMOJ6Gsh0zg0H/sDJVnGrMbPJwF+dc1tb+1jNEWZcUa+vABc45/KAScD1ZjauNQ8Wzwn9IyDwkzbDXxdTzrlDNafMzrl1QHsz6xmNY5tZe7ykWeKc+48gRWJSZ03FFcs68495AHgBmFhvU219mVk7oCtQEeu4nHMVzrmj/uJDQH4UwhkDTDGzMqAU+I6Z/aZemVjUV5Nxxai+ao79kf/4V+A/gZH1ikT0PRnPCX0tcJV/lfg84KBz7pNYB2VmZ9b0G5rZSLw6bvUk4B/zYeAd59y/higW9ToLJ65Y1JmZ9TKzbv58J+ASYFe9YmuBq/35GcDzzr+SFcu46vWxTsG7LtGqnHN3OOcynHOZeBc8n3fO/ahesajXVzhxxaK+/ON2NrP0mnngfwH1746L6Huyzf5ItJn9Fu/uh55mVg4swrtAhHPul8A6vCvEu4Eq4MdtJK4ZwDwzqwa+Aq5o7X9q3xjgSuDPfv8rwJ1A/4DYYlFn4cQVizrrA6wys2S8D5DVzrnfm9k9wBbn3Fq8D6LHzGw33oXwK1o5pnDjusnMpgDVflxFUYgrqDZQX+HEFav6+gbwn35bpR3wuHPuv83sWmid96S++i8ikiDiuctFREQCKKGLiCQIJXQRkQShhC4ikiCU0EVEEoQSuohIglBCFxFJEP8fTDO2Bvm5SakAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T32YmlLB7cLI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "04e64e4d-0083-429e-d401-79bad398c16c"
      },
      "source": [
        "test_loss, test_acc = model.evaluate(test_images, test_labels)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "10000/10000 [==============================] - 1s 109us/step\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HuGcHsSTBQW6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2f3db8fb-ec6d-40ff-d321-0497299fb07e"
      },
      "source": [
        "test_acc"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9851999878883362"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RaP7GKt-BR_5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}