docs/tutorials/optimizers_conditionalgradient.ipynb

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    "colab": {
      "name": "optimizers_conditionalgradient.ipynb",
      "provenance": [],
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "accelerator": "GPU"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pGUYKbJNWNgj",
        "colab_type": "text"
      },
      "source": [
        "##### Copyright 2019 The TensorFlow Authors."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1PzPJglSWgnW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#@title Licensed under the Apache License, Version 2.0\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b5P4BEg1XYd5",
        "colab_type": "text"
      },
      "source": [
        "# TensorFlow Addons Optimizers: ConditionalGradient\n",
        "\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/addons/tutorials/optimizers_conditionalgradient\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/addons/blob/master/docs/tutorials/optimizers_conditionalgradient.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/addons/blob/master/docs/tutorials/optimizers_conditionalgradient.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/addons/docs/tutorials/optimizers_conditionalgradient.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Faj8luWnYNSG",
        "colab_type": "text"
      },
      "source": [
        "# Overview\n",
        "This notebook will demonstrate how to use the Conditional Graident Optimizer from the Addons package."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MrDjqjY6YRYM",
        "colab_type": "text"
      },
      "source": [
        "# ConditionalGradient\n",
        "\n",
        "\n",
        "> Constraining the parameters of a neural network has been shown to be beneficial in training because of the underlying regularization effects.  Often, parameters are constrained via a soft penalty (which never guarantees the constraint satisfaction) or via a projection operation (which is computationally expensive). Conditional gradient (CG) optimizer, on the other hand, enforces the constraints strictly without the need for an expensive projection step. It works by minimizing a linear approximation of the objective within the constraint set. In this notebook, we demonstrate the appliction of Frobenius norm constraint via the CG optimizer on the MNIST dataset. CG is now available as a tensorflow API. More details of the optimizer are available at https://arxiv.org/pdf/1803.06453.pdf\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dooBaYGLYYnn",
        "colab_type": "text"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pc8HQET2O5KK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from __future__ import absolute_import, division, print_function, unicode_literals"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qYo0FkL4O7io",
        "colab_type": "code",
        "outputId": "d8e66fa1-ee27-44e1-d26e-1238b084e305",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "try:\n",
        "  %tensorflow_version 2.x\n",
        "except:\n",
        "  pass\n",
        "\n",
        "import tensorflow as tf"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TensorFlow 2.x selected.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SWGRw7vhO-kL",
        "colab_type": "code",
        "outputId": "bbe6c64a-845d-4be0-ae6c-aaf47312f1cd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "!pip install --no-deps tensorflow-addons~=0.6"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: tensorflow-addons~=0.6 in /usr/local/lib/python3.6/dist-packages (0.6.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oPbEvhbCih0t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import tensorflow_addons as tfa\n",
        "import tensorflow_datasets as tfds\n",
        "import numpy as np\n",
        "from matplotlib import pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kR0PnjrIirpJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Hyperparameters\n",
        "batch_size=64\n",
        "epochs=10"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-x0WBp-IYz7x",
        "colab_type": "text"
      },
      "source": [
        "# Build the Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4KzMDUT0i1QE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_1 = tf.keras.Sequential([\n",
        "    tf.keras.layers.Dense(64, input_shape=(784,), activation='relu', name='dense_1'),\n",
        "    tf.keras.layers.Dense(64, activation='relu', name='dense_2'),\n",
        "    tf.keras.layers.Dense(10, activation='softmax', name='predictions'),\n",
        "])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XGADNG3-Y7aa",
        "colab_type": "text"
      },
      "source": [
        "# Prep the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d6a-kbM_i1b2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Load MNIST dataset as NumPy arrays\n",
        "dataset = {}\n",
        "num_validation = 10000\n",
        "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()\n",
        "\n",
        "# Preprocess the data\n",
        "x_train = x_train.reshape(-1, 784).astype('float32') / 255\n",
        "x_test = x_test.reshape(-1, 784).astype('float32') / 255"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sOlB-WqjZp1Y",
        "colab_type": "text"
      },
      "source": [
        "# Define a Custom Callback Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8LCmRXUgZqyV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def frobenius_norm(m):\n",
        "    \"\"\"This function is to calculate the frobenius norm of the matrix of all\n",
        "    layer's weight.\n",
        "  \n",
        "    Args:\n",
        "        m: is a list of weights param for each layers.\n",
        "    \"\"\"\n",
        "    total_reduce_sum = 0\n",
        "    for i in range(len(m)):\n",
        "        total_reduce_sum = total_reduce_sum + tf.math.reduce_sum(m[i]**2)\n",
        "    norm = total_reduce_sum**0.5\n",
        "    return norm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "udSvzKm4Z5Zr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "CG_frobenius_norm_of_weight = []\n",
        "CG_get_weight_norm = tf.keras.callbacks.LambdaCallback(\n",
        "    on_epoch_end=lambda batch, logs: CG_frobenius_norm_of_weight.append(\n",
        "        frobenius_norm(model_1.trainable_weights).numpy()))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qfhE1DfwZC1i",
        "colab_type": "text"
      },
      "source": [
        "# Train and Evaluate: Using CG as Optimizer\n",
        "\n",
        "Simply replace typical keras optimizers with the new tfa optimizer "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6-AMaOYEi1kK",
        "colab_type": "code",
        "outputId": "959b8065-3689-47ff-98f4-6a4eb250bd95",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        }
      },
      "source": [
        "# Compile the model\n",
        "model_1.compile(\n",
        "    optimizer=tfa.optimizers.ConditionalGradient(\n",
        "        learning_rate=0.99949, lambda_=203),  # Utilize TFA optimizer\n",
        "    loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "    metrics=['accuracy'])\n",
        "\n",
        "history_cg = model_1.fit(\n",
        "    x_train,\n",
        "    y_train,\n",
        "    batch_size=batch_size,\n",
        "    validation_data=(x_test, y_test),\n",
        "    epochs=epochs,\n",
        "    callbacks=[CG_get_weight_norm])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/10\n",
            "60000/60000 [==============================] - 5s 82us/sample - loss: 0.3787 - accuracy: 0.8856 - val_loss: 0.2009 - val_accuracy: 0.9412\n",
            "Epoch 2/10\n",
            "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1825 - accuracy: 0.9449 - val_loss: 0.1512 - val_accuracy: 0.9541\n",
            "Epoch 3/10\n",
            "60000/60000 [==============================] - 4s 69us/sample - loss: 0.1475 - accuracy: 0.9559 - val_loss: 0.1343 - val_accuracy: 0.9583\n",
            "Epoch 4/10\n",
            "60000/60000 [==============================] - 4s 72us/sample - loss: 0.1315 - accuracy: 0.9599 - val_loss: 0.1513 - val_accuracy: 0.9534\n",
            "Epoch 5/10\n",
            "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1239 - accuracy: 0.9624 - val_loss: 0.1169 - val_accuracy: 0.9638\n",
            "Epoch 6/10\n",
            "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1171 - accuracy: 0.9645 - val_loss: 0.1498 - val_accuracy: 0.9517\n",
            "Epoch 7/10\n",
            "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1126 - accuracy: 0.9653 - val_loss: 0.1076 - val_accuracy: 0.9677\n",
            "Epoch 8/10\n",
            "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1103 - accuracy: 0.9656 - val_loss: 0.0960 - val_accuracy: 0.9707\n",
            "Epoch 9/10\n",
            "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1069 - accuracy: 0.9679 - val_loss: 0.1168 - val_accuracy: 0.9654\n",
            "Epoch 10/10\n",
            "60000/60000 [==============================] - 4s 69us/sample - loss: 0.1058 - accuracy: 0.9679 - val_loss: 0.1154 - val_accuracy: 0.9660\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8OJp4So9bYYR",
        "colab_type": "text"
      },
      "source": [
        "# Train and Evaluate: Using SGD as Optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SuizUueqn449",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_2 = tf.keras.Sequential([\n",
        "    tf.keras.layers.Dense(64, input_shape=(784,), activation='relu', name='dense_1'),\n",
        "    tf.keras.layers.Dense(64, activation='relu', name='dense_2'),\n",
        "    tf.keras.layers.Dense(10, activation='softmax', name='predictions'),\n",
        "])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V8QC3xCwbfNl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "SGD_frobenius_norm_of_weight = []\n",
        "SGD_get_weight_norm = tf.keras.callbacks.LambdaCallback(\n",
        "    on_epoch_end=lambda batch, logs: SGD_frobenius_norm_of_weight.append(\n",
        "        frobenius_norm(model_2.trainable_weights).numpy()))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9BNi4yXGcDlg",
        "colab_type": "code",
        "outputId": "f46e4f42-35da-4a75-873f-313c26e1b331",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        }
      },
      "source": [
        "# Compile the model\n",
        "model_2.compile(\n",
        "    optimizer=tf.keras.optimizers.SGD(0.01),  # Utilize SGD optimizer\n",
        "    loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "    metrics=['accuracy'])\n",
        "\n",
        "history_sgd = model_2.fit(\n",
        "    x_train,\n",
        "    y_train,\n",
        "    batch_size=batch_size,\n",
        "    validation_data=(x_test, y_test),\n",
        "    epochs=epochs,\n",
        "    callbacks=[SGD_get_weight_norm])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/10\n",
            "60000/60000 [==============================] - 4s 65us/sample - loss: 0.9356 - accuracy: 0.7564 - val_loss: 0.4145 - val_accuracy: 0.8895\n",
            "Epoch 2/10\n",
            "60000/60000 [==============================] - 3s 58us/sample - loss: 0.3784 - accuracy: 0.8936 - val_loss: 0.3236 - val_accuracy: 0.9074\n",
            "Epoch 3/10\n",
            "60000/60000 [==============================] - 4s 58us/sample - loss: 0.3171 - accuracy: 0.9094 - val_loss: 0.2884 - val_accuracy: 0.9192\n",
            "Epoch 4/10\n",
            "60000/60000 [==============================] - 3s 58us/sample - loss: 0.2847 - accuracy: 0.9178 - val_loss: 0.2619 - val_accuracy: 0.9260\n",
            "Epoch 5/10\n",
            "60000/60000 [==============================] - 4s 58us/sample - loss: 0.2615 - accuracy: 0.9247 - val_loss: 0.2424 - val_accuracy: 0.9312\n",
            "Epoch 6/10\n",
            "60000/60000 [==============================] - 3s 58us/sample - loss: 0.2427 - accuracy: 0.9303 - val_loss: 0.2269 - val_accuracy: 0.9351\n",
            "Epoch 7/10\n",
            "60000/60000 [==============================] - 4s 59us/sample - loss: 0.2272 - accuracy: 0.9351 - val_loss: 0.2138 - val_accuracy: 0.9395\n",
            "Epoch 8/10\n",
            "60000/60000 [==============================] - 4s 59us/sample - loss: 0.2138 - accuracy: 0.9386 - val_loss: 0.2038 - val_accuracy: 0.9405\n",
            "Epoch 9/10\n",
            "60000/60000 [==============================] - 3s 58us/sample - loss: 0.2014 - accuracy: 0.9417 - val_loss: 0.1952 - val_accuracy: 0.9435\n",
            "Epoch 10/10\n",
            "60000/60000 [==============================] - 4s 59us/sample - loss: 0.1908 - accuracy: 0.9448 - val_loss: 0.1845 - val_accuracy: 0.9474\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Myw0FVcd_Z9",
        "colab_type": "text"
      },
      "source": [
        "# Frobenius Norm of Weights: CG vs SGD"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0tJYQBRt-ZUl",
        "colab_type": "text"
      },
      "source": [
        "The current implementation of CG optimizer is based on Frobenius Norm, with considering Frobenius Norm as regularizer in the target function. Therefore, we compare CG’s regularized effect with SGD optimizer, which has not imposed Frobenius Norm regularizer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ewf17MW1cJVI",
        "colab_type": "code",
        "outputId": "b445243a-5be8-4fad-a082-ba6d7bd82573",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        }
      },
      "source": [
        "plt.plot(\n",
        "    CG_frobenius_norm_of_weight,\n",
        "    color='r',\n",
        "    label='CG_frobenius_norm_of_weights')\n",
        "plt.plot(\n",
        "    SGD_frobenius_norm_of_weight,\n",
        "    color='b',\n",
        "    label='SGD_frobenius_norm_of_weights')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Frobenius norm of weights')\n",
        "plt.legend(loc=1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f5d8db08780>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QVwnDP0/4cmBeMcRS6qxe7ZLEO+/AoUPQsiW89BLcdJMbJ2GMMWeTvLrVvnUm\nFxaRmcAAYLeqxvr2PQbcCvjXznxAVT/P4dx+wEtAOG5hpclnEktxOn4cPvzQJYp//9uNpr76alea\n6NLFShPGmLOXl15Sq3FVU4EO4kogT6rqvlxOnQW8Arydbf8Lqjolj/uFA6/iJjtMApaKyDxVXZdf\nrKG0fr1LEm+/7cZKNGsGzz0Hw4dbA7YxpnTw0uj9D1x32r/5tq8HKgC7cEnhipxOUtVFIhJTiJg6\nAZtVdSuAiLwHDMR16y1RUlJgzhyXKBYtcsuMDhniShPdu1tpwhhTunhJGJeoavuA7dUiskJV24vI\nsELc8w4RuRlXQrlHVX/P9n5dYEfAdhIlbLGmjRth+nSYNQv27YMmTeDpp2HECKhZM9TRGWNMcHiZ\nbShcRDr5N0SkI65tASC1gPd7DWgCxAG/As8V8PzTiMgYEVkmIsv27NmT/wmFdPIkfPCBW4a0eXPX\neN2jB3z9tUsg991nycIYU7p5KWGMBmaKSCXc5IOHgNEiUhF4qiA3U9Xf/K9FZAYwP4fDkoH6Adv1\nfPtyu+Z0fJMhxsfHZ29rOWNbt7rSxJtvwu7dEBMDkybBqFG2wJAxpmzxMpfUUqC1iFTxbR8MePuD\ngtxMRGqr6q++zcHAmhwOWwo0FZFGuERxPXBDQe5zpk6dgr//HaZNcyWI8HAYMMC1TVx6qds2xpiy\nJq+Be8NU9f9E5O5s+wFQ1efzurCIzAZ6ANVFJAl4FOghInG4XleJwJ98x9bBdZ/tr6qpInIH8CWu\n6mumqq4t3McrmG3bYMYM+OtfYdcuNyPs44/DLbdA3brFEYExxpRceZUwKvqeKxfmwqo6NIfdf83l\n2J1A/4Dtz4HTxmcEQ2oqfP65K0188YXr2dS/P/zpT3DZZVaaMMYYv7wG7r3ue368+MIpfidPullh\nK1aEhx6C0aOhQYNQR2WMMSWPl4F7zXC9m2qpaqyItAGuVNUngx5dMahQwS1MdOGFtoSpMcbkxUu3\n2hnAROAUgKr+jGuILjVat7ZkYYwx+fGSMCqo6pJs+wo6/sIYY8xZzkvC2CsiTfDNJyUiV+MG3Rlj\njClDvFTE3I4bGNdCRJKBX4AbgxqVMcaYEsfLwL2twCW+kd1hqno4+GEZY4wpafKtkhKRLSLyLnAT\nYB1OjTGmjPLShtESeB2oBjzrSyBzgxuWMcaYksZLwkjDdalNA9KB3b6HMcaYMsRLo/chYDXwPDAj\njxX2jDHGlGJeShhDgUXAfwHvicjjItI7uGEZY4wpabz0kvoU+FREWgCXAeOB+4DyQY7NGGNMCeKl\nl9QcEdkMvIRby/tmoGqwAzMqitlgAAAagklEQVTGGFOyeGnDeApYqappwQ7GGGNMyZVvCUNVlxUm\nWYjITBHZLSKnraonIveIiIpI9VzOTRORBN9jXkHvbYwxpugFc47WWcArwNuBO0WkPtAH2J7HucdV\nNS54oRljjCmoXEsYItLF9xxVmAur6iJgfw5vvYBrNNfCXNcYY0xo5FUl9bLveXFR3UxEBgLJqroq\nn0OjRWSZiPwoIoOK6v7GGGMKL68qqVMiMh2oKyIvZ39TVccV5EYiUgF4AFcdlZ+GqposIo2Bf4nI\nalXdkst1xwBjABrY2qrGGBM0eZUwBgD/Ak4Ay3N4FFQToBGwSkQSgXrAChE5P/uBqprse94KLATa\n5XZRVZ2uqvGqGl+jRo1ChGWMMcaLXEsYqroXN7J7vYcqpHyp6mqgpn/blzTiffchYH9V4Jiqpvh6\nUXUBnjnT+xtjjDkzXqYG2Scic31dZHf7BvLVy+8kEZmNa/9oLiJJInJLHsfGi8gbvs0LgWUisgpY\nAExW1XUe4jTGGBNEXrrVvgn8DbjGtz3Mt+/SvE5S1aH5vB8T8HoZMNr3+t9Aaw9xGWOMKUZeShg1\nVfVNVU31PWYB1lhgjDFljJeEsVdEholIuO8xDLApzo0xpozxkjBGAdcCu4BfgauBkcEMyhhjTMnj\nZXrzbcCVxRCLMcaYEsxLCcMYY4yxhGGMMcYbSxjGGGM8ybcNQ0TOxa2yFxN4fEHnkjLGGHN28zJw\n73PgR2A1kB7ccIwxxpRUXhJGtKreHfRIjDHGlGhe2jDeEZFbRaS2iJznfwQ9MmOMMSWKlxLGSeBZ\n4EEyV8lToHGwgjLGGFPyeEkY9wAXZJ+G3BhjTNnipUpqM3As2IEYY4wp2byUMI4CCSKyAEjx77Ru\ntcYYU7Z4SRif+B7GGGPKsDwThoiEA31U9cbCXFxEZuLWBt+tqrHZ3rsHmALUyKl9RESGAw/5Np9U\n1bcKE4MxxpiikWcbhqqmAQ1FpFwhrz8L6Jd9p4jUB/oA23M6yddt91GgM9AJeNS31rcxxpgQ8VIl\ntRX4QUTm4dozAFDV5/M7UVUXiUhMDm+9ANwHfJrLqX2Br1V1P4CIfI1LPLM9xGuMMSYIvCSMLb5H\nGFD5TG8oIgOBZFVdJSK5HVYX2BGwneTbl9P1xgBjABo0aHCm4RljjMmFlwWUHgcQkUq+7SOFvZmI\nVAAewFVHFQlVnQ5MB4iPj9d8DjfGGFNI+Y7DEJFYEVkJrAXWishyEWlVyPs1ARoBq0QkEagHrBCR\n87MdlwzUD9iu59tnjDEmRLwM3JsO3K2qDVW1IW7k94zC3ExVV6tqTVWNUdUYXFVTe1Xdle3QL4E+\nIlLV19jdx7fPGGNMiHhJGBVVdYF/Q1UXAhW9XFxEZgOLgeYikiQit+RxbLyIvOG7x37gL8BS3+MJ\nfwO4McaY0PDUS0pEHgbe8W0Pw/WcypeqDs3n/ZiA18uA0QHbM4GZXu5jjDEm+LyUMEYBNYCPfY8a\nvn3GGGPKEC+9pH4HbN4oY4wp47ys6d0MuJfT1/TuFbywjDHGlDRe2jA+BKYBbwBpwQ3HGGNMSeUl\nYaSq6mtBj8QYY0yJ5qXR++8i8l+2prcxxpRtXkoYw33PEwL22ZrexhhTxnjpJdWoOAIxxhhTsnmp\nkjLGGGMsYRhjjPHGEoYxxhhPvExv3kVEKvpeDxOR50WkYfBDM8YYU5J4KWG8BhwTkba4qc23AG8H\nNSpjjDEljpeEkaqqCgwEXlHVVymCpVqNMcacXbyMwzgsIhNx05p3E5EwIDK4YRljjClpvJQwrgNS\ngFt8K+PVA57N7yQRmSkiu0VkTcC+v4jIzyKSICJfiUidXM5N8x2TICLzPH4WY4wxQSSutikIFxbp\nBhwB3lbVWN++c1T1kO/1OKClqo7N4dwjqlqpoPeMj4/XZcuWnWHkxhhTdojIclWN93Ksl+nND+Om\nAgEoh6uOOqKqVfI6T1UXiUhMtn2HAjYrBlzXGGNMCedlapCMBm4REVzj90WFvaGITAJuBg4CPXM5\nLFpElgGpwGRV/aSw9zPGGFM0CjRwT51PgL6FvaGqPqiq9YF3gTtyOayhr4h0A/CiiDTJ7XoiMkZE\nlonIsj179hQ2LGOMMfnwUiU1JGAzDIgHThTBvd8FPgcezf6Gqib7nreKyEKgHW78x2lUdTowHVwb\nRhHEZYwxJgdeutVeEfA6FUjEVUsVmIg0VdVNvs2BwIYcjqkKHFPVFBGpDnQBninM/YwxxhQdL20Y\nIwtzYRGZDfQAqotIEq4k0V9EmgPpwDZgrO/YeGCsqo4GLgReF5F0XIlmsqquK0wMxhhjik6u3WpF\n5D5VfUZEppJDbyZVHRfs4ArKutUaY0zBFFW32vW+Z/sFNsYYk3vCUNW/+57fKr5wjDHGlFReekk1\nA+4FYgKPV9VewQvLGGNMSeOll9SHwDTgDSAtuOEYY4wpqbwkjFRVfS3okRhjjCnRvIz0/ruI/JeI\n1BaR8/yPoEdmjDGmRPFSwhjue54QsE+BxkUfjjHGmJLKy8C9RsURiDHGmJIt3yopEakgIg+JyHTf\ndlMRGRD80IwxxpQkXtow3gROAn/0bScDTwYtImOMMSWSl4TRRFWfAU4BqOoxQIIalTHGmBLHS8I4\nKSLl8c0n5VubIiWoURljjClxvPSSehT4AqgvIu/iphsfEcygjDHGlDxeekl9LSIrcMuyCnCXqu4N\nemTGGGNKFC8lDIDuwMW4aqlIYG7QIjLGGFMieelW+7+4hY5WA2uAP4nIq14uLiIzRWS3iKwJ2PcX\nEflZRBJE5CsRqZPLucNFZJPvMTynY4wxxhSfXBdQyjhAZANwofoOFJEwYK2qXpjvxUW6AUeAt1U1\n1rfvHFU95Hs9DmipqmOznXcebh2OeFypZjnQQVV/z+t+toCSMcYUTEEWUPLSS2oz0CBgu75vX75U\ndRGwP9u+QwGbFclhNT+gL/C1qu73JYmvgX5e7mmMMSY4cm3DEJG/437MKwPrRWSJ761OwJLczvNC\nRCYBNwMHgZ45HFIX2BGwneTbZ4wxJkTyavSeEqybquqDwIMiMhG4A9d1t1BEZAwwBqBBgwb5HG2M\nMWe51FTYuhXWrYP1693zyZPw/vtBv3VeS7R+638tIrWAjr7NJaq6u4ju/y7wOacnjGSgR8B2PWBh\nLnFOB6aDa8MooriMMSa0UlJg48bMpOB/3rjRJQi/evUgLg5UQYI7CYeXJVqvBZ7F/WALMFVEJqjq\nR4W5oYg0VdVNvs2BwIYcDvsS+B8Rqerb7gNMLMz9jDGmRDt6FDZsyJoU1q+HLVsgzbfIqQg0bgwX\nXgj9+0PLlu51ixZwzjnFFqqXcRgPAh39pQoRqQH8E8g3YYjIbFxJobqIJOFKEv1FpDmQDmzDddlF\nROKBsao6WlX3i8hfgKW+Sz2hqvtPu4Exxpwtfv/dJQJ/UvAnhm3bMo+JiICmTaF1a7juOpcUWraE\nZs2gfPnQxe7jpVvtalVtHbAdBqwK3FdSWLdaY0xIqcLu3acnhXXrYNeuzOOio13pwF9S8D9fcAFE\nRhZryAXpVuulhPGFiHwJzPZtX4drdzDGmLLp1CnYvh02bz49OewPqAypXNklg379siaHhg0hPDx0\n8ReSl7mkJojIENzUIADTVdWmBjHGlG4HDrh2hK1bMx/+7e3bM9sXAKpVc4ngmmsyk0LLllCnTtAb\nootTnglDRMKBf6pqT+Dj4gnJGGOKQWoqJCVlTQSBr3/PNrFEjRqu4fmii+CGG6BJE7fdsqV7rwzI\nM2GoapqIpItIFVU9WFxBGWNMkTh0KOcSwtatkJjokoZfRATExLhE0KmTSwb+pNCoUbH2RiqpvLRh\nHAFWi8jXwFH/TlUdF7SojDHGi7Q02Lkz5xLC1q2wN9tKDOed5xJA+/au+qhx48zEUK/eWdmuUJy8\nJIyPseooY0yo/fYbLF0KS5bA8uWuwTkxMesgtvBw16DcuDEMGZJZQvA/zj03ZOGXBnnNJdVAVber\n6lvFGVBIrFgBzZtDxYqhjsQYA3DkiPt3uWRJ5sM/XiEsDFq1gjZtYNCgrFVH9esXe7fUsiSvEsYn\nQHsAEZmjqlcVT0jFbN8+6NkT4uNh/vwSMTjGmDIlNRXWrs2aHNasgfR0935MDHTuDHfe6doW2re3\nP+5CJK+EEdgXrHGwAwmZatXglVdg+HD318qnn7pBNcaYoqfqSgo//ZSZHJYvh+PH3fvnneeSwqBB\n7rljR6hZM7Qxmwx5JQzN5XXpc9NNbiDOLbfAVVfBxx9DVFSoozLm7LdvX2a7g/+xZ497LyrKlRbG\njHHJoXNnV61UisYtlDZ5JYy2InIIV9Io73uNb1tVtXT1MRs1yhWN//QnuPZa+PBDKFcu1FEZc/Y4\nfhxWrsyaHLZsce+JuPEKAwa45NCpk5svydobzip5TW9e9vqXjRnjShp33AFDh8J779n/0MbkJC3N\nzbAamBx+/jlzXEP9+i4p+EsPHTq4aTLMWc1Lt9qy5fbb3f/048fDsGHw7rtuQI8xZVVqKmzaBAkJ\nrgSxdCksW+Z6MgFUqeLaGu67L7P0ULt2aGM2QWG/hDm56y5X0pgwwSWLt9+2AT2mbDh82JUUVq1y\nCSIhAVavhhMn3PvlyrnFekaMyEwOTZu6rq6m1LOEkZt773VJ44EHXLXUzJn2j8KUHqqQnJyZFPwJ\nYvPmzGOqVXPJ4fbboW1b97pFC6umLcMsYeRl4kSXNB591JU0pk+3pGHOPqdOufYGf3LwJ4h9+zKP\nueCCzJKDPznUrWs9lkwWQUsYIjITGADsVtVY375ngSuAk8AWYKSqHsjh3ETgMJAGpHpd3CMoHnnE\n/YN78kn3l9X//q/9IzIl14EDrkopMDmsXZs5fUZ0tOudNGSISwpxcW7bGqSNB8EsYcwCXgHeDtj3\nNTBRVVNF5GncOt3353J+T1Xdm8t7xeuJJ1zSePppV9J4+WVLGia0/APgAquTEhLc3Ep+NWu6hDB+\nfGZyaNrUOnGYQgva/zmqukhEYrLt+ypg80fg6mDdv0iJwFNPuaTx/POupPHcc5Y0TPFQdau5LVmS\nNTkc9K04IOLmQrvoIjeOyJ8czj8/tHGbUieUf2qMAt7P5T0FvhIRBV5X1em5XURExgBjABo0aFDk\nQQbcCKZMcV0MX3jBJY3Jky1pmOA4cQIWLIDPPnNznPkn3qtY0U26d8MNLim0bQuxsTa3kikWIUkY\nIvIgkAq8m8shF6tqsojUBL4WkQ2quiinA33JZDpAfHx8cKcwEYEXX3QljWeecUnjL3+xpGGKRnKy\nSxCffQb//CccOwYVKsAll8CDD0L37m5WVuvibUKk2BOGiIzANYb3VtUcf+BVNdn3vFtE5gKdgBwT\nRrETcZMVnjoFkya5pPHoo6GOypyN0tPdILj5812SWLnS7Y+JcVPVXH459Ohhk2GaEqNYE4aI9APu\nA7qr6rFcjqkIhKnqYd/rPsATxRhm/sLC4PXXXfXUY4+5pPHAA6GOypwNDh2Cr75ySeIf/4Ddu93/\nT126uE4Vl1/u5lyyUqspgYLZrXY20AOoLiJJwKO4XlFRuGomgB9VdayI1AHeUNX+QC1gru/9COBv\nqvpFsOIstLAweOMNV9J48EGXNCZMCHVUpiTatMkliPnzYdEi94dG1apw2WUuQfTr56b1NqaEC2Yv\nqaE57P5rLsfuBPr7Xm8F2gYrriIVHg6zZrkfgPvuc90V//znUEdlQu3kSfj++8wksWmT29+qFdx9\nt5ux9Q9/sO6t5qxj/8eeqYgIeOcdlzTuvtuVNO64I9RRmeK2e7erYpo/H7780s3JVK4c9OoF48a5\nkkSjRqGO0pgzYgmjKERGwt/+Btdc45aRjIx0/eFN6aXqxkL4u70uWeL21a4N11/vEkTv3lCpUqgj\nNabIWMIoKuXKwQcfuCkXxo51SWPUqFBHZYrS0aPwzTeZXV+Tk93+Tp3g8cddkmjXzhqsTallCaMo\nRUXBnDkwcCCMHu2qq26+OdRRmTOxYwf8/e+uFPGvf0FKiis19O3r2iIuuwxq1Qp1lMYUC0sYRS06\nGj75BK64AkaOdEnjhhtCHZUpiM2bXeKfM8eNkwA3YO6221yS6NrVlu81ZZIljGAoXx7mzYP+/eGm\nm1z11DXXhDoqkxtVN6OrP0msXu32x8e7OcQGDXJzNVlVkynjLGEES4UKrhrjssvc+uARETB4cKij\nMn6qsHx5ZpLYtMklhIsvdnOFDRkCwZybzJizkCWMYKpUCT7/HPr0geuucz9MV1wR6qjKrrQ0WLzY\n/Xf4+GPYvt2NpenVy3WJHjTIZng1Jg+WMIKtcmX44gu49FK4+mrXvnHZZaGOquw4dQq+/dYliU8+\ngV27XPtDnz6uZ9OVV9ooa2M8soRRHKpUcYO5LrnEVUvNm+d+sExwpKTA11+7JDFvHuzf76oI+/eH\nq65yz+ecE+oojTnrWMIoLlWruknnevd23W4/+8xVhZiicfSoG2k9Z477bg8fdon6iitckujb13VG\nMMYUmiWM4lStmvvLt2dP90P2j39At26hjursdeCA61gwZ46r9jtxAmrUcCOthwxxCdm6vxpTZCxh\nFLcaNdxo4R49XNXIl1+6qa2NN3v2wKefuiTxzTeujaJuXbj1VpckLr7YJvUzJkjsX1Yo1KrlRg33\n6OEawL/6yq3HbHKWnAxz57oksWiRW3iocWMYP94liU6d3HTzxpigsoQRKrVru6TRvburX//mGzdQ\nrKxSdYsL7duX+VizxiWJH390x7Rs6dYeGTLErWVtA+mMKVbBXEBpJm4p1t2qGuvb9yxwBXAS2AKM\nVNUDOZzbD3gJCMctrDQ5WHGGVN26mUnj0kvd63btQh3VmUtJcT/4+/dnTQA5PfzH7N/vpojPrn17\ntxTukCHQokXxfxZjTAbJZVntM7+wSDfgCPB2QMLoA/xLVVNF5GkAVb0/23nhwEbgUiAJWAoMVdV1\n+d0zPj5ely1bVrQfpDgkJrqkceSI63pbrpybyLBcuayvi3pfeHjecaWnw8GD+f/YZ38cPZr7NaOj\nXeO//3HeeVm3Ax8NGkC9ekX6VRtjshKR5arqqXojmCvuLRKRmGz7vgrY/BG4OodTOwGbfSvvISLv\nAQOBfBPGWSsmxpUuRo+GVavcim0nT7q/1P3PKSlFf9/w8NOTSLlyrj3g99/dIz0953NFXFdh/497\nnTrQunX+yaBChaL/HMaYYhHKNoxRwPs57K8L7AjYTgI6F0tEodSkCSxYkPv7qm5qi8AkEvjsdZ+X\n49PSsiaDnB5VquRfQjHGlCohSRgi8iCQCrxbBNcaA4wBaFCaJ4sTcd1FIyKgYsVQR2OMKYOKvS+i\niIzANYbfqDk3oCQD9QO26/n25UhVp6tqvKrG16hRo0hjNcYYk6lYE4av99N9wJWqeiyXw5YCTUWk\nkYiUA64H5hVXjMYYY3IWtIQhIrOBxUBzEUkSkVuAV4DKwNcikiAi03zH1hGRzwFUNRW4A/gSWA98\noKprgxWnMcYYb4LWrTYUztputcYYEyIF6VZr8ykYY4zxxBKGMcYYTyxhGGOM8cQShjHGGE9KVaO3\niOwBthXy9OrA3iIM52xm30VW9n1kZd9HptLwXTRUVU+D2EpVwjgTIrLMa0+B0s6+i6zs+8jKvo9M\nZe27sCopY4wxnljCMMYY44kljEzTQx1ACWLfRVb2fWRl30emMvVdWBuGMcYYT6yEYYwxxpMynzBE\npJ+I/EdENovIf4c6nlASkfoiskBE1onIWhG5K9QxhZqIhIvIShGZH+pYQk1EzhWRj0Rkg4isF5E/\nhDqmUBKRP/v+nawRkdkiEh3qmIKtTCcM3/rhrwKXAS2BoSLSMrRRhVQqcI+qtgQuAm4v498HwF24\nWZMNvAR8oaotgLaU4e9FROoC44B4VY0FwnFLMZRqZTphELB+uKqeBPzrh5dJqvqrqq7wvT6M+0Go\nG9qoQkdE6gGXA2+EOpZQE5EqQDfgrwCqelJVD4Q2qpCLAMqLSARQAdgZ4niCrqwnjJzWDy+zP5CB\nRCQGaAf8FNpIQupF3IJf6aEOpARoBOwB3vRV0b0hImV2rWBVTQamANuBX4GDqvpVaKMKvrKeMEwO\nRKQSMAcYr6qHQh1PKIjIAGC3qi4PdSwlRATQHnhNVdsBR4Ey2+YnIlVxtRGNgDpARREZFtqogq+s\nJ4wCrR9eFohIJC5ZvKuqH4c6nhDqAlwpIom4qspeIvJ/oQ0ppJKAJFX1lzg/wiWQsuoS4BdV3aOq\np4CPgT+GOKagK+sJw9YPDyAigqujXq+qz4c6nlBS1YmqWk9VY3D/X/xLVUv9X5C5UdVdwA4Rae7b\n1RtYF8KQQm07cJGIVPD9u+lNGegEEBHqAEJJVVNFxL9+eDgws4yvH94FuAlYLSIJvn0PqOrnIYzJ\nlBx3Au/6/rjaCowMcTwho6o/ichHwApc78KVlIFR3zbS2xhjjCdlvUrKGGOMR5YwjDHGeGIJwxhj\njCeWMIwxxnhiCcMYY4wnljCMKQARSRORhIBHkY12FpEYEVlTVNczpqiV6XEYxhTCcVWNC3UQxoSC\nlTCMKQIikigiz4jIahFZIiIX+PbHiMi/RORnEflGRBr49tcSkbkissr38E8rES4iM3zrLHwlIuVD\n9qGMycYShjEFUz5bldR1Ae8dVNXWwCu4mW4BpgJvqWob4F3gZd/+l4FvVbUtbk4m/wwDTYFXVbUV\ncAC4KsifxxjPbKS3MQUgIkdUtVIO+xOBXqq61TeB4y5VrSYie4HaqnrKt/9XVa0uInuAeqqaEnCN\nGOBrVW3q274fiFTVJ4P/yYzJn5UwjCk6msvrgkgJeJ2GtTOaEsQShjFF57qA58W+1/8mc+nOG4Hv\nfK+/AW6DjHXDqxRXkMYUlv31YkzBlA+YyRfcGtf+rrVVReRnXClhqG/fnbhV6ibgVqzzz/B6FzBd\nRG7BlSRuw63cZkyJZW0YxhQBXxtGvKruDXUsxgSLVUkZY4zxxEoYxhhjPLEShjHGGE8sYRhjjPHE\nEoYxxhhPLGEYY4zxxBKGMcYYTyxhGGOM8eT/AZ3/cOKNxK1OAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JGtutiXuoZyx",
        "colab_type": "text"
      },
      "source": [
        "# Train and Validation Accuracy: CG vs SGD\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s-SNIr10o2va",
        "colab_type": "code",
        "outputId": "bf493f94-9a53-4911-bbb5-8720cfbf6b55",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        }
      },
      "source": [
        "plt.plot(history_cg.history['accuracy'], color='r', label='CG_train')\n",
        "plt.plot(history_cg.history['val_accuracy'], color='g', label='CG_test')\n",
        "plt.plot(history_sgd.history['accuracy'], color='pink', label='SGD_train')\n",
        "plt.plot(history_sgd.history['val_accuracy'], color='b', label='SGD_test')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.legend(loc=4)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f5d8dbb86a0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5W7Z0KXz6KfzhD3Y1oFNwueBPf7Ix5Ysv7EJBf/gDXHNNkJZ1rqq2zUwHC+x+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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}