03. Gradient Descent Variants/02. Nesterov Accelerated Gradient/02. Nesterov Accelerated Gradient - MXNet.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "L3KIZndDdgt4",
        "colab_type": "code",
        "outputId": "758b97e6-ae44-4cc5-b132-9e206028778a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 155
        }
      },
      "source": [
        "!pip install mxnet-cu100"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: mxnet-cu100 in /usr/local/lib/python3.6/dist-packages (1.4.1)\n",
            "Requirement already satisfied: graphviz<0.9.0,>=0.8.1 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (0.8.4)\n",
            "Requirement already satisfied: 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: requests>=2.20.0 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (2.21.0)\n",
            "Requirement already satisfied: urllib3<1.25,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (1.24.3)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2019.3.9)\n",
            "Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (3.0.4)\n",
            "Requirement already satisfied: idna<2.9,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2.8)\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",
        "data_ctx = mx.cpu()\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.MNIST(train = True, transform = transform)\n",
        "test_mnist = gluon.data.vision.MNIST(train = False, transform = transform)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sAXcT8nSWEYo",
        "colab_type": "code",
        "outputId": "2ddaa7f0-bfd6-4fa9-fb0c-bf9713e47bd3",
        "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": "df332ce1-0603-4626-88fd-ab6f993fcb2c",
        "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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/KZZX+tol+qrkdWv5Z37bQyS9LOkLkjZKekLSvIh4vqWN1GB7g6SOiKj8ghDbZ0raLWll\nRJxYLPsHSdsjYnHxD+f4iLiqTXq7TtLuqqdtL2aTmtxzWnlJcyVdogpfu0RfF6qC162KI/8sSa9G\nxPqI2CvpbknnV9BH24uIxyRt/9Di8yWtKO6vUPf/PC1Xo7e2EBGbI+Kp4v4uSQenla/0tUv0VYkq\nwj9F0i96PN6oCl+AXoSkH9l+0vaCqpvpxaSI2Fzcf0vSpCqb6UWf07a30oemlW+b166e6e7Lxgm/\nj5odEZ+T9CVJVxRvb9tSdH9ma6ex2n5N294qvUwr/ytVvnb1TndftirCv0nS1B6PP1UsawsRsan4\nu1XSA2q/qce3HJwhufi7teJ+fqWdpm3vbVp5tcFr107T3VcR/ickzbA9zfZwSV+RtKqCPj7C9uji\nRIxsj5Z0rtpv6vFVkuYX9+dLerDCXn5Nu0zbXmtaeVX82rXddPcR0fKbpPPUfcb/NUl/UUUPNfo6\nWtLTxe25qnuTdJe63wbuU/e5kcskfULSakmvSPoPSRPaqLd/k/SspGfUHbTJFfU2W91v6Z+RtLa4\nnVf1a5foq5LXjct7gUxxwg/IFOEHMkX4gUwRfiBThB/IFOEHMkX4gUz9P9qP2WzRJoUOAAAAAElF\nTkSuQmCC\n",
            "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",
        "vs = []\n",
        "for param in params:\n",
        "    param.attach_grad()\n",
        "    vs.append(param.zeros_like())\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 NAG Optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hvFKa4WuI9c-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def nag(params = params, vs = vs, lr = 0.001, mr = 0.9):\n",
        "    for param, v in zip(params, vs):\n",
        "        v_prev = v.copy()\n",
        "        v[:] = mr * v - lr * param.grad / batch_size\n",
        "        param[:] = param + ((-mr * v_prev) + ((1 + mr) * v))"
      ],
      "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": "UlkEn5XxFPkd",
        "colab_type": "text"
      },
      "source": [
        "##Training the  model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kVao6lbWCizF",
        "colab_type": "code",
        "outputId": "6c0489cf-afaa-4be1-91bf-73325887e60c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 190
        }
      },
      "source": [
        "epochs = 10\n",
        "num_batches = 60000/batch_size\n",
        "learning_rate = .01\n",
        "losses = []\n",
        "accs = []\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    cumulative_loss = 0\n",
        "    cumulative_acc = 0\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",
        "        nag(params, vs, lr = learning_rate) # NAG OPTIMIZER\n",
        "        cumulative_loss += loss\n",
        "        acc = accuracy(output, labels)\n",
        "        cumulative_acc += acc\n",
        "    loss = cumulative_loss.asscalar()/num_batches\n",
        "    acc = cumulative_acc.asscalar()/num_batches\n",
        "    losses.append(loss)\n",
        "    accs.append(acc)\n",
        "    print(f'Epoch: {epoch} | Loss: {loss:.5f} | Accuracy: {acc:.5f}')"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch: 0 | Loss: 72.08955 | Accuracy: 0.60927\n",
            "Epoch: 1 | Loss: 17.75527 | Accuracy: 0.92048\n",
            "Epoch: 2 | Loss: 10.91432 | Accuracy: 0.95073\n",
            "Epoch: 3 | Loss: 7.75498 | Accuracy: 0.96532\n",
            "Epoch: 4 | Loss: 5.97464 | Accuracy: 0.97373\n",
            "Epoch: 5 | Loss: 4.72869 | Accuracy: 0.97880\n",
            "Epoch: 6 | Loss: 3.91832 | Accuracy: 0.98242\n",
            "Epoch: 7 | Loss: 3.28540 | Accuracy: 0.98522\n",
            "Epoch: 8 | Loss: 2.72346 | Accuracy: 0.98815\n",
            "Epoch: 9 | Loss: 2.34401 | Accuracy: 0.98958\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",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b07b612c-48b2-4b8d-c861-8bbbe0e83e77"
      },
      "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": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Test Accuracy: 0.9754179936305732\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('Optimizer Step')\n",
        "    plt.ylabel('Loss')\n",
        "    plt.show()\n",
        "    \n",
        "    plt.plot(accs, 'g')\n",
        "    plt.title('Accuracy during Training')\n",
        "    plt.xlabel('Optimizer Step')\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: {predictions}, Target: {labels}')\n",
        "        plt.show()\n",
        "        if i == samples:\n",
        "            break"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mkorWu1EYu2b",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 3477
        },
        "outputId": "c396fcdb-2f9e-49ed-fbc8-8a2a9a562e7a"
      },
      "source": [
        "plot(samples = 10)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mj7s7CHixj69tRv4+dvN30Zm/j86a4fs4NCJ6bVIpJAgGkqS2iGgtuo564e9j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\nn1rZRHnf5AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ib0Sc1YXPkotCbYGBFQM547gz8g7FzCwz5d4NBSRPb0fEXRHx7jKqzwfWRMTa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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5EzdwzL6F9fMv+W5hfYiKf4VOW3xGxdped/v7+q3kLb9Zohx+s0Q5/GaJcvjNEuXwmyXK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\n+M0S5fCbJcrhN0uUw2+WqP8HMSMTgWJpncQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8Zoly+M0S5fCbJcrhN0uUw2+WKJ/n3wZsnLRTxdrIl6e0sZPX2vzsmoq12FB++TaNLn//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\nRU5ErkJggg==\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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Ov1miHH6zRPmQXmuqB859dcXa/Yd8tanzvmHt+Iq1S884pvC+ox4sPlx4S+A1v1miHH6z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\nawvz0N0dgQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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4zTLl8JtlyuE3y5R/ursVfnlPaXnLGr9tPHu/E0vry3fu3nH+rc/7eVP3X/L9XavW7txr\nQVOPneNx/Fbymt8sUw6/WaYcfrNMOfxmmXL4zTLl8JtlyuE3y5SP8/eAUTffVVrf+ubO9NEOLy6e\nUL24V3OPHfvMLK3r1oXNLWAj5zW/WaYcfrNMOfxmmXL4zTLl8JtlyuE3y5TDb5apek7RPQ24CJhM\ncUru+RFxlqRJwHeB6RSn6T46Ip5tX6s2IpX8gvwmTa57fBy/OfWM/hrgUxGxC7A38DFJuwAnAzdG\nxM7Ajem2mY0QNcMfEQMRcVe6vgK4H9geOBy4MM12IXBEu5o0s9bboPddkqYDuwO3A5MjYiCVllJs\nFpjZCFF3+CVtDlwJfCIinq+sRXHCv2FP+idprqR+Sf2rWdVUs2bWOnWFX9IYiuBfGhHfT5OflDQl\n1acAy4a7b0TMj4i+iOgbQ/d+iNLM1lcz/JIEnA/cHxFfrShdA8xJ1+cAV7e+PTNrl3q+0rsPMBu4\nR9LgsZXPAqcDV0g6FngMOLo9LdqIVnIG+HWs61wf9jI1wx8RP6P60dpZrW3HzDrFn/Azy5TDb5Yp\nh98sUw6/WaYcfrNMOfxmmfJPd1tbrRvX+LH8p9b64+Dt5DW/WaYcfrNMOfxmmXL4zTLl8JtlyuE3\ny5TDb5YpH+e3trrkoHOr1u5/qfwzAMcs+ExpfQdua6gnK3jNb5Yph98sUw6/WaYcfrNMOfxmmXL4\nzTLl8Jtlysf5ra1O++17qtZe+Ob2pffd4Uofx28nr/nNMuXwm2XK4TfLlMNvlimH3yxTDr9Zphx+\ns0zVPM4vaRpwETCZ4mzr8yPiLEnzgOOAp9Ksn42Ia9vVqI1Qs56oWhpP9Zq1Xz0f8lkDfCoi7pI0\nAbhT0vWpdmZEfKV97ZlZu9QMf0QMAAPp+gpJ9wPlH80ys563Qdv8kqYDuwO3p0knSLpb0gWSJla5\nz1xJ/ZL6V+PTL5n1irrDL2lz4ErgExHxPHAOMAOYSfHO4Izh7hcR8yOiLyL6xjC2BS2bWSvUFX5J\nYyiCf2lEfB8gIp6MiLURsQ44D9izfW2aWavVDL8kAecD90fEVyumT6mY7UhgUevbM7N2qWdv/z7A\nbOAeSQvTtM8Cx0iaSXH4bzFwfFs6NLO2qGdv/88ADVPyMX2zEcyf8DPLlMNvlimH3yxTDr9Zphx+\ns0w5/GaZcvjNMuXwm2XK4TfLlMNvlimH3yxTDr9Zphx+s0w5/GaZUkR0bmHSU8BjFZO2AZ7uWAMb\npld769W+wL01qpW97RgR29YzY0fD/7KFS/0R0de1Bkr0am+92he4t0Z1qze/7TfLlMNvlqluh39+\nl5dfpld769W+wL01qiu9dXWb38y6p9trfjPrEoffLFNdCb+kgyQ9KOkRSSd3o4dqJC2WdI+khZL6\nu9zLBZKWSVpUMW2SpOslPZz+HfYciV3qbZ6kJWnsFko6pEu9TZN0k6T7JN0r6eNpelfHrqSvroxb\nx7f5JY0CHgLeBTwB3AEcExH3dbSRKiQtBvoiousfCJH0NmAlcFFE7JamfRl4JiJOTy+cEyPipB7p\nbR6wstunbU9nk5pSeVp54Ajgw3Rx7Er6OpoujFs31vx7Ao9ExKMR8RLwHeDwLvTR8yLiFuCZIZMP\nBy5M1y+k+OPpuCq99YSIGIiIu9L1FcDgaeW7OnYlfXVFN8K/PfB4xe0n6OIADCOA6yTdKWlut5sZ\nxuSIGEjXlwKTu9nMMGqetr2ThpxWvmfGrpHT3bead/i93L4RsQdwMPCx9Pa2J0WxzdZLx2rrOm17\npwxzWvk/6+bYNXq6+1brRviXANMqbk9N03pCRCxJ/y4DrqL3Tj3+5OAZktO/y7rcz5/10mnbhzut\nPD0wdr10uvtuhP8OYGdJr5K0KfA+4Jou9PEyksanHTFIGg8cQO+devwaYE66Pge4uou9rKdXTtte\n7bTydHnseu509xHR8QtwCMUe/98An+tGD1X6ejXw63S5t9u9AZdTvA1cTbFv5Fhga+BG4GHgBmBS\nD/V2MXAPcDdF0KZ0qbd9Kd7S3w0sTJdDuj12JX11Zdz88V6zTHmHn1mmHH6zTDn8Zply+M0y5fCb\nZcrhN8uUw2+Wqf8HUhwCDoDKAlkAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F+YCh5psnaUDSwHa2NlWsmbVOXeGXNJoi+N+IiOvT5HWSJqX2ScD6oeaNiP6I6IuIvtGM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\nMuXwm2XK4TfLlMNvlimH3yxTDr9Zpv4fvKOx8+BAmnEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NMuXwm2XK4TfLlMNvlimH3yxT/kqvJb00+SPJ+uP7XJysz1v9ZtXa0Bffbqgnaw1v+c0y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\nDr9Zphx+s0w5/GaZ+n8ipiWeX9R7+gAAAABJRU5ErkJggg==\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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            "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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ptT5rw7v3K6zfsO9XC6rFnza96b8OK6yP4jeF9b7AW36zRDn8Zoly+M0S5fCbJcrhN0uU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\nZoly+M0S9f/UgQT5U0ay5AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "59YfC3nthjfA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q0bTWSV-hjeE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "name": "Nesterov Accelerated Gradient Optimizer.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}