04_mnist_basics.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/github/MUKESHRAJMAHENDRAN/Deep-Learning--fastai/blob/main/04_mnist_basics.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "L6POuOtqrM7o"
      },
      "outputs": [],
      "source": [
        "#hide\n",
        "! [ -e /content ] && pip install -Uqq fastbook\n",
        "import fastbook\n",
        "fastbook.setup_book()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "ckzyTO6nrM7v"
      },
      "outputs": [],
      "source": [
        "#hide\n",
        "from fastai.vision.all import *\n",
        "from fastbook import *\n",
        "\n",
        "matplotlib.rc('image', cmap='Greys')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ibfabejarM75"
      },
      "source": [
        "# Under the Hood: Training a Digit Classifier"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AIvACciNrM79"
      },
      "source": [
        "## Pixels: The Foundations of Computer Vision"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "En9t8ho8rM7_"
      },
      "source": [
        "## Sidebar: Tenacity and Deep Learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_xwzzHIOrM8B"
      },
      "source": [
        "## End sidebar"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "X7wIjXIbrM8D"
      },
      "outputs": [],
      "source": [
        "path = untar_data(URLs.MNIST_SAMPLE)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "path"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pnt555oOrwqO",
        "outputId": "30cfb281-3c06-407e-9b0a-4ed38f38b1f5"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Path('/root/.fastai/data/mnist_sample')"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "U1r6DemZrM8G"
      },
      "outputs": [],
      "source": [
        "#hide\n",
        "Path.BASE_PATH = path"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v-DDDHnRrM8I",
        "outputId": "30ebe5ba-69e1-4b8a-a3c3-24af95e79200"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(#3) [Path('train'),Path('labels.csv'),Path('valid')]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "path.ls()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "Xcmf1HpRrM8J",
        "outputId": "f69469f0-0d10-41d3-82b1-3985cf2b0977"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(#2) [Path('train/3'),Path('train/7')]"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "(path/'train').ls()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
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        "id": "T9L45T0vrM8K",
        "outputId": "a94e0288-6f38-411e-c020-95345871dec9"
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      "outputs": [
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          "data": {
            "text/plain": [
              "(#6131) [Path('train/3/10.png'),Path('train/3/10000.png'),Path('train/3/10011.png'),Path('train/3/10031.png'),Path('train/3/10034.png'),Path('train/3/10042.png'),Path('train/3/10052.png'),Path('train/3/1007.png'),Path('train/3/10074.png'),Path('train/3/10091.png')...]"
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          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "threes = (path/'train'/'3').ls().sorted()\n",
        "sevens = (path/'train'/'7').ls().sorted()\n",
        "threes"
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        "im3_path = threes[1]\n",
        "im3 = Image.open(im3_path)\n",
        "im3"
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              "  font-size: 6pt;\n",
              "  background-color: #545454;\n",
              "  color: #f1f1f1;\n",
              "}\n",
              "#T_34899_row8_col12 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #f1f1f1;\n",
              "  color: #000000;\n",
              "}\n",
              "#T_34899_row9_col5 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #f7f7f7;\n",
              "  color: #000000;\n",
              "}\n",
              "#T_34899_row9_col7 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #030303;\n",
              "  color: #f1f1f1;\n",
              "}\n",
              "#T_34899_row9_col12 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #181818;\n",
              "  color: #f1f1f1;\n",
              "}\n",
              "#T_34899_row9_col13 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #303030;\n",
              "  color: #f1f1f1;\n",
              "}\n",
              "#T_34899_row9_col14 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #a9a9a9;\n",
              "  color: #f1f1f1;\n",
              "}\n",
              "#T_34899_row9_col15 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #fefefe;\n",
              "  color: #000000;\n",
              "}\n",
              "#T_34899_row10_col8, #T_34899_row10_col9 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #bababa;\n",
              "  color: #000000;\n",
              "}\n",
              "#T_34899_row10_col10 {\n",
              "  font-size: 6pt;\n",
              "  background-color: #393939;\n",
              "  color: #f1f1f1;\n",
              "}\n",
              "</style>\n",
              "<table id=\"T_34899_\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr>\n",
              "      <th class=\"blank level0\" >&nbsp;</th>\n",
              "      <th class=\"col_heading level0 col0\" >0</th>\n",
              "      <th class=\"col_heading level0 col1\" >1</th>\n",
              "      <th class=\"col_heading level0 col2\" >2</th>\n",
              "      <th class=\"col_heading level0 col3\" >3</th>\n",
              "      <th class=\"col_heading level0 col4\" >4</th>\n",
              "      <th class=\"col_heading level0 col5\" >5</th>\n",
              "      <th class=\"col_heading level0 col6\" >6</th>\n",
              "      <th class=\"col_heading level0 col7\" >7</th>\n",
              "      <th class=\"col_heading level0 col8\" >8</th>\n",
              "      <th class=\"col_heading level0 col9\" >9</th>\n",
              "      <th class=\"col_heading level0 col10\" >10</th>\n",
              "      <th class=\"col_heading level0 col11\" >11</th>\n",
              "      <th class=\"col_heading level0 col12\" >12</th>\n",
              "      <th class=\"col_heading level0 col13\" >13</th>\n",
              "      <th class=\"col_heading level0 col14\" >14</th>\n",
              "      <th class=\"col_heading level0 col15\" >15</th>\n",
              "      <th class=\"col_heading level0 col16\" >16</th>\n",
              "      <th class=\"col_heading level0 col17\" >17</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
              "      <td id=\"T_34899_row0_col0\" class=\"data row0 col0\" >0</td>\n",
              "      <td id=\"T_34899_row0_col1\" class=\"data row0 col1\" >0</td>\n",
              "      <td id=\"T_34899_row0_col2\" class=\"data row0 col2\" >0</td>\n",
              "      <td id=\"T_34899_row0_col3\" class=\"data row0 col3\" >0</td>\n",
              "      <td id=\"T_34899_row0_col4\" class=\"data row0 col4\" >0</td>\n",
              "      <td id=\"T_34899_row0_col5\" class=\"data row0 col5\" >0</td>\n",
              "      <td id=\"T_34899_row0_col6\" class=\"data row0 col6\" >0</td>\n",
              "      <td id=\"T_34899_row0_col7\" class=\"data row0 col7\" >0</td>\n",
              "      <td id=\"T_34899_row0_col8\" class=\"data row0 col8\" >0</td>\n",
              "      <td id=\"T_34899_row0_col9\" class=\"data row0 col9\" >0</td>\n",
              "      <td id=\"T_34899_row0_col10\" class=\"data row0 col10\" >0</td>\n",
              "      <td id=\"T_34899_row0_col11\" class=\"data row0 col11\" >0</td>\n",
              "      <td id=\"T_34899_row0_col12\" class=\"data row0 col12\" >0</td>\n",
              "      <td id=\"T_34899_row0_col13\" class=\"data row0 col13\" >0</td>\n",
              "      <td id=\"T_34899_row0_col14\" class=\"data row0 col14\" >0</td>\n",
              "      <td id=\"T_34899_row0_col15\" class=\"data row0 col15\" >0</td>\n",
              "      <td id=\"T_34899_row0_col16\" class=\"data row0 col16\" >0</td>\n",
              "      <td id=\"T_34899_row0_col17\" class=\"data row0 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
              "      <td id=\"T_34899_row1_col0\" class=\"data row1 col0\" >0</td>\n",
              "      <td id=\"T_34899_row1_col1\" class=\"data row1 col1\" >0</td>\n",
              "      <td id=\"T_34899_row1_col2\" class=\"data row1 col2\" >0</td>\n",
              "      <td id=\"T_34899_row1_col3\" class=\"data row1 col3\" >0</td>\n",
              "      <td id=\"T_34899_row1_col4\" class=\"data row1 col4\" >0</td>\n",
              "      <td id=\"T_34899_row1_col5\" class=\"data row1 col5\" >29</td>\n",
              "      <td id=\"T_34899_row1_col6\" class=\"data row1 col6\" >150</td>\n",
              "      <td id=\"T_34899_row1_col7\" class=\"data row1 col7\" >195</td>\n",
              "      <td id=\"T_34899_row1_col8\" class=\"data row1 col8\" >254</td>\n",
              "      <td id=\"T_34899_row1_col9\" class=\"data row1 col9\" >255</td>\n",
              "      <td id=\"T_34899_row1_col10\" class=\"data row1 col10\" >254</td>\n",
              "      <td id=\"T_34899_row1_col11\" class=\"data row1 col11\" >176</td>\n",
              "      <td id=\"T_34899_row1_col12\" class=\"data row1 col12\" >193</td>\n",
              "      <td id=\"T_34899_row1_col13\" class=\"data row1 col13\" >150</td>\n",
              "      <td id=\"T_34899_row1_col14\" class=\"data row1 col14\" >96</td>\n",
              "      <td id=\"T_34899_row1_col15\" class=\"data row1 col15\" >0</td>\n",
              "      <td id=\"T_34899_row1_col16\" class=\"data row1 col16\" >0</td>\n",
              "      <td id=\"T_34899_row1_col17\" class=\"data row1 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
              "      <td id=\"T_34899_row2_col0\" class=\"data row2 col0\" >0</td>\n",
              "      <td id=\"T_34899_row2_col1\" class=\"data row2 col1\" >0</td>\n",
              "      <td id=\"T_34899_row2_col2\" class=\"data row2 col2\" >0</td>\n",
              "      <td id=\"T_34899_row2_col3\" class=\"data row2 col3\" >48</td>\n",
              "      <td id=\"T_34899_row2_col4\" class=\"data row2 col4\" >166</td>\n",
              "      <td id=\"T_34899_row2_col5\" class=\"data row2 col5\" >224</td>\n",
              "      <td id=\"T_34899_row2_col6\" class=\"data row2 col6\" >253</td>\n",
              "      <td id=\"T_34899_row2_col7\" class=\"data row2 col7\" >253</td>\n",
              "      <td id=\"T_34899_row2_col8\" class=\"data row2 col8\" >234</td>\n",
              "      <td id=\"T_34899_row2_col9\" class=\"data row2 col9\" >196</td>\n",
              "      <td id=\"T_34899_row2_col10\" class=\"data row2 col10\" >253</td>\n",
              "      <td id=\"T_34899_row2_col11\" class=\"data row2 col11\" >253</td>\n",
              "      <td id=\"T_34899_row2_col12\" class=\"data row2 col12\" >253</td>\n",
              "      <td id=\"T_34899_row2_col13\" class=\"data row2 col13\" >253</td>\n",
              "      <td id=\"T_34899_row2_col14\" class=\"data row2 col14\" >233</td>\n",
              "      <td id=\"T_34899_row2_col15\" class=\"data row2 col15\" >0</td>\n",
              "      <td id=\"T_34899_row2_col16\" class=\"data row2 col16\" >0</td>\n",
              "      <td id=\"T_34899_row2_col17\" class=\"data row2 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
              "      <td id=\"T_34899_row3_col0\" class=\"data row3 col0\" >0</td>\n",
              "      <td id=\"T_34899_row3_col1\" class=\"data row3 col1\" >93</td>\n",
              "      <td id=\"T_34899_row3_col2\" class=\"data row3 col2\" >244</td>\n",
              "      <td id=\"T_34899_row3_col3\" class=\"data row3 col3\" >249</td>\n",
              "      <td id=\"T_34899_row3_col4\" class=\"data row3 col4\" >253</td>\n",
              "      <td id=\"T_34899_row3_col5\" class=\"data row3 col5\" >187</td>\n",
              "      <td id=\"T_34899_row3_col6\" class=\"data row3 col6\" >46</td>\n",
              "      <td id=\"T_34899_row3_col7\" class=\"data row3 col7\" >10</td>\n",
              "      <td id=\"T_34899_row3_col8\" class=\"data row3 col8\" >8</td>\n",
              "      <td id=\"T_34899_row3_col9\" class=\"data row3 col9\" >4</td>\n",
              "      <td id=\"T_34899_row3_col10\" class=\"data row3 col10\" >10</td>\n",
              "      <td id=\"T_34899_row3_col11\" class=\"data row3 col11\" >194</td>\n",
              "      <td id=\"T_34899_row3_col12\" class=\"data row3 col12\" >253</td>\n",
              "      <td id=\"T_34899_row3_col13\" class=\"data row3 col13\" >253</td>\n",
              "      <td id=\"T_34899_row3_col14\" class=\"data row3 col14\" >233</td>\n",
              "      <td id=\"T_34899_row3_col15\" class=\"data row3 col15\" >0</td>\n",
              "      <td id=\"T_34899_row3_col16\" class=\"data row3 col16\" >0</td>\n",
              "      <td id=\"T_34899_row3_col17\" class=\"data row3 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
              "      <td id=\"T_34899_row4_col0\" class=\"data row4 col0\" >0</td>\n",
              "      <td id=\"T_34899_row4_col1\" class=\"data row4 col1\" >107</td>\n",
              "      <td id=\"T_34899_row4_col2\" class=\"data row4 col2\" >253</td>\n",
              "      <td id=\"T_34899_row4_col3\" class=\"data row4 col3\" >253</td>\n",
              "      <td id=\"T_34899_row4_col4\" class=\"data row4 col4\" >230</td>\n",
              "      <td id=\"T_34899_row4_col5\" class=\"data row4 col5\" >48</td>\n",
              "      <td id=\"T_34899_row4_col6\" class=\"data row4 col6\" >0</td>\n",
              "      <td id=\"T_34899_row4_col7\" class=\"data row4 col7\" >0</td>\n",
              "      <td id=\"T_34899_row4_col8\" class=\"data row4 col8\" >0</td>\n",
              "      <td id=\"T_34899_row4_col9\" class=\"data row4 col9\" >0</td>\n",
              "      <td id=\"T_34899_row4_col10\" class=\"data row4 col10\" >0</td>\n",
              "      <td id=\"T_34899_row4_col11\" class=\"data row4 col11\" >192</td>\n",
              "      <td id=\"T_34899_row4_col12\" class=\"data row4 col12\" >253</td>\n",
              "      <td id=\"T_34899_row4_col13\" class=\"data row4 col13\" >253</td>\n",
              "      <td id=\"T_34899_row4_col14\" class=\"data row4 col14\" >156</td>\n",
              "      <td id=\"T_34899_row4_col15\" class=\"data row4 col15\" >0</td>\n",
              "      <td id=\"T_34899_row4_col16\" class=\"data row4 col16\" >0</td>\n",
              "      <td id=\"T_34899_row4_col17\" class=\"data row4 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
              "      <td id=\"T_34899_row5_col0\" class=\"data row5 col0\" >0</td>\n",
              "      <td id=\"T_34899_row5_col1\" class=\"data row5 col1\" >3</td>\n",
              "      <td id=\"T_34899_row5_col2\" class=\"data row5 col2\" >20</td>\n",
              "      <td id=\"T_34899_row5_col3\" class=\"data row5 col3\" >20</td>\n",
              "      <td id=\"T_34899_row5_col4\" class=\"data row5 col4\" >15</td>\n",
              "      <td id=\"T_34899_row5_col5\" class=\"data row5 col5\" >0</td>\n",
              "      <td id=\"T_34899_row5_col6\" class=\"data row5 col6\" >0</td>\n",
              "      <td id=\"T_34899_row5_col7\" class=\"data row5 col7\" >0</td>\n",
              "      <td id=\"T_34899_row5_col8\" class=\"data row5 col8\" >0</td>\n",
              "      <td id=\"T_34899_row5_col9\" class=\"data row5 col9\" >0</td>\n",
              "      <td id=\"T_34899_row5_col10\" class=\"data row5 col10\" >43</td>\n",
              "      <td id=\"T_34899_row5_col11\" class=\"data row5 col11\" >224</td>\n",
              "      <td id=\"T_34899_row5_col12\" class=\"data row5 col12\" >253</td>\n",
              "      <td id=\"T_34899_row5_col13\" class=\"data row5 col13\" >245</td>\n",
              "      <td id=\"T_34899_row5_col14\" class=\"data row5 col14\" >74</td>\n",
              "      <td id=\"T_34899_row5_col15\" class=\"data row5 col15\" >0</td>\n",
              "      <td id=\"T_34899_row5_col16\" class=\"data row5 col16\" >0</td>\n",
              "      <td id=\"T_34899_row5_col17\" class=\"data row5 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
              "      <td id=\"T_34899_row6_col0\" class=\"data row6 col0\" >0</td>\n",
              "      <td id=\"T_34899_row6_col1\" class=\"data row6 col1\" >0</td>\n",
              "      <td id=\"T_34899_row6_col2\" class=\"data row6 col2\" >0</td>\n",
              "      <td id=\"T_34899_row6_col3\" class=\"data row6 col3\" >0</td>\n",
              "      <td id=\"T_34899_row6_col4\" class=\"data row6 col4\" >0</td>\n",
              "      <td id=\"T_34899_row6_col5\" class=\"data row6 col5\" >0</td>\n",
              "      <td id=\"T_34899_row6_col6\" class=\"data row6 col6\" >0</td>\n",
              "      <td id=\"T_34899_row6_col7\" class=\"data row6 col7\" >0</td>\n",
              "      <td id=\"T_34899_row6_col8\" class=\"data row6 col8\" >0</td>\n",
              "      <td id=\"T_34899_row6_col9\" class=\"data row6 col9\" >0</td>\n",
              "      <td id=\"T_34899_row6_col10\" class=\"data row6 col10\" >249</td>\n",
              "      <td id=\"T_34899_row6_col11\" class=\"data row6 col11\" >253</td>\n",
              "      <td id=\"T_34899_row6_col12\" class=\"data row6 col12\" >245</td>\n",
              "      <td id=\"T_34899_row6_col13\" class=\"data row6 col13\" >126</td>\n",
              "      <td id=\"T_34899_row6_col14\" class=\"data row6 col14\" >0</td>\n",
              "      <td id=\"T_34899_row6_col15\" class=\"data row6 col15\" >0</td>\n",
              "      <td id=\"T_34899_row6_col16\" class=\"data row6 col16\" >0</td>\n",
              "      <td id=\"T_34899_row6_col17\" class=\"data row6 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
              "      <td id=\"T_34899_row7_col0\" class=\"data row7 col0\" >0</td>\n",
              "      <td id=\"T_34899_row7_col1\" class=\"data row7 col1\" >0</td>\n",
              "      <td id=\"T_34899_row7_col2\" class=\"data row7 col2\" >0</td>\n",
              "      <td id=\"T_34899_row7_col3\" class=\"data row7 col3\" >0</td>\n",
              "      <td id=\"T_34899_row7_col4\" class=\"data row7 col4\" >0</td>\n",
              "      <td id=\"T_34899_row7_col5\" class=\"data row7 col5\" >0</td>\n",
              "      <td id=\"T_34899_row7_col6\" class=\"data row7 col6\" >0</td>\n",
              "      <td id=\"T_34899_row7_col7\" class=\"data row7 col7\" >14</td>\n",
              "      <td id=\"T_34899_row7_col8\" class=\"data row7 col8\" >101</td>\n",
              "      <td id=\"T_34899_row7_col9\" class=\"data row7 col9\" >223</td>\n",
              "      <td id=\"T_34899_row7_col10\" class=\"data row7 col10\" >253</td>\n",
              "      <td id=\"T_34899_row7_col11\" class=\"data row7 col11\" >248</td>\n",
              "      <td id=\"T_34899_row7_col12\" class=\"data row7 col12\" >124</td>\n",
              "      <td id=\"T_34899_row7_col13\" class=\"data row7 col13\" >0</td>\n",
              "      <td id=\"T_34899_row7_col14\" class=\"data row7 col14\" >0</td>\n",
              "      <td id=\"T_34899_row7_col15\" class=\"data row7 col15\" >0</td>\n",
              "      <td id=\"T_34899_row7_col16\" class=\"data row7 col16\" >0</td>\n",
              "      <td id=\"T_34899_row7_col17\" class=\"data row7 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
              "      <td id=\"T_34899_row8_col0\" class=\"data row8 col0\" >0</td>\n",
              "      <td id=\"T_34899_row8_col1\" class=\"data row8 col1\" >0</td>\n",
              "      <td id=\"T_34899_row8_col2\" class=\"data row8 col2\" >0</td>\n",
              "      <td id=\"T_34899_row8_col3\" class=\"data row8 col3\" >0</td>\n",
              "      <td id=\"T_34899_row8_col4\" class=\"data row8 col4\" >0</td>\n",
              "      <td id=\"T_34899_row8_col5\" class=\"data row8 col5\" >11</td>\n",
              "      <td id=\"T_34899_row8_col6\" class=\"data row8 col6\" >166</td>\n",
              "      <td id=\"T_34899_row8_col7\" class=\"data row8 col7\" >239</td>\n",
              "      <td id=\"T_34899_row8_col8\" class=\"data row8 col8\" >253</td>\n",
              "      <td id=\"T_34899_row8_col9\" class=\"data row8 col9\" >253</td>\n",
              "      <td id=\"T_34899_row8_col10\" class=\"data row8 col10\" >253</td>\n",
              "      <td id=\"T_34899_row8_col11\" class=\"data row8 col11\" >187</td>\n",
              "      <td id=\"T_34899_row8_col12\" class=\"data row8 col12\" >30</td>\n",
              "      <td id=\"T_34899_row8_col13\" class=\"data row8 col13\" >0</td>\n",
              "      <td id=\"T_34899_row8_col14\" class=\"data row8 col14\" >0</td>\n",
              "      <td id=\"T_34899_row8_col15\" class=\"data row8 col15\" >0</td>\n",
              "      <td id=\"T_34899_row8_col16\" class=\"data row8 col16\" >0</td>\n",
              "      <td id=\"T_34899_row8_col17\" class=\"data row8 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
              "      <td id=\"T_34899_row9_col0\" class=\"data row9 col0\" >0</td>\n",
              "      <td id=\"T_34899_row9_col1\" class=\"data row9 col1\" >0</td>\n",
              "      <td id=\"T_34899_row9_col2\" class=\"data row9 col2\" >0</td>\n",
              "      <td id=\"T_34899_row9_col3\" class=\"data row9 col3\" >0</td>\n",
              "      <td id=\"T_34899_row9_col4\" class=\"data row9 col4\" >0</td>\n",
              "      <td id=\"T_34899_row9_col5\" class=\"data row9 col5\" >16</td>\n",
              "      <td id=\"T_34899_row9_col6\" class=\"data row9 col6\" >248</td>\n",
              "      <td id=\"T_34899_row9_col7\" class=\"data row9 col7\" >250</td>\n",
              "      <td id=\"T_34899_row9_col8\" class=\"data row9 col8\" >253</td>\n",
              "      <td id=\"T_34899_row9_col9\" class=\"data row9 col9\" >253</td>\n",
              "      <td id=\"T_34899_row9_col10\" class=\"data row9 col10\" >253</td>\n",
              "      <td id=\"T_34899_row9_col11\" class=\"data row9 col11\" >253</td>\n",
              "      <td id=\"T_34899_row9_col12\" class=\"data row9 col12\" >232</td>\n",
              "      <td id=\"T_34899_row9_col13\" class=\"data row9 col13\" >213</td>\n",
              "      <td id=\"T_34899_row9_col14\" class=\"data row9 col14\" >111</td>\n",
              "      <td id=\"T_34899_row9_col15\" class=\"data row9 col15\" >2</td>\n",
              "      <td id=\"T_34899_row9_col16\" class=\"data row9 col16\" >0</td>\n",
              "      <td id=\"T_34899_row9_col17\" class=\"data row9 col17\" >0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th id=\"T_34899_level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
              "      <td id=\"T_34899_row10_col0\" class=\"data row10 col0\" >0</td>\n",
              "      <td id=\"T_34899_row10_col1\" class=\"data row10 col1\" >0</td>\n",
              "      <td id=\"T_34899_row10_col2\" class=\"data row10 col2\" >0</td>\n",
              "      <td id=\"T_34899_row10_col3\" class=\"data row10 col3\" >0</td>\n",
              "      <td id=\"T_34899_row10_col4\" class=\"data row10 col4\" >0</td>\n",
              "      <td id=\"T_34899_row10_col5\" class=\"data row10 col5\" >0</td>\n",
              "      <td id=\"T_34899_row10_col6\" class=\"data row10 col6\" >0</td>\n",
              "      <td id=\"T_34899_row10_col7\" class=\"data row10 col7\" >43</td>\n",
              "      <td id=\"T_34899_row10_col8\" class=\"data row10 col8\" >98</td>\n",
              "      <td id=\"T_34899_row10_col9\" class=\"data row10 col9\" >98</td>\n",
              "      <td id=\"T_34899_row10_col10\" class=\"data row10 col10\" >208</td>\n",
              "      <td id=\"T_34899_row10_col11\" class=\"data row10 col11\" >253</td>\n",
              "      <td id=\"T_34899_row10_col12\" class=\"data row10 col12\" >253</td>\n",
              "      <td id=\"T_34899_row10_col13\" class=\"data row10 col13\" >253</td>\n",
              "      <td id=\"T_34899_row10_col14\" class=\"data row10 col14\" >253</td>\n",
              "      <td id=\"T_34899_row10_col15\" class=\"data row10 col15\" >187</td>\n",
              "      <td id=\"T_34899_row10_col16\" class=\"data row10 col16\" >22</td>\n",
              "      <td id=\"T_34899_row10_col17\" class=\"data row10 col17\" >0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "im3_t = tensor(im3)\n",
        "df = pd.DataFrame(im3_t[4:15,4:22])\n",
        "df.style.set_properties(**{'font-size':'6pt'}).background_gradient('Greys')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "65TDrwa8rM8N"
      },
      "source": [
        "## First Try: Pixel Similarity"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4xXwFK5jrM8O",
        "outputId": "8efec019-6571-49f4-ffa6-15f5730c217b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(6131, 6265)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "seven_tensors = [tensor(Image.open(o)) for o in sevens]\n",
        "three_tensors = [tensor(Image.open(o)) for o in threes]\n",
        "len(three_tensors),len(seven_tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "id": "jWBuYb3NrM8O",
        "outputId": "7b14d499-030d-4eb4-f149-61fb49b94040"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "show_image(three_tensors[1]);"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "show_image(seven_tensors[4])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "IFLYmu9ks5H8",
        "outputId": "1617f334-e793-400b-ebf8-a69a6dc9c450"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fb10255e110>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "doc(show_image)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "URPtUO8lsdtr",
        "outputId": "966bc337-2f78-4f66-e17d-ed4e01aa56f1"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "show_image(im, ax=None, figsize=None, title=None, ctx=None, cmap=None, norm=None, aspect=None, interpolation=None, alpha=None, vmin=None, vmax=None, origin=None, extent=None, filternorm=1, filterrad=4.0, resample=None, url=None, *, data=None, **kwargs)\n",
            "Show a PIL or PyTorch image on `ax`.\n",
            "\n",
            "To get a prettier result with hyperlinks to source code and documentation, install nbdev: pip install nbdev\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9tiFmV88rM8P",
        "outputId": "55f28eea-caa8-420b-d835-e7a8070e54d4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([6131, 28, 28])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "stacked_sevens = torch.stack(seven_tensors).float()/255\n",
        "stacked_threes = torch.stack(three_tensors).float()/255\n",
        "stacked_threes.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FQXyoZmLrM8P",
        "outputId": "d7e6c002-6dc6-481f-b7f7-e26b1feeecc3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "len(stacked_threes.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WOG7tgfcrM8Q",
        "outputId": "03a1a0bb-2b03-4d05-e758-599ec6700b16"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "stacked_threes.ndim"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "id": "mhTJuaJ-rM8Q",
        "outputId": "e04df7cc-5805-40ea-d41b-a979d60c0db8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "mean3 = stacked_threes.mean(0)\n",
        "show_image(mean3);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "id": "HagtCbD6rM8R",
        "outputId": "43ca1f45-2f0b-467e-f342-088598c7ca6c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "mean7 = stacked_sevens.mean(0)\n",
        "show_image(mean7);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "id": "GiQuKrC3rM8R",
        "outputId": "2243360c-59d3-492c-866e-ace4a734b0f4"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAJHElEQVR4nO2bXXMSZxuAL1jYXYQsiCYxIWIIjImJ0TaVTu2H41FnnGmPPOtMf0NP+i/6H9oDx+OOOtMjW6cdGz/Sk1ZqxkRDhCTQEAjfsLDsvgeWbbMmxgrEzDtcR5ln+bi5eJ5n7/t+iM0wDPr8g/1tB3DY6Aux0BdioS/EQl+IBcc+1/+fb0G23Qb7M8RCX4iFvhALfSEW+kIs9IVY6Aux0BdiYb/ErGMMw6DVatFsNqlUKmiaRrPZpNls0mg0Xnq8LMtIkoSu6+i6jtPpxOFw4HQ6EQQBWZZxOHoXds+FaJpGvV4nHo/zww8/kMlkSKVSxONxnjx5wr/7MTabjffee4+pqSmq1SqqqjIyMsKxY8eIRCIMDw8zOzuLz+frWbxdF6LrujkDisUilUqFbDbLn3/+yeLiIoVCgfX1dTKZDJVKBVEUEUWRer1OrVZjZWUFh8NhCqlUKmxublIulzl+/DgTExM9FWLbp2P2n2sZVVXZ3t5mdXWV77//nlQqxaNHj8jlcqTTaQzDwDAMZFnG7XYzODhIIBDgyZMnPH/+HLvdjt1uN2eOzWbDZrPh8/nwer1cv36daDT6hh93B7vWMh3PEE3TqNVq1Go1UqkUlUqFVCrFysoKT58+pVQqIQgCExMTRKNRnE4nkiQhiiIulwtFUfB6vczOzpLJZFheXubZs2eUy2VqtZr5Po1GA1VV0XW905BfScdCVFUlFovx22+/8c0331CpVGg2m7RaLRqNBoFAgGg0ysWLF7l69Soejwe3220+3263Y7PZ0HUdwzC4ceMG165dIxaLkUwmOw3vP9OxEMMwaDQaVKtVSqUS1WoVXdex2+2IokggEGBubo5z587h8/lwOp04nU7z+e0l8e+lJAgCNtvOGe33+wkGg8iy3GnIr6QrQqrVKrVaDVVV0TQNAFEUOXr0KHNzc3zxxRf4fD4URXnpg7ZpjzudTux2+0vXpqenmZmZQVGUTkN+JR0LcTqdhEIhRFEkn8/TbDaBF0Lcbjdzc3N4vV5EUdxTBrzYizRNI5/Pk8/nzRzFZrMhCALDw8OEw2FcLlenIb+SjoVIksTp06cJh8N88MEH5nh7KQiCgCiK+75Oo9GgVCqxtrZGMpmkWq0CmM+PRCJEo9Ed+08v6FhI+1sXBGHH3tC+Zp3+e7G+vs7PP//M77//TqlUQtM0BEEgHA4zPj7OzMwMJ06ceOk9uk1XErP2bHidmbAXd+7c4auvvkLTNHRdx+FwIIoiFy9eJBqN8u6773LixIluhPtKep66WzEMA13XqdfrlMtlM2FbWFgwN2S73U4kEiESifDhhx8SjUZ7vpm2OXAhuq6jaRrZbJbHjx/z448/cvPmTbLZrHm7djgcXLhwgY8//phPP/2UkydPHlh8B1LtGoZBsVhkdXXVrGWSySSrq6ssLS2Ry+Wo1+vAi3zD7/dz+vRpzp8/z8DAQK9D3MGBlf/JZJLvvvuO5eVlHjx4gKqqO1LzNkNDQ0xPT3PhwgUmJyd7fpu1ciBLRtd1CoUCjx49Yn19HVVVzXzFSiaTIRaLcevWLeLxOMeOHcPj8TA2NobX62VwcLCnkg5syWxtbfHgwQM0TTM31t3IZDJkMhnW19dxu90oioLH4+HKlSucP3+eS5cuIcvyK5O8Tuh6+f/SC/y9ZDY2Nrh9+zblcplCoUCxWCSXy5mPi8fjLC0tmT0UURRxOp1mv2RqaorR0VE++ugjzpw5w9mzZ/F6vQiC8Nq5joVdjfZciJVarWbKWFtbM8d/+uknfvnlF1ZXV0mn07s+t91Ri0QifP3110xOTiJJEoIgvEkovemH/FecTieKoiDL8o7O19DQEJcuXWJtbY10Ok0mkyGXy3H//n3i8TjwYrYlEgmq1SrPnz9ncHCQ48ePv6mQXTlwIQ6HA4fDgcvlwuv1muPDw8NMT09TrVbNW/TKygrZbNYUArC5uUkulyMejxMKhTh69Gh34+vqq3VAuxBsd9VlWSYYDBKPx/nrr79IJBJsb28DL2bKxsYG8XicU6dOdTWOQ3Mu0y4EJUkye63BYJDZ2VmmpqZ2pO6GYZgzR1XVrsZxaITsRbtwtI55vd6eVL+HXgjAbndCt9uN3+/v6oYKh2gPsVIsFtne3mZhYYGHDx/uyFlsNhunTp0iEol01HLYjUMppF0MJpNJEokEiURiR2YrCAJDQ0P4/f6uH2seOiHVapVKpcK9e/e4c+cOf/zxh3lEATA5Ocn4+DiBQABZlt80S92TQyOk/YHr9TrZbJZYLMb8/DypVMq8ZrfbCQaDRCIRvF4vDoej6zXNoRFSKBRIp9Pcvn2bu3fv8vjxY5LJpNknGRgYwO12c/XqVS5fvszo6Oiu5zed8laFtCthwzDI5/M8ffqUhw8fcuPGDbO3Ci820SNHjjA4OMi5c+cIhUI9kQFvUYiqqqiqysbGBktLS9y9e5f5+XkSiQTNZtNcJi6XC1mW+fLLL/nkk08Ih8M9kwFdFvLvb9yaULXH2383Gg0KhQLxeJz5+XkWFha4d++e+fj2me/AwACKonD27FneeecdPB5Pz2RAF4Vomka1WqVcLrO2toaiKIyMjJiH3pVKha2tLUqlEpubmywvL7O4uGjWKfl8HvgnM41EIoTDYa5cuUI0GiUUCqEoSk9/PQRdFNJqtSiVSmxtbRGLxRgdHUWSJPMXRLlcjuXlZba2tsxl0u6tqqq645RPFEXGx8cJh8NEo1FmZmbMhlGv6ZqQfD7Pt99+SzKZ5P79++Zhd6vVotVqmecwqqqaM6ZSqZgb5/DwMGNjY7z//vtmk/nkyZMoioIkSV3PN/aia0IajQaJRIJnz56xuLj4Wj9ssdlsSJKEJEmMjY0RiUQ4c+YM0WiUiYkJ/H5/t8J7bbomxOPxcPnyZTweD7/++uu+QmRZ5siRI3z++ed89tlnhEIhRkZGcLlcB7Y8dqNrQhwOB8FgkHQ6TSAQMI8l98LlcuHz+ZicnGR2dpahoaEdHbS3RdeazK1WyzxvKRaL+7/x3w0ht9ttdsm6XcrvF8KugwfddT9E9P+j6nXoC7HQF2KhL8TCfrfd3lVRh5T+DLHQF2KhL8RCX4iFvhALfSEW/gcMlBno19ugeQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "a_3 = stacked_threes[1]\n",
        "show_image(a_3);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0H8HVFTarM8S",
        "outputId": "57b902df-766b-4c54-aced-a6bb46236447"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.1114), tensor(0.2021))"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "dist_3_abs = (a_3 - mean3).abs().mean()\n",
        "dist_3_sqr = ((a_3 - mean3)**2).mean().sqrt()\n",
        "dist_3_abs,dist_3_sqr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "laZOWFg7rM8S",
        "outputId": "4614ba11-5f24-4dc2-a206-8e65e7b8a14e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.1586), tensor(0.3021))"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "dist_7_abs = (a_3 - mean7).abs().mean()\n",
        "dist_7_sqr = ((a_3 - mean7)**2).mean().sqrt()\n",
        "dist_7_abs,dist_7_sqr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CaiCqz1CrM8S",
        "outputId": "d1a5830f-71d3-4478-b111-0f13d4f4bb66"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.1586), tensor(0.3021))"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "F.l1_loss(a_3.float(),mean7), F.mse_loss(a_3,mean7).sqrt()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MinabPsPrM8T"
      },
      "source": [
        "### NumPy Arrays and PyTorch Tensors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "P5BLKoyUrM8T"
      },
      "outputs": [],
      "source": [
        "data = [[1,2,3],[4,5,6]]\n",
        "arr = array (data)\n",
        "tns = tensor(data)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0zfIxesErM8U",
        "outputId": "ac716e96-2eed-4e87-c58a-31a6b59dae20"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ],
      "source": [
        "arr  # numpy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tN73QqYarM8U",
        "outputId": "14a9aedb-bfe7-4a2c-89f7-8860eb2760fc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1, 2, 3],\n",
              "        [4, 5, 6]])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "tns  # pytorch"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X0MRaQj9rM8U",
        "outputId": "70c655b3-670f-4265-8e90-d7f4f8109293"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([4, 5, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "tns[1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ymmEIv4yrM8V",
        "outputId": "d7916ceb-b8de-48a0-8235-d20cd5992e29"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2, 5])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "tns[:,1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fFziqLH9rM8V",
        "outputId": "1108bc8b-7602-467c-fefc-50c79bfe5ab6"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([5, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "tns[1,1:3]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zkuTEOtorM8V",
        "outputId": "f8076af1-fbde-43c0-ff6d-5122d5e6b66e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[2, 3, 4],\n",
              "        [5, 6, 7]])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "tns+1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "Cq8ciwDdrM8W",
        "outputId": "540ced59-bc77-4ca3-9151-2afb1d69f961"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'torch.LongTensor'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "tns.type()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QipavzqbrM8W",
        "outputId": "94f42a7a-e80a-4d8e-9055-6bbe308e3088"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1.5000, 3.0000, 4.5000],\n",
              "        [6.0000, 7.5000, 9.0000]])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "tns*1.5"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dXCJpGImrM8W"
      },
      "source": [
        "## Computing Metrics Using Broadcasting"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8gEIKEFMrM8X",
        "outputId": "99ed18d7-500b-459c-9ba7-03b40d76c487"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([1010, 28, 28]), torch.Size([1028, 28, 28]))"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "valid_3_tens = torch.stack([tensor(Image.open(o)) \n",
        "                            for o in (path/'valid'/'3').ls()])\n",
        "valid_3_tens = valid_3_tens.float()/255\n",
        "valid_7_tens = torch.stack([tensor(Image.open(o)) \n",
        "                            for o in (path/'valid'/'7').ls()])\n",
        "valid_7_tens = valid_7_tens.float()/255\n",
        "valid_3_tens.shape,valid_7_tens.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0cvVXcTerM8X",
        "outputId": "a1d5ac8b-cd3b-4867-8d7d-73b554ff0532"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.1114)"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "def mnist_distance(a,b): return (a-b).abs().mean((-1,-2))\n",
        "mnist_distance(a_3, mean3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k0ELEiJWrM8Y",
        "outputId": "edf6638b-b22f-4733-cee7-0649fcefc8bd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([0.1093, 0.1229, 0.1293,  ..., 0.1043, 0.1229, 0.1267]),\n",
              " torch.Size([1010]))"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "valid_3_dist = mnist_distance(valid_3_tens, mean3)\n",
        "valid_3_dist, valid_3_dist.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y9ebKzjErM8Y",
        "outputId": "8ff45907-3cdf-43c4-a807-674fc6fa91f1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ],
      "source": [
        "tensor([1,2,3]) + tensor(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ikGGsz6jrM8Y",
        "outputId": "3c96478a-2026-4fb9-956a-fbcab1507d42"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([1010, 28, 28])"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "(valid_3_tens-mean3).shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "GBi0L_tDrM8Y"
      },
      "outputs": [],
      "source": [
        "def is_3(x): return mnist_distance(x,mean3) < mnist_distance(x,mean7)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8Y-Dbd-yrM8Z",
        "outputId": "38da5b29-fa5a-41e2-c83c-3bdc2b13a377"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(True), tensor(1.))"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "is_3(a_3), is_3(a_3).float()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SdBRgeY4rM8Z",
        "outputId": "8b378973-eb89-4116-9622-921131410c9b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([True, True, True,  ..., True, True, True])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ],
      "source": [
        "is_3(valid_3_tens)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hbop9oqnrM8Z",
        "outputId": "497e4298-f1dd-40dd-eecc-deea2c26d7ca"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.9168), tensor(0.9854), tensor(0.9511))"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "accuracy_3s =      is_3(valid_3_tens).float() .mean()\n",
        "accuracy_7s = (1 - is_3(valid_7_tens).float()).mean()\n",
        "\n",
        "accuracy_3s,accuracy_7s,(accuracy_3s+accuracy_7s)/2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vFr3NRGurM8a"
      },
      "source": [
        "## Stochastic Gradient Descent (SGD)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "D_z-ARMyrM8a",
        "outputId": "3cedef81-aba7-4ff0-9c2a-67fd9671333b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.files.Source at 0x7fb102033190>"
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          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "gv('''\n",
        "init->predict->loss->gradient->step->stop\n",
        "step->predict[label=repeat]\n",
        "''')"
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    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "5HCYWp2rrM8a"
      },
      "outputs": [],
      "source": [
        "def f(x): return x**2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
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      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plot_function(f, 'x', 'x**2')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "dzyytoMFrM8b",
        "outputId": "e981b744-9da4-41d8-8020-81d6de992c1c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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I0Lpvv2uiu0d1p0OgLy9u0LMCpVqr1zYnUlhWySOTY+2O0uxapI9ARGJwLFu5vZbdY0Rkn4h8KiID6vjzC0QkXkTis7KyLExqjSB/H+aP78GGo5kcTM+zO45SqpEulJTz2pYkpg7oTL/O7eyO0+wsLwQiEgy8BzxujLlQY/duoLsxZgjwIvBBbe9hjFlsjIkzxsSFh4dbG9gic8bG0C7Ahxc3nLA7ilKqkZZtTiK/pMItzwbA4kIgIr44isAKY8yamvuNMReMMQXO7XWAr4i45erv7QJ8mTuuB58fOsuRjJr1UCnlqgpKK3h1cyJT+kUwMDLE7jiWsHLUkACvAkeMMc/V0aazsx0iMtKZJ9uqTHabNy6GID9vXtIRREq1Gm9uSya3qJwfT+ltdxTLWDlJxjhgNnBARPY6X/sl0A3AGPMycBvwoIhUAMXAncaN77xqH+jHnLExvPyfk5w4m0/vTm3tjqSUqkdRWQWvbDzFhN5hDI1ub3ccy1hWCIwx3wD1rtRgjHkJeMmqDK7o/gk9WbYliee/PMFLdw23O45Sqh7LtyaTXVjG4z9w37MB0DuLW1xokB/3jo3hkwMZHD+bb3ccpVQdisoq+JfzbKC1LkrfUFoIbHD/hJ4E+nrzwpc6gkgpV/XG1mRyCst4/Ad97I5iOS0ENtCzAqVcW2FpBYs3nmJin3BGdO9gdxzLaSGwycWzguf1rEApl/P/zwbcu2/gIi0ENukQ5MfckELW7UvnaEQPiImBFSvsjqWUxysorWDxxpNM7BPO8G7ufzYAWgjss2IF9z/zIMFlxfx13F2QnAwLFmgxUMpmr32TyPmicn52jfv3DVykhcAuTz1F+/NZzN/5AZ/3HcuBTr2gqAieesruZEp5rLyichZvOsUPrujEEDe+b6AmLQR2SUkBYN7OD2lffIG/TJj9ndeVUi3vlU2nyC+p4KcedDYAWgjs060bAO3Kinhg+3t83SuOXZH9vn1dKdWysgtKWbo5kRsGd6F/V/ebYbQ+Wgjs8swzEBgIwL27Pyas8Dx/uepex+tKqRb3r42nKCmv5CceMlKoOi0Edrn7bli8GLp3J7CijIeO/Zst0YPYPOqHdidTyuOcySth2ZYkbh4aSWyE580BVm8hEJF2IvK9xTlFZLB1kTzI3XdDUhJUVXHXJ6/SNSSAP392FDeed08pl/TChhNUGcNPPKxv4KI6C4GI3A4cBd5zLj5/ZbXdr1sdzNME+Hrz+DV92JeWx+eHztgdRymPkXiukFU7U7lrZDeiQwPtjmOL+s4IfgmMMMYMBX4ELBeRW5z76p1VVDXNjGGR9AoP4v++OE5FZZXdcZTyCM+tP46ftxePTPa8voGL6isE3saYDABjzA7gauBXIvIooNcuLODj7cXPr+1LQmYBa/ak2x1HKbd3MD2PtftOM298DOFt/e2OY5v6CkF+9f4BZ1GYBEwHal1kXl2+qQM7MzgqhL+tP05JeaXdcZRya//3xTFC2viyYOL3ukI9Sn2F4EFqXAIyxuQDU4F5l3pjEYkWka9E5LCzj+GxWtqIiLwgIgkisl9EPH6lFhHhF1P7cTqvhDe3JdsdRym3tfVkNl8fy+LBSb0IaeNrdxxb1VkIjDH7gBgAEZlS7fVyY0xDJsSpAH5mjOkPjAYeFpH+NdpcB/R2PhYA/2xUejc1LjaMCb3DeHFDAnlF5XbHUcrtVFUZ/vjpEbqEBDB3bIzdcWx3qfsIrhKRcTguCTWKMSbDGLPbuZ0PHAEiazSbDrxhHLYB7UWkS2OP5Y6euK4fF0rK+cd/dKF7pZrbJwcy2J+Wx8+u7UuAr7fdcWxX3/DR3wD+wL8BPxF5uqkHEZEYYBiwvcauSCC12vM0vl8sEJEFIhIvIvFZWVlNjdGqDOgawi1DI3ltcxKnc4vtjqOU2yirqOLZz4/Rr3Nbbhn2vV83Hqm+S0O/w3EfwW+Bo8aYRU05gIgEA+8BjxtjLjTlPYwxi40xccaYuPDw8Ka8Rav002sdN7c8t/64zUmUch9vbU8mJaeIX1zXD28vHQkPl7401NYY8yegSfdci4gvjiKwwhizppYm6UB0tedRztcUENUhkLljY3hvdxpHMppUQ5VS1VwoKeeFDQmM6dmRSX0850vlpVyqEByq8d8GExEBXgWOGGOeq6PZR8Ac5+ih0UDexXsXlMPDk2IJaePLM58c0aknlLpM//jqJDmFZfzy+itw/IpSYGFnMTAOmA1MFpG9zsf1IrJQRBY626wDTgEJwCvAQ004jlsLCfTl0cm9+SbhHF8f84z+EaWskJpTxNLNicwYFsmgqBC747gUn7p21OgsfkFEnm5MP4Ex5hsuMRWFcXzFfbih7+mp7hndneXbknlm3REm9A7Dx1snjVWqsf78+TG8BH7+w752R3E5lncWq8vn5+PFE9f1IyGzgJU7Uy/9B5RS37En5Txr951mwYSedG3fxu44LudSXy3bAWuB4OovisgkqwKp2l3bvxMje4Tyt/XHuVCiN5kp1VDGGP7wyRHC2/rzwFWePZVEXeotBMaYvwHvAIHODt02IvIi8McWSae+JSL8+ob+ZBeW8fcNepOZUg318f4MdiWf52fX9CHIv86r4R6tIRebR+EY4rkF2AmcxtERrFrYoKgQZo6IYunmRBLPFdodRymXV1xWyf9+epQBXdsxMy760n/AQzWkEJQDxUAbIABINMboZPk2+a+pffHz9uKZT47YHUUpl7d44ynSc4v5zU0D9OaxejSkEOzEUQiuBCYAs0TkXUtTqTpFtA3gkcm9+feRs2w6ocNJlarL6dxi/vmfBG4Y3IWRPULtjuPSGlII5htjnnbOOpphjJmO40YwZZN542Po3jGQRWsP60pmStXhfz89ijHw5HX97I7i8i5ZCIwx8bW8ttyaOKoh/H28eer6KziRWcByXbNAqe/ZmZTDR/tO88BVvYjq4JnrEDeG3pnUSl3TvxMTeofx3PrjnCsotTuOUi6jorKKX39wkK4hASy8qqfdcVoFLQStlIjw22kDKCmv5E+fHrU7jlIuY8X2FI6eyefXN/Yn0E+HizaEFoJWrFd4MPPG9+DdXWnsTjlvdxylbHeuoJS/fHGM8bFhTB3Y2e44rYYWglbu0cm96dTOn998eIjKKp2dVHm2Zz87RlFZJb+d1l9nF20ELQStXJC/D0/d0J8D6Xms3JFidxylbLMn5Tyr4lOZP74HsRFNWkLFY2khcAM3De7C2F4d+fNnR7XjWHmkisoqnnr/IJ3bBfDjKb3tjtPqaCFwAyLCoukDKS6v5H/0jmPlgZZtTeZwxgV+c1N/gnU+oUbTQuAmYiOCeWBiL9bsSWfLyXN2x1GqxZzJK+G5L44xqW+4dhA3kWWFQESWikimiBysY/8kEcmrtnrZ01Zl8RSPTI6lW2ggv/7gIGUVesex8gy///gwFVWGRdMGagdxE1l5RvA6MPUSbTYZY4Y6H7rwzWUK8PXmd9MHcDKrkMUbT9odRynLfX0sk08OZPDjybF066h3EDeVZYXAGLMRyLHq/VXtru4bwQ2DuvDChgROZRXYHUcpyxSVVfCrDw4SGxHM/RP1DuLLYXcfwRgR2Scin4rIgLoaicgCEYkXkfisLJ1x81J+c1N//H28+OX7B3AsC62U+3nui+OknS/mjzMG4e/jbXecVs3OQrAb6G6MGQK8CHxQV0NjzGJjTJwxJi48PLzFArZWEe0C+OX1V7DtVA7vxqfZHUepZncgLY+lmxO5a1Q3rozRKaYvl22FwBhzwRhT4NxeB/iKSJhdedzNHXHRjIwJ5Zl1R8jK13sLlPuoqKziiTX7CQv25xdTdYrp5mBbIRCRzuLs4heRkc4s2XblcTdeXsL/zBhEcVklv117yO44SjWbJd8kcuj0BX43bQAhbXztjuMWrBw+uhLYCvQVkTQRmS8iC0VkobPJbcBBEdkHvADcafSCdrOKjQjm0SmxfLI/g88OnrE7jlKX7WRWAc+tP861/TvpPQPNyLJb8Iwxsy6x/yXgJauOrxweuKoX6w6c4dcfHmR0z1DaB/rZHUmpJqmsMvz36v208fXmDzfrPQPNye5RQ8pivt5ePDtzMOcLy1j08WG74yjVZG9sTWJX8nmevrE/Ee0C7I7jVrQQeIABXUN4cFIv1uxO56ujmXbHUarRUrKL+PNnjmkkZgyPtDuO29FC4CEemRxL74hgnlxzgLyicrvjKNVgVVWG/1q9D28v4X9uGaSXhCyghcBD+Pt485fbh5BVUKqjiFSr8tqWJLYn5vD0Tf3p2r6N3XHckhYCDzI4qj0PXx3L+3vS+exght1xlLqkhMwC/vzZUab0i2DmiCi747gtLQQe5pGrYxnQtR1PvX9QF7FRLq2isoqfvbuPNn7e/HGGXhKykhYCD+Pn48Vztw8lv6SCp3QuIuXC/vn1Sfal5vKHmwfqKCGLaSHwQH07t+Vn1/bh80NndS4i5ZL2peby/JcnuGlIV24c3NXuOG5PC4GHum9CT0b3DOW3aw+RnF1odxylvlVUVsHjq/YS0dafP0wfaHccj6CFwEN5ewnP3T4UHy/h8VV7qajUFc2Ua/j9x0dIyi7kL7cPJSRQ5xJqCVoIPFjX9m145pZB7EnJ5cUNCXbHUYr1h8+yckcKCyb2ZEyvjnbH8RhaCDzcTUO6MmNYJC9uOMGORF1QTtnnTF4J/716H/27tOOn1/SxO45H0UKgWHTzQLqFBvLY23vILSqzO47yQJVVhsfe3kNpRRUv3jVMVxxrYVoIFMH+Prw4azjnCkr5r9X7dUipanEvbUhge2IOi6YPpFd4sN1xPI4WAgXAoKgQfjG1H+sPn2X5tmS74ygPsiMxh+e/PM4twyK5VSeUs4WVC9MsFZFMETlYx34RkRdEJEFE9ovIcKuyqIaZP74Hk/tF8IePj3AgLc/uOMoDZBeU8ujKPXQLDeT3usaAbaw8I3gdmFrP/uuA3s7HAuCfFmZRDSAi/N/MIXQM9uOht3bpLKXKUpVVhsdX7SWnqIy/3z2cYH/L1slSl2BZITDGbATqG4YyHXjDOGwD2otIF6vyqIYJDfLjpbuGk5Fbws9X79P+AmWZFzecYNOJc/xu2gAGdA2xO45Hs7OPIBJIrfY8zfmastmI7h148vorWH/4LK9sOmV3HOWGvjlxjue/PMGMYZHceWW03XE8XqvoLBaRBSISLyLxWVlZdsfxCPPGxXDdwM786bNjbD2ZbXcc5UbSc4t59O09xIYH84dbtF/AFdhZCNKB6l8FopyvfY8xZrExJs4YExceHt4i4TydiPDn2wYT0zGQR97azencYrsjKTdQUl7JwuW7KK+o4uXZIwj0034BV2BnIfgImOMcPTQayDPG6GopLqRtgC//mh1HaUUVD765i5LySrsjqVbMGMOvPjjIgfQ8nrtjqN4v4EKsHD66EtgK9BWRNBGZLyILRWShs8k64BSQALwCPGRVFtV0sRHB/OX2IexLy+PpDw9q57Fqsje3JbN6VxqPTunNNf072R1HVWPZeZkxZtYl9hvgYauOr5rPDwd05seTY3lxQwL9u7Rj7rgedkdSrczWk9n8bu1hJveL4PEpve2Oo2poFZ3Fyn4/+UEfrunfiUUfH2bjce2wVw2Xkl3Egyt2ERMWxN/uHIqXl3YOuxotBKpBvLyEv94xlD6d2vLwW7s5mVVgdyTVCuSXlDN/2U4AlsyJo12Ari/girQQqAYL9vfhlTlx+Hl7cf+yeJ2pVNXLMaPoXhLPFfKPu4cTExZkdyRVBy0EqlGiQwN5efYI0s4X88DyXZRW6Egi9X3GGH639hAbjmby22kDGNsrzO5Iqh5aCFSjXRkTyrMzB7M9MYcn3jugI4nU97z6TSJvbE1mwcSe3DO6u91x1CXo3RyqSaYPjSQ1p4j/++I40aGBuqKU+tZnB8/wzLojXDewM09M7Wd3HNUAWghUkz18dSwpOUW88OUJItsHcMeV3eyOpGy2KzmHx97ew9Do9vz1Dh0h1FpoIVBNJiI8c8sgMvNLeXLNAToE+nHtgM52x1I2OX42n3mvx9O1fRuWzIkjwFeXm2wttI9AXRZfby/+cfdwBkW158cr97Ajsb6Zx5W7Ss8tZs6rO+3NDgIAAA/xSURBVPD38eKNeSPpGOxvdyTVCFoI1GUL9PPhtblXEtmhDfOX7eRIxgW7I6kWlF1QypxXt1NYWsGyeSOJDg20O5JqJC0EqlmEBvnxxryRBPv7MPvV7XrDmYfIKy5nztIdpJ0vZsm9cVzRpZ3dkVQTaCFQzSaqQyBv3jcKgHuWbCc1p8jmRMpKhaUVzHt9J8fP5vPy7BGM6tnR7kiqibQQqGbVKzyY5fNHUVRWyd1LtnMmr8TuSMoCJeWVLFgez97UXF6cNYyr+0bYHUldBi0Eqtld0aUdy+aNJKewjFmvbNNi4GZKyiu5/414tpzM5tnbBjN1oC413tppIVCWGBrdnmXzRpKVX6rFwI1cLALfJJzjz7cOZsbwKLsjqWaghUBZZkT3Dt8WgzsXbyUjT5e7bM2Kyyq5b5mjCDx72xBmxumi8+7C0kIgIlNF5JiIJIjIE7XsnysiWSKy1/m4z8o8quWN6N6BN+aPJLugjJkvbyU5u9DuSKoJ8kvKuXfpDjafdBSB20bomYA7sXKpSm/g78B1QH9gloj0r6XpKmPMUOdjiVV5lH2Gd+vAW/ePprC0gpkvb+XE2Xy7I6lGOF9Yxt1LtrM75Twv3DlMi4AbsvKMYCSQYIw5ZYwpA94Gplt4POXCBkWFsOqBMQDc/q+t7E/LtTmRaoizF0q4Y/FWjp7J51+zR3DTkK52R1IWsLIQRAKp1Z6nOV+r6VYR2S8iq0Wk1ouOIrJAROJFJD4rS5dJbK36dGrLuwvHEOTvw52Lt/H1sUy7I6l6JGTmM+MfW0g7X8zrc69kyhW64Ly7sruzeC0QY4wZDKwHltXWyBiz2BgTZ4yJCw8Pb9GAqnl17xjEmgfHEtMxiPuWxbN6V5rdkVQt4pNyuPWfWymtqGLVgjGMjdWFZdyZlYUgHaj+DT/K+dq3jDHZxphS59MlwAgL8ygXEdEugFUPjGZ0z478/N19vPDlCV3cxoV8eiCDu5dsJzTIjzUPjmVQVIjdkZTFrCwEO4HeItJDRPyAO4GPqjcQkep3okwDjliYR7mQtgG+LJ17JTOGRfLc+uM8vmovJeW67KWdjDG8tOEED67YzYCu7XjvwbF066gTyHkCy9YjMMZUiMgjwOeAN7DUGHNIRBYB8caYj4BHRWQaUAHkAHOtyqNcj5+PF3+5fQi9IoJ59vNjpOQUsXh2HOFtdQrjllZSXsmTaw7w/p50bh7alf+9dbCuJ+BBpLWdksfFxZn4+Hi7Y6hm9umBDH7yzl46BPrxj7uHM6xbB7sjeYzTucU8+OYu9qXl8fNr+/Dw1bGI6Mpi7kZEdhlj4mrbZ3dnsVIAXDeoC6sXjsXbS7jjX9tYuSPF7kgeYcvJc9z04jeczCrk5XtG8Mjk3loEPJAWAuUyBkaGsPaR8YzqGcqTaw7wX+/uo6iswu5YbqmqyvDPr09yz5LttA/05YOHxzF1oC4z6ql0zWLlUjoE+fH6j0by1/XH+fvXCexJzeWlu4bRr7MueNJcsvJL+ek7e9l04hw3DOrCn24bTLC//irwZHpGoFyOt5fw8x/2Zfm8UeQWlTP9pc0s35asQ0ybwcbjWVz3/CZ2JObwP7cM4qW7hmkRUFoIlOsa3zuMTx+bwKieHfn1Bwe597WdOp11ExWVVfCrDw4wZ+kOOgT68uEj47hrVDftD1CAFgLl4sLb+vP63Cv5/fQB7EzM4dq//of396Tp2UEj7EzK4brnN7Fiewr3je/B2h+P10tt6ju0ECiX5+UlzB4Tw7rHJtC7U1t+smof9762k5RsXRO5PnlF5Ty55gAzX95KZZVh5f2j+dWN/fX+APU9eh+BalUqqwzLtybx7OfHqDSGx6b0Yf74Hvj56Heai4wxrN2fwaK1h8kpLGX++B785Jo+BPppX4Anq+8+Ai0EqlU6nVvMbz46xPrDZ+kRFsRT11/BlCsiPP6a94G0PBZ9fIidSecZFBnCH2cMYmCkzhWktBAoN/bVsUx+//FhTmUVMqF3GL+Y2s8jf/Gl5xbzt/XHWb07jdBAP37+w77cHheNt5dnF0b1/2khUG6tvLKKN7Ym88KXJ8grLueGQV346bV96BUebHc0y50rKOUfX53kzW3JAMwZ051Hf9CbdgG+NidTrkYLgfIIF0rKWbLxFEu+SaSkvJIbBndl4VU9GdDV/c4QTucW88qmU7y9I5XSikpuGxHFYz/oQ2T7NnZHUy5KC4HyKOcKSnll0ylWbEuhoLSCSX3DmTeuB+Njw/Bq5ZdKDqbn8fqWJD7cm06VgelDu/LQpFhiI9z/7EddHi0EyiPlFZWzfFsSr29J4lxBGT3CgrhndHdmDIukQ5Cf3fEarLisks8PneGNrUnsTsmlja83t8dFcf/EnkR10PUCVMNoIVAerbSikk8PnGHZ1iT2pOTi6y1c3TeCGcMjmdQ3wiXH1VdWGXYk5vD+njTWHThDQWkFMR0DmT0mhttGRBHSRvsAVOPUVwh0YLFye/4+3tw8LJKbh0Vy+PQF1uxO44O9p/ni8FkC/byZ1Deca/t3ZmKfcEJtPFMoKqtg26lsPj94ln8fOUt2YRlBft5cN6gLM4ZFMrpnx1Z/aUu5JkvPCERkKvA8jhXKlhhj/rfGfn/gDRxrFWcDdxhjkup7Tz0jUM2horKKLSez+fzQGb44fJasfMfS2f27tGN87zDiundgSHR7OrULsCxDXlE5+9Nz2Z2cy+aT59iTcp7ySkOwvw9X94vg2v6dmHJFhN4IppqFLZeGRMQbOA5cA6ThWMN4ljHmcLU2DwGDjTELReRO4BZjzB31va8WAtXcqqoM+9Jy2Zxwjs0J2exKPk9ZZRUAndsF0K9LW2LDg+kVEUx0h0A6h/jTqV0AbRswRLOkvJKzF0o4k1dCem4xJ7MKOJlZyLGz+SSeKwRABAZ2DWFsbEfG9QpjVM9Q/H1c73KVat3sKgRjgN8aY37ofP4kgDHmj9XafO5ss1VEfIAzQLipJ5QWAmW1kvJKDmdcYG9KLvvScjl+toBTWQWUVlR9p52ftxfBAT4E+Xvj7+PNxYs25ZVVFJRWUlBaTkn5d/+Mj5fQvWMgsRHBDI5qz9Do9gyKCtFx/8pydvURRAKp1Z6nAaPqauNc7D4P6Aicq95IRBYACwC6detmVV6lAAjw9WZ4tw4Mr7ZuclWVIT23mPTc4m+/4Z8vKqegtJzC0kpKKyq/bevj5UWQvw9tA3xoF+BDp3YBdA4JoEtIG7p3DMTXW+dFUq6lVVx8NMYsBhaD44zA5jjKA3l5CdGhgUSH6nBN5X6s/GqSDkRXex7lfK3WNs5LQyE4Oo2VUkq1ECsLwU6gt4j0EBE/4E7goxptPgLudW7fBmyor39AKaVU87Ps0pDzmv8jwOc4ho8uNcYcEpFFQLwx5iPgVWC5iCQAOTiKhVJKqRZkaR+BMWYdsK7Ga09X2y4BZlqZQSmlVP10+IJSSnk4LQRKKeXhtBAopZSH00KglFIertVNQy0iWUByE/94GDXuWnYRrpoLXDeb5moczdU47piruzEmvLYdra4QXA4Ria9rrg07uWoucN1smqtxNFfjeFouvTSklFIeTguBUkp5OE8rBIvtDlAHV80FrptNczWO5mocj8rlUX0ESimlvs/TzgiUUkrVoIVAKaU8nFsXAhF5VkSOish+EXlfRNrX0W6qiBwTkQQReaIFcs0UkUMiUiUidQ4FE5EkETkgIntFxPL1ORuRq0U/L+cxQ0VkvYiccP63Qx3tKp2f114RqTnteXNlqffnFxF/EVnl3L9dRGKsyNGEXHNFJKva53NfC+VaKiKZInKwjv0iIi84c+8XkeEukmuSiORV+7yerq2dBbmiReQrETns/P/xsVraNO9nZoxx2wdwLeDj3P4T8Kda2ngDJ4GegB+wD+hvca4rgL7A10BcPe2SgLAW/LwumcuOz8t53D8DTzi3n6jt79K5r8DiHJf8+YGHgJed23cCq1rg82lIrrnASy3176nacScCw4GDdey/HvgUEGA0sN1Fck0CPrbh8+oCDHdutwWO1/J32ayfmVufERhjvjDGVDifbsOxSlpNI4EEY8wpY0wZ8DYw3eJcR4wxx6w8RlM0MFeLf15O04Flzu1lwM0tcMzaNOTnr551NTBFRARr2fX3cknGmI041hupy3TgDeOwDWgvIl1cIJctjDEZxpjdzu184AiO9d2ra9bPzK0LQQ3zcFTQmiKB1GrP0/j+h24XA3whIrtEZIHdYZzs+rw6GWMynNtngE51tAsQkXgR2SYiVhSLhvz837ZxfhHJAzpakKWxuQBudV5KWC0i0bXst4Mr/z84RkT2icinIjKgpQ/uvKw4DNheY1ezfmatYvH6+ojIv4HOtex6yhjzobPNU0AFsMKVcjXAeGNMuohEAOtF5KjzW4zduSxRX7bqT4wxRkTqGvfc3fmZ9QQ2iMgBY8zJ5s7aSq0FVhpjSkXkARxnLZNtzuTKduP491QgItcDHwC9W+rgIhIMvAc8boy5YOWxWn0hMMb8oL79IjIXuBGYYpwX12pIB6p/M4pyvmZprga+R7rzv5ki8j6O0//LKgTNkMuSzwvqzyYiZ0WkizEmw3kKnFnHe1z8zE6JyNc4vk01ZyFoyM9/sU2aiPgAIUB2M2ZoUi5jTPUMS3D0u7gCy/5NXY7qv3yNMetE5B8iEmaMsXwyOhHxxVEEVhhj1tTSpFk/M7e+NCQiU4H/BqYZY4rqaLYT6C0iPUTED0fnniWjTRpDRIJEpO3FbRwd37WObmhhdn1eHwH3OrfvBb539iIiHUTE37kdBowDDjdzjob8/NWz3gZsqONLSIvmqnENeRqOa8+u4CNgjnMkzGggr9plQNuISOeLfTsiMhLH70urCzrOY74KHDHGPFdHs+b9zFq6R7wlH0ACjutoe52PiyM5ugLrqrW7HkfP/Ekcl0isznULjmt6pcBZ4POauXCM/tjnfBxylVx2fF7OY3YEvgROAP8GQp2vxwFLnNtjgQPOz+wAMN+iLN/7+YFFOL5wAAQA7zr//e0AerbQZ3SpXH90/lvaB3wF9GuhXCuBDKDc+e9rPrAQWOjcL8DfnbkPUM9IuhbO9Ui1z2sbMLaFco3H0T+4v9rvruut/Mx0igmllPJwbn1pSCml1KVpIVBKKQ+nhUAppTycFgKllPJwWgiUUsrDaSFQSikPp4VAKaU8nBYCpS6TiFzpnMgtwHlH+CERGWh3LqUaSm8oU6oZiMgfcNxR3AZIM8b80eZISjWYFgKlmoFzfp+dQAmOqQgqbY6kVIPppSGlmkdHIBjHilIBNmdRqlH0jECpZiCO9ZHfBnoAXYwxj9gcSakGa/XrEShlNxGZA5QbY94SEW9gi4hMNsZssDubUg2hZwRKKeXhtI9AKaU8nBYCpZTycFoIlFLKw2khUEopD6eFQCmlPJwWAqWU8nBaCJRSysP9P8QfuSZ+rjEqAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plot_function(f, 'x', 'x**2')\n",
        "plt.scatter(-1.5, f(-1.5), color='red');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T1THB24zrM8b"
      },
      "source": [
        "### Calculating Gradients"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "NkvYjsrerM8b"
      },
      "outputs": [],
      "source": [
        "xt = tensor(3.).requires_grad_()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4qWW7wDGrM8c",
        "outputId": "b7433ac8-1fb9-460c-cb2b-04b4fa0be01a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(9., grad_fn=<PowBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ],
      "source": [
        "yt = f(xt)\n",
        "yt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "0EFzdJJArM8c"
      },
      "outputs": [],
      "source": [
        "yt.backward()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jvu7y_aNrM8c",
        "outputId": "74bd6a5d-52a1-4f98-87b0-622c5053e2d9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(6.)"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ],
      "source": [
        "\n",
        "xt.grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oeLnAdw-rM8d",
        "outputId": "79843627-e6a8-457a-cc6b-c61ca10b5c6c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 3.,  4., 10.], requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "xt = tensor([3.,4.,10.]).requires_grad_()\n",
        "xt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Clpp4rPrM8d",
        "outputId": "e9de7157-5bdc-40aa-cccf-5ea9375dfd89"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(125., grad_fn=<SumBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ],
      "source": [
        "def f(x): return (x**2).sum()\n",
        "\n",
        "yt = f(xt)\n",
        "yt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rVeHKK5zrM8d",
        "outputId": "ef4ff07d-6807-4df4-e970-59c369568113"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 6.,  8., 20.])"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "yt.backward()\n",
        "xt.grad"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sg1Tv6QbrM8e"
      },
      "source": [
        "### Stepping With a Learning Rate"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2VaWlK4rM8e"
      },
      "source": [
        "### An End-to-End SGD Example"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aPynUbW-rM8e",
        "outputId": "af2cbb56-c157-4b16-d4b9-ecea118971d4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19.])"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ],
      "source": [
        "time = torch.arange(0,20).float(); time"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "5YJy5LIdrM8e",
        "outputId": "235abf0b-d08a-4a6e-9bd9-0af47bf1cd9b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "speed = torch.randn(20)*3 + 0.75*(time-9.5)**2 + 1\n",
        "plt.scatter(time,speed);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "DzPTC1b1rM8f"
      },
      "outputs": [],
      "source": [
        "def f(t, params):\n",
        "    a,b,c = params\n",
        "    return a*(t**2) + (b*t) + c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "X0eVr6dSrM8f"
      },
      "outputs": [],
      "source": [
        "def mse(preds, targets): return ((preds-targets)**2).mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DoZjGUyyrM8f"
      },
      "source": [
        "#### Step 1: Initialize the parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "id": "8fKSZqiKrM8f"
      },
      "outputs": [],
      "source": [
        "params = torch.randn(3).requires_grad_()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "id": "-OEkJpRRrM8g"
      },
      "outputs": [],
      "source": [
        "#hide\n",
        "orig_params = params.clone()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DmDHqfuArM8g"
      },
      "source": [
        "#### Step 2: Calculate the predictions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "id": "q_qW2DmWrM8g"
      },
      "outputs": [],
      "source": [
        "preds = f(time, params)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "preds"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tmRzHY8avOk8",
        "outputId": "fe313451-ee5c-4cc4-9dee-56ac76c6880d"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 1.3525e+00, -1.6391e-01, -3.2121e+00, -7.7919e+00, -1.3903e+01, -2.1547e+01, -3.0721e+01, -4.1428e+01, -5.3666e+01, -6.7436e+01, -8.2738e+01, -9.9571e+01, -1.1794e+02, -1.3783e+02,\n",
              "        -1.5926e+02, -1.8222e+02, -2.0671e+02, -2.3274e+02, -2.6029e+02, -2.8938e+02], grad_fn=<AddBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "id": "q9diFH2nrM8g"
      },
      "outputs": [],
      "source": [
        "def show_preds(preds, ax=None):\n",
        "    if ax is None: ax=plt.subplots()[1]\n",
        "    ax.scatter(time, speed)\n",
        "    ax.scatter(time, to_np(preds), color='red')\n",
        "    ax.set_ylim(-300,100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "id": "QVYGrqWirM8h",
        "outputId": "5e4681a1-c699-4fe0-e939-336cb487c956"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "show_preds(preds)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wWRziLXQrM8h"
      },
      "source": [
        "#### Step 3: Calculate the loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oKbC9E1NrM8h",
        "outputId": "d8f29bd7-d08e-4314-dc69-3a8647046dbe"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(25823.8086, grad_fn=<MeanBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ],
      "source": [
        "loss = mse(preds, speed)\n",
        "loss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6NaRyig2rM8h"
      },
      "source": [
        "#### Step 4: Calculate the gradients"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I8ZWccZNrM8i",
        "outputId": "114aba7f-1efd-465e-9b7f-23ec33dd707b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-53195.8633,  -3419.7148,   -253.8908])"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ],
      "source": [
        "loss.backward()\n",
        "params.grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KYxi_gtcrM8i",
        "outputId": "3f17f855-bd3b-493c-9d1f-523035f8683b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-0.5320, -0.0342, -0.0025])"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ],
      "source": [
        "params.grad * 1e-5"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aLrfO8wCrM8i",
        "outputId": "1684f0ab-4b47-459c-8874-21cc9b5c9c20"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-0.7658, -0.7506,  1.3525], requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ],
      "source": [
        "params"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P4BhcGv4rM8j"
      },
      "source": [
        "#### Step 5: Step the weights. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "id": "Ea082BZFrM8j"
      },
      "outputs": [],
      "source": [
        "lr = 1e-5\n",
        "params.data -= lr * params.grad.data\n",
        "params.grad = None"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Mt09DlKcrM8j",
        "outputId": "c15916f5-4a6d-40a2-a948-be0ba8a3c11d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5435.5356, grad_fn=<MeanBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ],
      "source": [
        "preds = f(time,params)\n",
        "mse(preds, speed)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "id": "vwYFaAeJrM8j",
        "outputId": "83bff02c-9e75-4e1a-aa25-a30d2db9b72c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "show_preds(preds)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "id": "Y5_1PDR0rM8k"
      },
      "outputs": [],
      "source": [
        "def apply_step(params, prn=True):\n",
        "    preds = f(time, params)\n",
        "    loss = mse(preds, speed)\n",
        "    loss.backward()\n",
        "    params.data -= lr * params.grad.data\n",
        "    params.grad = None\n",
        "    if prn: print(loss.item())\n",
        "    return preds"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i2dCwdiarM8k"
      },
      "source": [
        "#### Step 6: Repeat the process "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9fqUuzrorM8k",
        "outputId": "c52cb6a0-c588-4949-ac80-8d8189087ea5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5435.53564453125\n",
            "1577.44921875\n",
            "847.3778076171875\n",
            "709.2225341796875\n",
            "683.0758056640625\n",
            "678.1243896484375\n",
            "677.1838989257812\n",
            "677.0023803710938\n",
            "676.9645385742188\n",
            "676.9537353515625\n"
          ]
        }
      ],
      "source": [
        "for i in range(10): apply_step(params)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "id": "3snSzkh0rM8l"
      },
      "outputs": [],
      "source": [
        "#hide\n",
        "params = orig_params.detach().requires_grad_()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        },
        "id": "W6MNcIRdrM8l",
        "outputId": "ddb37d94-d7ad-4901-d7ed-aea6cc4854c9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x216 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "_,axs = plt.subplots(1,4,figsize=(12,3))\n",
        "for ax in axs: show_preds(apply_step(params, False), ax)\n",
        "plt.tight_layout()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IQnH1_4drM8l"
      },
      "source": [
        "#### Step 7: stop"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ufcEp5Z6rM8m"
      },
      "source": [
        "### Summarizing Gradient Descent"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "VQfV2rixrM8m",
        "outputId": "ce45d43e-33e4-4ab3-e006-48947b062692"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.files.Source at 0x7fb0ff386150>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"597pt\" height=\"78pt\"\n viewBox=\"0.00 0.00 596.69 78.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 74)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-74 592.6863,-74 592.6863,4 -4,4\"/>\n<!-- init -->\n<g id=\"node1\" class=\"node\">\n<title>init</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">init</text>\n</g>\n<!-- predict -->\n<g id=\"node2\" class=\"node\">\n<title>predict</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"127.3968\" cy=\"-18\" rx=\"36.2938\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"127.3968\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">predict</text>\n</g>\n<!-- init&#45;&gt;predict -->\n<g id=\"edge1\" class=\"edge\">\n<title>init&#45;&gt;predict</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.1688,-18C62.3543,-18 71.5827,-18 80.6596,-18\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"80.7795,-21.5001 90.7795,-18 80.7795,-14.5001 80.7795,-21.5001\"/>\n</g>\n<!-- loss -->\n<g id=\"node3\" class=\"node\">\n<title>loss</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"227.7935\" cy=\"-52\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"227.7935\" y=\"-48.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">loss</text>\n</g>\n<!-- predict&#45;&gt;loss -->\n<g id=\"edge2\" class=\"edge\">\n<title>predict&#45;&gt;loss</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M157.5191,-28.2011C168.9806,-32.0826 182.1139,-36.5303 193.9014,-40.5222\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"192.8259,-43.8532 203.4202,-43.7458 195.0713,-37.2231 192.8259,-43.8532\"/>\n</g>\n<!-- gradient -->\n<g id=\"node4\" class=\"node\">\n<title>gradient</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"365.7399\" cy=\"-52\" rx=\"40.8928\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"365.7399\" y=\"-48.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">gradient</text>\n</g>\n<!-- loss&#45;&gt;gradient -->\n<g id=\"edge3\" class=\"edge\">\n<title>loss&#45;&gt;gradient</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M255.0473,-52C272.0415,-52 294.4481,-52 314.6545,-52\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"314.671,-55.5001 324.671,-52 314.671,-48.5001 314.671,-55.5001\"/>\n</g>\n<!-- step -->\n<g id=\"node5\" class=\"node\">\n<title>step</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"470.6863\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"470.6863\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">step</text>\n</g>\n<!-- gradient&#45;&gt;step -->\n<g id=\"edge4\" class=\"edge\">\n<title>gradient&#45;&gt;step</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M398.9456,-41.2422C410.9558,-37.3512 424.5297,-32.9536 436.6132,-29.0388\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"437.9112,-32.2975 446.3457,-25.8857 435.7537,-25.6382 437.9112,-32.2975\"/>\n</g>\n<!-- step&#45;&gt;predict -->\n<g id=\"edge6\" class=\"edge\">\n<title>step&#45;&gt;predict</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M443.4266,-18C384.9297,-18 246.7861,-18 174.0495,-18\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"173.8098,-14.5001 163.8098,-18 173.8097,-21.5001 173.8098,-14.5001\"/>\n<text text-anchor=\"middle\" x=\"289.7935\" y=\"-21.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">repeat</text>\n</g>\n<!-- stop -->\n<g id=\"node6\" class=\"node\">\n<title>stop</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"561.6863\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"561.6863\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">stop</text>\n</g>\n<!-- step&#45;&gt;stop -->\n<g id=\"edge5\" class=\"edge\">\n<title>step&#45;&gt;stop</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M497.9893,-18C506.2676,-18 515.508,-18 524.3268,-18\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"524.4026,-21.5001 534.4025,-18 524.4025,-14.5001 524.4026,-21.5001\"/>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {},
          "execution_count": 76
        }
      ],
      "source": [
        "gv('''\n",
        "init->predict->loss->gradient->step->stop\n",
        "step->predict[label=repeat]\n",
        "''')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jt5zHWjMrM8m"
      },
      "source": [
        "## The MNIST Loss Function"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "id": "ENnALJwcrM8m"
      },
      "outputs": [],
      "source": [
        "train_x = torch.cat([stacked_threes, stacked_sevens]).view(-1, 28*28)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CLvi7jonrM8n",
        "outputId": "a6f84b21-5f5c-437f-a364-16f4c7fc69d5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([12396, 784]), torch.Size([12396, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ],
      "source": [
        "train_y = tensor([1]*len(threes) + [0]*len(sevens)).unsqueeze(1)\n",
        "train_x.shape,train_y.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Os5bmiuYrM8n",
        "outputId": "4908da44-8e3a-48dc-accc-3691b08f0b7f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784]), tensor([1]))"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ],
      "source": [
        "dset = list(zip(train_x,train_y))\n",
        "x,y = dset[0]\n",
        "x.shape,y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "id": "n2E7a5zDrM8n"
      },
      "outputs": [],
      "source": [
        "valid_x = torch.cat([valid_3_tens, valid_7_tens]).view(-1, 28*28)\n",
        "valid_y = tensor([1]*len(valid_3_tens) + [0]*len(valid_7_tens)).unsqueeze(1)\n",
        "valid_dset = list(zip(valid_x,valid_y))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "id": "oHJv4yi3rM8o"
      },
      "outputs": [],
      "source": [
        "def init_params(size, std=1.0): return (torch.randn(size)*std).requires_grad_()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "id": "RqwmnXEPrM8o"
      },
      "outputs": [],
      "source": [
        "weights = init_params((28*28,1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "id": "YMQYcqc3rM8o"
      },
      "outputs": [],
      "source": [
        "bias = init_params(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0LTBLeE6rM8p",
        "outputId": "38ce18d5-5bd1-4be7-dd45-6cc20a6fa822"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([20.2336], grad_fn=<AddBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ],
      "source": [
        "(train_x[0]*weights.T).sum() + bias"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BnIIbeTHrM8p",
        "outputId": "0f85ff89-1479-4f2a-d068-dd7161ae07c2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[20.2336],\n",
              "        [17.0644],\n",
              "        [15.2384],\n",
              "        ...,\n",
              "        [18.3804],\n",
              "        [23.8567],\n",
              "        [28.6816]], grad_fn=<AddBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ],
      "source": [
        "def linear1(xb): return xb@weights + bias\n",
        "preds = linear1(train_x)\n",
        "preds"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0UHXWMc9rM8p",
        "outputId": "45475d94-208a-428c-f818-e90c41a82878"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ True],\n",
              "        [ True],\n",
              "        [ True],\n",
              "        ...,\n",
              "        [False],\n",
              "        [False],\n",
              "        [False]])"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ],
      "source": [
        "corrects = (preds>0.0).float() == train_y\n",
        "corrects"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 87,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3LFxMZ26rM8p",
        "outputId": "40072578-709e-470b-d7a8-f0eee0da45d8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4912068545818329"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ],
      "source": [
        "corrects.float().mean().item()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {
        "id": "3jDKIw1urM8q"
      },
      "outputs": [],
      "source": [
        "with torch.no_grad(): weights[0] *= 1.0001"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 89,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zqNW0dktrM8q",
        "outputId": "6c53ef27-71da-496d-9931-f9173369817f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4912068545818329"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ],
      "source": [
        "preds = linear1(train_x)\n",
        "((preds>0.0).float() == train_y).float().mean().item()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "id": "bwcgAq13rM8q"
      },
      "outputs": [],
      "source": [
        "trgts  = tensor([1,0,1])\n",
        "prds   = tensor([0.9, 0.4, 0.2])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "id": "_WH_xSLYrM8q"
      },
      "outputs": [],
      "source": [
        "def mnist_loss(predictions, targets):\n",
        "    return torch.where(targets==1, 1-predictions, predictions).mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KeqOw4VurM8r",
        "outputId": "fbf82524-8759-4535-859a-6de92de5b241"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.1000, 0.4000, 0.8000])"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ],
      "source": [
        "torch.where(trgts==1, 1-prds, prds)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q2VLwwX8rM8r",
        "outputId": "142ddf2e-bbd8-4e42-e568-ff6f05443526"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.4333)"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ],
      "source": [
        "mnist_loss(prds,trgts)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 94,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sPU7RLgArM8r",
        "outputId": "9123ca5d-9165-4ab7-819c-9898c0b6acbc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.2333)"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ],
      "source": [
        "mnist_loss(tensor([0.9, 0.4, 0.8]),trgts)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yAcTPjvcrM8s"
      },
      "source": [
        "### Sigmoid"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {
        "id": "BNxvMnJcrM8s"
      },
      "outputs": [],
      "source": [
        "def sigmoid(x): return 1/(1+torch.exp(-x))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "dKQB2zubrM8s",
        "outputId": "c3fbb21f-213d-459a-a7f2-055835552abb"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plot_function(torch.sigmoid, title='Sigmoid', min=-4, max=4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 97,
      "metadata": {
        "id": "FQuwBq4HrM8t"
      },
      "outputs": [],
      "source": [
        "def mnist_loss(predictions, targets):\n",
        "    predictions = predictions.sigmoid()\n",
        "    return torch.where(targets==1, 1-predictions, predictions).mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JfQ4nBeArM8t"
      },
      "source": [
        "### SGD and Mini-Batches"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-Y309X5NrM8t",
        "outputId": "a090a875-5fac-4754-b281-36e7994073e7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[tensor([ 3, 12,  8, 10,  2]),\n",
              " tensor([ 9,  4,  7, 14,  5]),\n",
              " tensor([ 1, 13,  0,  6, 11])]"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ],
      "source": [
        "coll = range(15)\n",
        "dl = DataLoader(coll, batch_size=5, shuffle=True)\n",
        "list(dl)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 99,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mwlydSRNrM8t",
        "outputId": "97064b1f-0d17-4b60-c7bc-a42cdfd16799"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(#26) [(0, 'a'),(1, 'b'),(2, 'c'),(3, 'd'),(4, 'e'),(5, 'f'),(6, 'g'),(7, 'h'),(8, 'i'),(9, 'j')...]"
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ],
      "source": [
        "ds = L(enumerate(string.ascii_lowercase))\n",
        "ds"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 100,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zdbqjK5KrM8u",
        "outputId": "ea3a2dba-2dbb-4f53-8ca6-3b8385464739"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(tensor([17, 18, 10, 22,  8, 14]), ('r', 's', 'k', 'w', 'i', 'o')),\n",
              " (tensor([20, 15,  9, 13, 21, 12]), ('u', 'p', 'j', 'n', 'v', 'm')),\n",
              " (tensor([ 7, 25,  6,  5, 11, 23]), ('h', 'z', 'g', 'f', 'l', 'x')),\n",
              " (tensor([ 1,  3,  0, 24, 19, 16]), ('b', 'd', 'a', 'y', 't', 'q')),\n",
              " (tensor([2, 4]), ('c', 'e'))]"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ],
      "source": [
        "dl = DataLoader(ds, batch_size=6, shuffle=True)\n",
        "list(dl)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SWaiXiNHrM8u"
      },
      "source": [
        "## Putting It All Together"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "id": "S2X6_SoarM8u"
      },
      "outputs": [],
      "source": [
        "weights = init_params((28*28,1))\n",
        "bias = init_params(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 102,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fX3TthpKrM8v",
        "outputId": "83449aaf-c801-489d-aa18-eb24503ffc01"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([256, 784]), torch.Size([256, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ],
      "source": [
        "dl = DataLoader(dset, batch_size=256)\n",
        "xb,yb = first(dl)\n",
        "xb.shape,yb.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 103,
      "metadata": {
        "id": "HTXbdZK6rM8v"
      },
      "outputs": [],
      "source": [
        "valid_dl = DataLoader(valid_dset, batch_size=256)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 104,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LhQnolgHrM8v",
        "outputId": "83f2095b-4374-4983-e9aa-eb3448facc09"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([4, 784])"
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ],
      "source": [
        "batch = train_x[:4]\n",
        "batch.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 105,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "upsuU_5zrM8w",
        "outputId": "d064c03b-6ee8-45e7-c7d6-d132c7f247b3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-2.1876],\n",
              "        [-8.3973],\n",
              "        [ 2.5000],\n",
              "        [-4.9473]], grad_fn=<AddBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ],
      "source": [
        "preds = linear1(batch)\n",
        "preds"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 106,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HQTR7_5arM8w",
        "outputId": "46c576a6-1ac0-4d15-8364-760794b5926b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.7419, grad_fn=<MeanBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ],
      "source": [
        "loss = mnist_loss(preds, train_y[:4])\n",
        "loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 107,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZM_uw5slrM8w",
        "outputId": "757636be-8580-479e-ae0d-83926fd254bc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784, 1]), tensor(-0.0061), tensor([-0.0420]))"
            ]
          },
          "metadata": {},
          "execution_count": 107
        }
      ],
      "source": [
        "loss.backward()\n",
        "weights.grad.shape,weights.grad.mean(),bias.grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 108,
      "metadata": {
        "id": "HYN_JS77rM8x"
      },
      "outputs": [],
      "source": [
        "def calc_grad(xb, yb, model):\n",
        "    preds = model(xb)\n",
        "    loss = mnist_loss(preds, yb)\n",
        "    loss.backward()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 109,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Na54IQNMrM8x",
        "outputId": "81202c46-8175-474f-8ebf-b092563af751"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(-0.0121), tensor([-0.0840]))"
            ]
          },
          "metadata": {},
          "execution_count": 109
        }
      ],
      "source": [
        "calc_grad(batch, train_y[:4], linear1)\n",
        "weights.grad.mean(),bias.grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 110,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KKUdcUJlrM8x",
        "outputId": "d49d142a-0a81-4e62-a660-9911df047a27"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(-0.0182), tensor([-0.1260]))"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ],
      "source": [
        "calc_grad(batch, train_y[:4], linear1)\n",
        "weights.grad.mean(),bias.grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 111,
      "metadata": {
        "id": "zC0fp9qErM8x"
      },
      "outputs": [],
      "source": [
        "weights.grad.zero_()\n",
        "bias.grad.zero_();"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 112,
      "metadata": {
        "id": "V-sp5AG3rM8y"
      },
      "outputs": [],
      "source": [
        "def train_epoch(model, lr, params):\n",
        "    for xb,yb in dl:\n",
        "        calc_grad(xb, yb, model)\n",
        "        for p in params:\n",
        "            p.data -= p.grad*lr\n",
        "            p.grad.zero_()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 113,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3oGBNSwsrM8y",
        "outputId": "edc6fd2e-e4a5-4621-9fc0-559f3ea93bba"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[False],\n",
              "        [False],\n",
              "        [ True],\n",
              "        [False]])"
            ]
          },
          "metadata": {},
          "execution_count": 113
        }
      ],
      "source": [
        "(preds>0.0).float() == train_y[:4]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 114,
      "metadata": {
        "id": "RMRE9z3GrM8z"
      },
      "outputs": [],
      "source": [
        "def batch_accuracy(xb, yb):\n",
        "    preds = xb.sigmoid()\n",
        "    correct = (preds>0.5) == yb\n",
        "    return correct.float().mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 115,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IPghJibarM80",
        "outputId": "cf1ecf22-7b33-4f32-96d9-4cd3bca0f759"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.2500)"
            ]
          },
          "metadata": {},
          "execution_count": 115
        }
      ],
      "source": [
        "batch_accuracy(linear1(batch), train_y[:4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 116,
      "metadata": {
        "id": "JcKKANk1rM80"
      },
      "outputs": [],
      "source": [
        "def validate_epoch(model):\n",
        "    accs = [batch_accuracy(model(xb), yb) for xb,yb in valid_dl]\n",
        "    return round(torch.stack(accs).mean().item(), 4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 117,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kTVHTYDsrM80",
        "outputId": "19e4b733-f315-401d-e456-2f900462e059"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5262"
            ]
          },
          "metadata": {},
          "execution_count": 117
        }
      ],
      "source": [
        "validate_epoch(linear1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 118,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cw1xwlt7rM81",
        "outputId": "c64deee4-8f34-43d0-92e2-5c1d47f98e6d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6663"
            ]
          },
          "metadata": {},
          "execution_count": 118
        }
      ],
      "source": [
        "lr = 1.\n",
        "params = weights,bias\n",
        "train_epoch(linear1, lr, params)\n",
        "validate_epoch(linear1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 119,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3mBi_VfJrM81",
        "outputId": "b8630243-8093-4a6e-b4a0-2e59bb78fc89"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.8265 0.8899 0.9182 0.9275 0.9397 0.9466 0.9505 0.9524 0.9559 0.9578 0.9598 0.9608 0.9612 0.9617 0.9632 0.9637 0.9647 0.9657 0.9671 0.9676 "
          ]
        }
      ],
      "source": [
        "for i in range(20):\n",
        "    train_epoch(linear1, lr, params)\n",
        "    print(validate_epoch(linear1), end=' ')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K-Krgkb3rM81"
      },
      "source": [
        "### Creating an Optimizer"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 120,
      "metadata": {
        "id": "XOOBS0-hrM82"
      },
      "outputs": [],
      "source": [
        "linear_model = nn.Linear(28*28,1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 121,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pEOQMvMyrM82",
        "outputId": "c5979e78-faaf-49c4-aa7e-90a91c7b94c9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([1, 784]), torch.Size([1]))"
            ]
          },
          "metadata": {},
          "execution_count": 121
        }
      ],
      "source": [
        "w,b = linear_model.parameters()\n",
        "w.shape,b.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 122,
      "metadata": {
        "id": "ceV7WcEcrM82"
      },
      "outputs": [],
      "source": [
        "class BasicOptim:\n",
        "    def __init__(self,params,lr): self.params,self.lr = list(params),lr\n",
        "\n",
        "    def step(self, *args, **kwargs):\n",
        "        for p in self.params: p.data -= p.grad.data * self.lr\n",
        "\n",
        "    def zero_grad(self, *args, **kwargs):\n",
        "        for p in self.params: p.grad = None"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 123,
      "metadata": {
        "id": "SP5UVR6mrM83"
      },
      "outputs": [],
      "source": [
        "opt = BasicOptim(linear_model.parameters(), lr)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 124,
      "metadata": {
        "id": "ToXBSbZLrM83"
      },
      "outputs": [],
      "source": [
        "def train_epoch(model):\n",
        "    for xb,yb in dl:\n",
        "        calc_grad(xb, yb, model)\n",
        "        opt.step()\n",
        "        opt.zero_grad()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 125,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gxYofME8rM83",
        "outputId": "f96466d9-cbc6-4ced-f580-285ebc57e896"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4609"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ],
      "source": [
        "validate_epoch(linear_model)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 126,
      "metadata": {
        "id": "0Mb3VNSprM83"
      },
      "outputs": [],
      "source": [
        "def train_model(model, epochs):\n",
        "    for i in range(epochs):\n",
        "        train_epoch(model)\n",
        "        print(validate_epoch(model), end=' ')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 127,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i88knc7brM84",
        "outputId": "55920be0-c5ca-42bf-817b-c1ea6c0d3fcd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.4932 0.7686 0.8555 0.9136 0.9345 0.9482 0.957 0.9633 0.9657 0.9677 0.9696 0.9716 0.9736 0.9745 0.976 0.977 0.9775 0.9775 0.978 0.9785 "
          ]
        }
      ],
      "source": [
        "train_model(linear_model, 20)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 128,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kThItFBvrM84",
        "outputId": "0d725a99-5dd6-4a6c-dc8c-3fff30e4bcde"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.4932 0.8179 0.8496 0.914 0.9345 0.9482 0.957 0.9618 0.9657 0.9672 0.9692 0.9711 0.9741 0.975 0.976 0.9775 0.9775 0.978 0.9785 0.9789 "
          ]
        }
      ],
      "source": [
        "linear_model = nn.Linear(28*28,1)\n",
        "opt = SGD(linear_model.parameters(), lr)\n",
        "train_model(linear_model, 20)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 129,
      "metadata": {
        "id": "99eYgHL5rM84"
      },
      "outputs": [],
      "source": [
        "dls = DataLoaders(dl, valid_dl)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 130,
      "metadata": {
        "id": "JXFiyPDWrM85"
      },
      "outputs": [],
      "source": [
        "learn = Learner(dls, nn.Linear(28*28,1), opt_func=SGD,\n",
        "                loss_func=mnist_loss, metrics=batch_accuracy)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 131,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "6aVWRkiXrM85",
        "outputId": "50e98b55-4031-4a6a-896c-620abb36914d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<style>\n",
              "    /* Turns off some styling */\n",
              "    progress {\n",
              "        /* gets rid of default border in Firefox and Opera. */\n",
              "        border: none;\n",
              "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "        background-size: auto;\n",
              "    }\n",
              "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "        background: #F44336;\n",
              "    }\n",
              "</style>\n"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: left;\">\n",
              "      <th>epoch</th>\n",
              "      <th>train_loss</th>\n",
              "      <th>valid_loss</th>\n",
              "      <th>batch_accuracy</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <td>0</td>\n",
              "      <td>0.636709</td>\n",
              "      <td>0.503144</td>\n",
              "      <td>0.495584</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>1</td>\n",
              "      <td>0.429828</td>\n",
              "      <td>0.248517</td>\n",
              "      <td>0.777233</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>2</td>\n",
              "      <td>0.161680</td>\n",
              "      <td>0.155361</td>\n",
              "      <td>0.861629</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>3</td>\n",
              "      <td>0.072948</td>\n",
              "      <td>0.097722</td>\n",
              "      <td>0.917566</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>4</td>\n",
              "      <td>0.040128</td>\n",
              "      <td>0.073205</td>\n",
              "      <td>0.936212</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>5</td>\n",
              "      <td>0.027210</td>\n",
              "      <td>0.059466</td>\n",
              "      <td>0.950442</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>6</td>\n",
              "      <td>0.021837</td>\n",
              "      <td>0.050799</td>\n",
              "      <td>0.957802</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>7</td>\n",
              "      <td>0.019398</td>\n",
              "      <td>0.044980</td>\n",
              "      <td>0.964181</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>8</td>\n",
              "      <td>0.018122</td>\n",
              "      <td>0.040853</td>\n",
              "      <td>0.966143</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>9</td>\n",
              "      <td>0.017330</td>\n",
              "      <td>0.037788</td>\n",
              "      <td>0.968106</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "learn.fit(10, lr=lr)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k-htMghXrM86"
      },
      "source": [
        "## Adding a Nonlinearity"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 132,
      "metadata": {
        "id": "1z6siNRarM86"
      },
      "outputs": [],
      "source": [
        "def simple_net(xb): \n",
        "    res = xb@w1 + b1\n",
        "    res = res.max(tensor(0.0))\n",
        "    res = res@w2 + b2\n",
        "    return res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 133,
      "metadata": {
        "id": "zLM3lwfQrM86"
      },
      "outputs": [],
      "source": [
        "w1 = init_params((28*28,30))\n",
        "b1 = init_params(30)\n",
        "w2 = init_params((30,1))\n",
        "b2 = init_params(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 134,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "O9oXxUD5rM86",
        "outputId": "eb9cd880-d029-4c61-9a97-aa075e3e65af"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plot_function(F.relu)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 135,
      "metadata": {
        "id": "xKAMfgB6rM87"
      },
      "outputs": [],
      "source": [
        "simple_net = nn.Sequential(\n",
        "    nn.Linear(28*28,30),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(30,1)\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 136,
      "metadata": {
        "id": "BNqb1HCbrM87"
      },
      "outputs": [],
      "source": [
        "learn = Learner(dls, simple_net, opt_func=SGD,\n",
        "                loss_func=mnist_loss, metrics=batch_accuracy)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 137,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "1umO6gpzrM87",
        "outputId": "3b9c8b03-8748-48fa-9d1a-5114cfbcb2d6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<style>\n",
              "    /* Turns off some styling */\n",
              "    progress {\n",
              "        /* gets rid of default border in Firefox and Opera. */\n",
              "        border: none;\n",
              "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "        background-size: auto;\n",
              "    }\n",
              "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "        background: #F44336;\n",
              "    }\n",
              "</style>\n"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: left;\">\n",
              "      <th>epoch</th>\n",
              "      <th>train_loss</th>\n",
              "      <th>valid_loss</th>\n",
              "      <th>batch_accuracy</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <td>0</td>\n",
              "      <td>0.333021</td>\n",
              "      <td>0.396112</td>\n",
              "      <td>0.512267</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>1</td>\n",
              "      <td>0.152461</td>\n",
              "      <td>0.235238</td>\n",
              "      <td>0.797350</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>2</td>\n",
              "      <td>0.083573</td>\n",
              "      <td>0.117471</td>\n",
              "      <td>0.911678</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>3</td>\n",
              "      <td>0.054309</td>\n",
              "      <td>0.078720</td>\n",
              "      <td>0.940628</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>4</td>\n",
              "      <td>0.040829</td>\n",
              "      <td>0.061228</td>\n",
              "      <td>0.956330</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>5</td>\n",
              "      <td>0.034006</td>\n",
              "      <td>0.051490</td>\n",
              "      <td>0.963690</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>6</td>\n",
              "      <td>0.030123</td>\n",
              "      <td>0.045381</td>\n",
              "      <td>0.966634</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>7</td>\n",
              "      <td>0.027619</td>\n",
              "      <td>0.041218</td>\n",
              "      <td>0.968106</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>8</td>\n",
              "      <td>0.025825</td>\n",
              "      <td>0.038200</td>\n",
              "      <td>0.969087</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>9</td>\n",
              "      <td>0.024441</td>\n",
              "      <td>0.035901</td>\n",
              "      <td>0.969578</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>10</td>\n",
              "      <td>0.023321</td>\n",
              "      <td>0.034082</td>\n",
              "      <td>0.971541</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>11</td>\n",
              "      <td>0.022387</td>\n",
              "      <td>0.032598</td>\n",
              "      <td>0.972031</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>12</td>\n",
              "      <td>0.021592</td>\n",
              "      <td>0.031353</td>\n",
              "      <td>0.974485</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>13</td>\n",
              "      <td>0.020904</td>\n",
              "      <td>0.030284</td>\n",
              "      <td>0.975466</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>14</td>\n",
              "      <td>0.020300</td>\n",
              "      <td>0.029352</td>\n",
              "      <td>0.975466</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>15</td>\n",
              "      <td>0.019766</td>\n",
              "      <td>0.028526</td>\n",
              "      <td>0.975466</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>16</td>\n",
              "      <td>0.019288</td>\n",
              "      <td>0.027788</td>\n",
              "      <td>0.976448</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>17</td>\n",
              "      <td>0.018857</td>\n",
              "      <td>0.027124</td>\n",
              "      <td>0.977429</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>18</td>\n",
              "      <td>0.018465</td>\n",
              "      <td>0.026523</td>\n",
              "      <td>0.978410</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>19</td>\n",
              "      <td>0.018107</td>\n",
              "      <td>0.025977</td>\n",
              "      <td>0.978901</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>20</td>\n",
              "      <td>0.017777</td>\n",
              "      <td>0.025479</td>\n",
              "      <td>0.978901</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>21</td>\n",
              "      <td>0.017473</td>\n",
              "      <td>0.025022</td>\n",
              "      <td>0.979392</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>22</td>\n",
              "      <td>0.017191</td>\n",
              "      <td>0.024601</td>\n",
              "      <td>0.980373</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>23</td>\n",
              "      <td>0.016927</td>\n",
              "      <td>0.024213</td>\n",
              "      <td>0.980373</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>24</td>\n",
              "      <td>0.016680</td>\n",
              "      <td>0.023855</td>\n",
              "      <td>0.981354</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>25</td>\n",
              "      <td>0.016449</td>\n",
              "      <td>0.023521</td>\n",
              "      <td>0.981354</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>26</td>\n",
              "      <td>0.016230</td>\n",
              "      <td>0.023211</td>\n",
              "      <td>0.981354</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>27</td>\n",
              "      <td>0.016023</td>\n",
              "      <td>0.022922</td>\n",
              "      <td>0.981354</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>28</td>\n",
              "      <td>0.015827</td>\n",
              "      <td>0.022653</td>\n",
              "      <td>0.981845</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>29</td>\n",
              "      <td>0.015641</td>\n",
              "      <td>0.022401</td>\n",
              "      <td>0.981845</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>30</td>\n",
              "      <td>0.015463</td>\n",
              "      <td>0.022165</td>\n",
              "      <td>0.981845</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>31</td>\n",
              "      <td>0.015294</td>\n",
              "      <td>0.021944</td>\n",
              "      <td>0.983317</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>32</td>\n",
              "      <td>0.015132</td>\n",
              "      <td>0.021736</td>\n",
              "      <td>0.982826</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>33</td>\n",
              "      <td>0.014977</td>\n",
              "      <td>0.021541</td>\n",
              "      <td>0.982826</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>34</td>\n",
              "      <td>0.014828</td>\n",
              "      <td>0.021357</td>\n",
              "      <td>0.982336</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>35</td>\n",
              "      <td>0.014686</td>\n",
              "      <td>0.021184</td>\n",
              "      <td>0.982336</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>36</td>\n",
              "      <td>0.014549</td>\n",
              "      <td>0.021019</td>\n",
              "      <td>0.982336</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>37</td>\n",
              "      <td>0.014417</td>\n",
              "      <td>0.020864</td>\n",
              "      <td>0.982336</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>38</td>\n",
              "      <td>0.014290</td>\n",
              "      <td>0.020716</td>\n",
              "      <td>0.982336</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>39</td>\n",
              "      <td>0.014168</td>\n",
              "      <td>0.020576</td>\n",
              "      <td>0.982336</td>\n",
              "      <td>00:00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "learn.fit(40, 0.1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 138,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        },
        "id": "SuY0hAFYrM88",
        "outputId": "7ebfc5b3-eaef-4a1f-8a7c-56286fd25372"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.plot(L(learn.recorder.values).itemgot(2));"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 139,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zRnUaE8zrM88",
        "outputId": "bf69fbe0-b5da-4611-bc24-376087512830"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.98233562707901"
            ]
          },
          "metadata": {},
          "execution_count": 139
        }
      ],
      "source": [
        "learn.recorder.values[-1][2]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e9V0z0a9rM88"
      },
      "source": [
        "### Going Deeper"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 140,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "uBeIpfKfrM88",
        "outputId": "562c381d-5de9-4289-eeb3-2ea478301e6a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<style>\n",
              "    /* Turns off some styling */\n",
              "    progress {\n",
              "        /* gets rid of default border in Firefox and Opera. */\n",
              "        border: none;\n",
              "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "        background-size: auto;\n",
              "    }\n",
              "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "        background: #F44336;\n",
              "    }\n",
              "</style>\n"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: left;\">\n",
              "      <th>epoch</th>\n",
              "      <th>train_loss</th>\n",
              "      <th>valid_loss</th>\n",
              "      <th>accuracy</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <td>0</td>\n",
              "      <td>0.071416</td>\n",
              "      <td>0.015663</td>\n",
              "      <td>0.994603</td>\n",
              "      <td>00:17</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "dls = ImageDataLoaders.from_folder(path)\n",
        "learn = vision_learner(dls, resnet18, pretrained=False,\n",
        "                    loss_func=F.cross_entropy, metrics=accuracy)\n",
        "learn.fit_one_cycle(1, 0.1)"
      ]
    }
  ],
  "metadata": {
    "jupytext": {
      "split_at_heading": true
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.7"
    },
    "colab": {
      "name": "04_mnist_basics.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "Sg1Tv6QbrM8e",
        "IQnH1_4drM8l"
      ],
      "include_colab_link": true
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}