谢焕宜_Ch4.ipynb

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    "colab": {
      "name": "“04_mnist_full_set.ipynb”的副本",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/StuPidMRE/assignment/blob/main/%E8%B0%A2%E7%84%95%E5%AE%9C_Ch4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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          "base_uri": "https://localhost:8080/"
        },
        "outputId": "954a78c2-b436-43bf-fb65-09e83e5070f1"
      },
      "source": [
        "!pip install -Uqq fastbook\n",
        "import fastbook\n",
        "fastbook.setup_book()"
      ],
      "execution_count": null,
      "outputs": [
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          "text": [
            "\u001b[K     |████████████████████████████████| 727kB 8.4MB/s \n",
            "\u001b[K     |████████████████████████████████| 1.2MB 44.8MB/s \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d984jeb0Ao-_"
      },
      "source": [
        "from fastai.vision.all import *\n",
        "from fastbook import *\n",
        "\n",
        "matplotlib.rc('image', cmap='Greys')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2oVrDUE_nzmu"
      },
      "source": [
        "# Rerun Chapter 4 with the full MNIST dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zQ-L91uh_cX0"
      },
      "source": [
        "## Load full MNIST dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ECAC3RfxAo_D"
      },
      "source": [
        "We are try to rerun the two classifiers built before to classify images as a 3 or a 7, but using the full dataset with 10 digits. So let's download the full MNIST datasets:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z51wexCkAo_D",
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          "height": 17
        },
        "outputId": "9a9b0e5e-69c8-43cf-df7f-fb3762d32fb5"
      },
      "source": [
        "path = untar_data(URLs.MNIST)    # Full dataset (0s to 9s)"
      ],
      "execution_count": null,
      "outputs": [
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      "source": [
        "Path.BASE_PATH = path"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7q8C99uoAo_D"
      },
      "source": [
        "We can see what's in this directory by using `ls`, a method added by fastai. This method returns an object of a special fastai class called `L`, which has all the same functionality of Python's built-in `list`, plus a lot more. One of its handy features is that, when printed, it displays the count of items, before listing the items themselves (if there are more than 10 items, it just shows the first few):"
      ]
    },
    {
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        "outputId": "326c78bf-74c8-4ca4-d20e-58f8448ed988"
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      "source": [
        "path.ls()"
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      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(#2) [Path('testing'),Path('training')]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
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      "source": [
        "The MNIST dataset follows a common layout for machine learning datasets: separate folders for the training set and the validation set (and/or test set). Note, though, that the names of both image folders have changed: `train` into `training` and `valid` into `testing`. Keep this in mind when you look for images in the code below.\n",
        "\n",
        "Let's see what's inside the training set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7N8WAogvAo_G",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "12ead3ed-871e-4c64-d19a-f5c1f64db0d8"
      },
      "source": [
        "(path/'training').ls()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(#10) [Path('training/4'),Path('training/6'),Path('training/3'),Path('training/5'),Path('training/1'),Path('training/2'),Path('training/9'),Path('training/7'),Path('training/8'),Path('training/0')]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2pVC0CapAo_H"
      },
      "source": [
        "There's a folder for each digit from 0s to 9s. Let's take a look in one of these folders (using `sorted` to ensure we all get the same order of files). To do so, it is convenient to use a `dict`, indexed by the digit (0 -> 9). It prevents us from creating 10 different variables and from writing 10 times tvery similar code. We also could use a list of lists.\n",
        "``` python\n",
        "    paths_dict = {0: [list of the paths to images of 0],\n",
        "                  1: [list of the paths to images of 1],\n",
        "\n",
        "                  i: [list of the paths to images of i],\n",
        "\n",
        "                  9: [list of the paths to images of 9],\n",
        "                 }\n",
        "```"
      ]
    },
    {
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      "metadata": {
        "id": "NPjkeRxyAo_H",
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          "base_uri": "https://localhost:8080/"
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        "outputId": "e69838f5-8eca-4da6-95b2-9bfa259cc618"
      },
      "source": [
        "paths_dict = {}         # Create an empty dictionary to hold the paths list for each digit\n",
        "for i in range(10):\n",
        "    paths_dict[i] = (path/'training'/f\"{i}\").ls().sorted()   # add the list of path for digit i to the dict\n",
        "\n",
        "paths_dict"
      ],
      "execution_count": null,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: (#5923) [Path('training/0/1.png'),Path('training/0/1000.png'),Path('training/0/10005.png'),Path('training/0/10010.png'),Path('training/0/10022.png'),Path('training/0/10025.png'),Path('training/0/10026.png'),Path('training/0/10045.png'),Path('training/0/10069.png'),Path('training/0/10071.png')...],\n",
              " 1: (#6742) [Path('training/1/10006.png'),Path('training/1/10007.png'),Path('training/1/1002.png'),Path('training/1/10020.png'),Path('training/1/10027.png'),Path('training/1/1003.png'),Path('training/1/10040.png'),Path('training/1/10048.png'),Path('training/1/10058.png'),Path('training/1/10067.png')...],\n",
              " 2: (#5958) [Path('training/2/10009.png'),Path('training/2/10016.png'),Path('training/2/10024.png'),Path('training/2/10029.png'),Path('training/2/10072.png'),Path('training/2/10073.png'),Path('training/2/10075.png'),Path('training/2/10078.png'),Path('training/2/10081.png'),Path('training/2/10082.png')...],\n",
              " 3: (#6131) [Path('training/3/10.png'),Path('training/3/10000.png'),Path('training/3/10011.png'),Path('training/3/10031.png'),Path('training/3/10034.png'),Path('training/3/10042.png'),Path('training/3/10052.png'),Path('training/3/1007.png'),Path('training/3/10074.png'),Path('training/3/10091.png')...],\n",
              " 4: (#5842) [Path('training/4/10013.png'),Path('training/4/10018.png'),Path('training/4/10033.png'),Path('training/4/1004.png'),Path('training/4/1006.png'),Path('training/4/10060.png'),Path('training/4/1008.png'),Path('training/4/10103.png'),Path('training/4/10104.png'),Path('training/4/10114.png')...],\n",
              " 5: (#5421) [Path('training/5/0.png'),Path('training/5/100.png'),Path('training/5/10008.png'),Path('training/5/10015.png'),Path('training/5/10030.png'),Path('training/5/10035.png'),Path('training/5/10049.png'),Path('training/5/10051.png'),Path('training/5/10056.png'),Path('training/5/10062.png')...],\n",
              " 6: (#5918) [Path('training/6/10017.png'),Path('training/6/10032.png'),Path('training/6/10036.png'),Path('training/6/10037.png'),Path('training/6/10044.png'),Path('training/6/10053.png'),Path('training/6/10076.png'),Path('training/6/10089.png'),Path('training/6/10101.png'),Path('training/6/10108.png')...],\n",
              " 7: (#6265) [Path('training/7/10002.png'),Path('training/7/1001.png'),Path('training/7/10014.png'),Path('training/7/10019.png'),Path('training/7/10039.png'),Path('training/7/10046.png'),Path('training/7/10050.png'),Path('training/7/10063.png'),Path('training/7/10077.png'),Path('training/7/10086.png')...],\n",
              " 8: (#5851) [Path('training/8/10001.png'),Path('training/8/10012.png'),Path('training/8/10021.png'),Path('training/8/10041.png'),Path('training/8/10054.png'),Path('training/8/10057.png'),Path('training/8/10061.png'),Path('training/8/10064.png'),Path('training/8/10066.png'),Path('training/8/10079.png')...],\n",
              " 9: (#5949) [Path('training/9/10003.png'),Path('training/9/10004.png'),Path('training/9/10023.png'),Path('training/9/10028.png'),Path('training/9/10038.png'),Path('training/9/10043.png'),Path('training/9/10047.png'),Path('training/9/1005.png'),Path('training/9/10055.png'),Path('training/9/10059.png')...]}"
            ]
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          "execution_count": 9
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    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "312NwVltAo_I"
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      "source": [
        "Let’s take a look at one image for each of the digits:"
      ]
    },
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      "source": [
        "for i in range(10):\n",
        "    img_paths = paths_dict[i][3]\n",
        "    img = Image.open(img_paths)\n",
        "    display(img)"
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      "execution_count": null,
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "enZri5pkAo_J"
      },
      "source": [
        "We can store the image in a tensor and slice it to pick some part of the image. We then use a Pandas DataFrame to color-code the values using a gradient, which shows us clearly how the image is created from the pixel values:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zbju2SOjAo_K"
      },
      "source": [
        "## Baseline model: Pixel Similarity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nZ0g9n7sAo_K"
      },
      "source": [
        "So, here is a first idea: how about we find the average pixel value for every pixel for each digit (0 to 9). Then, to classify an image as one digit or the other, we see which of these ideal digits the image is most similar to. This certainly seems like it should be better than nothing, so it will make a good baseline."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Nu_zxJnAo_L"
      },
      "source": [
        "Step one for our simple model is to get the average of pixel values for the groups of images for each pixel.\n",
        "\n",
        "Let's create a tensor containing all of the images representing a single digit, stacked together. We use the same list comnprehension as in `04_mnist_basic`. But since we have 10 groups, we again use a dictionary indexed with the digit 0 to 9, to hold the stacked images, instead of 10 variables. You also can use a list of tensors here. There are also other methods that may be faster."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K-QBaP57Ao_L"
      },
      "source": [
        "tensors_dict = {}\n",
        "for i in range(10):\n",
        "    tensors_dict[i] = [tensor(Image.open(o)) for o in paths_dict[i]]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "3lr9h45QANvp",
        "outputId": "144e559c-b64a-47dc-a37e-d624ef39c73b"
      },
      "source": [
        "# Show the number of images for each digit\n",
        "print(f'Total number of images: {sum([len(v) for k, v in tensors_dict.items()]):,d}')\n",
        "display([f\"{len(v):,d} images for {k}\" for k, v in tensors_dict.items()])\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Total number of images: 60,000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "['5,923 images for 0',\n",
              " '6,742 images for 1',\n",
              " '5,958 images for 2',\n",
              " '6,131 images for 3',\n",
              " '5,842 images for 4',\n",
              " '5,421 images for 5',\n",
              " '5,918 images for 6',\n",
              " '6,265 images for 7',\n",
              " '5,851 images for 8',\n",
              " '5,949 images for 9']"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lLNeQOo3Ao_M"
      },
      "source": [
        "We'll also check that one of the images looks okay. Since we now have tensors (which Jupyter by default will print as values), rather than PIL images (which Jupyter by default will display as images), we need to use fastai's `show_image` function to display it:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fhPxcHn1Ao_M",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        },
        "outputId": "821b398f-6c80-4411-f8f2-a55317db8374"
      },
      "source": [
        "show_image(tensors_dict[2][1])\n",
        "show_image(tensors_dict[9][1]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAIEElEQVR4nO2bW08TWxuAn5lOT9N2WiwFEd0oIKeCEvBENBo1IZp4YfQHGK/8F174U/wBGi/0xgMXhqgxMaJQBUWgVFpoKRZ7mrbT7gvT2e7KJ3trB/Hb8yS96azQNU/e9a613rUQKpUKJn8h/uoObDdMITWYQmowhdRgCqlB2uT5//MUJGz0pRkhNZhCajCF1GAKqWGzpPrTaJpGsVikXC6jaRqVSoVyuUy5XKZUKuntqt/JsozNZsNqtSJJEoKwYe4zDMOFZLNZPnz4wKdPn5ifnyeTyZBOp1ldXWV5eVlvl0qlWF1dZXR0lFOnTtHV1UUgEADYUimGCalUKlQqFbLZLO/fvycajTI/P0+hUCCXy7G+vk4sFtPbJxIJUqkUMzMzuFwuJElC0zR8Ph9Op3PLpAib7HZ/eB1SHRITExNcv36dSCTC3NwcVqsVm82mD58qqqpSKBSQJAmLxcLhw4fp7u7m2rVr9Pf3I4oioljXlLehYUMjpFwuo6oqyWQSq9VKb28vfr+fpqamb9rH43Gi0SjRaJREIkE4HMZisfDy5UtcLhfNzc24XC5EUTQ0WgwVomka+Xye1dVVjh8/zuXLl+nq6mLfvn3ftJ+dneXp06fcu3ePO3fusLCwQDgc5sOHD7S2tnLjxg0OHz6M3W5HkoxLfYYmVUEQ8Pv9nDlzhr6+Pjo6OvD7/djt9m/aBgIB+vv7+fjxI2traywsLJBIJMhms4TDYUKhEC0tLezatQtZlg2LFMNzSKFQIJVK4Xa78Xg8CIKw4YtUk3A1+d65c4exsTHC4TCrq6ucO3eO3t5erly5Qnt7O3a7HYvF8qPdg63OIYIgIIoikiTh8Xiw2WzfTYpVUR6Ph9bWVoLBIOl0mmw2SzweJxwOY7fbWVxcxOfz0djY+LNCNsRQIZIkIUkSdrv9H4e3x+PB4/EwOjpKX18fqVSKN2/eMDU1xfT0NHv37kVVVU6ePInD4ah7v7dk6f5vxno1UpxOJw0NDfh8PlwuFxaLBU3TSKVSxGIxisWiIX3dtnsZh8NBIBCgpaWF5uZmHA4HlUqFeDzO3Nwcqqoa8rvbVojFYsFms/HHH38wNDREQ0MDACsrK8RiMbLZLKVSiXofoxi+l/lRqpu7AwcOkMlkWF5eZnFxUd8Pra2tUSwWEQShrsl120YIfMknsizT1NSELMsA5HI5Pn36hKqqlMvl/06EVHG5XLS2tuLxeABYX18nl8uRTqe/2Q/Vg20dIb8CU0gNppAaTCE1bPukqqoqqVRKX4g5HA5cLhdOp9OQHe+2j5B8Pq+XAQBkWcbr9eqbxXoL2bYRomkamqYxOzvL+Pg4kUgEQRDYvXs3nZ2dNDQ0YLVa/1tCCoUCoVCIsbExvSDd1tZGe3s7iqJgtVrr/rtbJqRaY83n83z+/HnT9tWicyQSYWVlhXw+jyAIKIpCU1OTITJgi4VomkYmk2FhYWHT9sVikWKxSCwWY21tDQBRFPF4PAQCAcPqqoYLKRaL5HI5EokEb9++ZXp6momJiU2X3JIkIYoik5OTwJclvNvtZmBggKNHj+JyuQzpr+FCSqUSa2trTE9Pc/v2bUKhEE+ePAG+LRx9LcntdiPLsj68ZFnG5/PR3d3Nnj17sNlshvTX8HOZeDzOrVu3ePfuHePj4wAEg0H6+vro6enRi8/v3r1jdnaWV69eMT8/Tz6f1xMrfBHi9/vJZrN8/vxZL0/WG8PPZRKJBOPj48zMzPD27Vva2toYGhpieHiY0dFRFEXB5/MxMTHBo0ePSCaTzM/PUyqV/nYY7nA4UBRF3+kqikKlUvl9pt10Os3U1BSPHz/m+fPnlEolmpubOX/+PFevXsXv99PY2Ki3t9vtyLL8P2ePaDRKKpXi5s2b3L9/n9OnT9PR0UFfXx9ut7tu/TZMSCaT4fnz54RCISKRCIqi0NLSQm9vLwcPHsRisSCKIsVikUKhgMVi0T/wV7G5+qneGhgbG9Or+PF4nL179/4eQsrlMtlsVs8BnZ2dXLhwgeHhYSRJIpfL6VcgYrEYDx484OHDh0QiEQAOHTpEMBikv7+fjo4OXr58SSQSoVAoUC6XAVhYWGB9fR2v14vVaq3LYbihQgqFApqmAV+OKgcGBvRhoqoqy8vLzM3N6VPxixcv9BppZ2cnQ0NDnD17lj179tDU1MTr16/1itnKygrpdFr/jXol2C1bmMXjcSYnJ8nlcmQyGUKhEM+ePWNpaYmZmRn98szQ0BAHDx7k0qVLDA4O4vV6sdvtBINBOjo69Eq7qqpomkZLS8ump4L/BsOPMquzQLVyXp19JiYmePLkCUtLS0SjUSRJwuFw0NnZyeDgIN3d3ezcuVPPIYqioCiK/verBeav80w9MEyILMsMDAyQTCYRBIHFxUXu3r2L0+nE7XaTTCZJJpOIokggEODixYucP3+e9vZ2mpubURTluy/69bN6Tr2GCZEkiUAggNfrRRRFstks6XRaf16dUXbs2EFjYyMHDhxgZGQEj8eD0+kEvv+iRl2aMUyIw+Ggt7eXVCpFT08PiUSCaDSqP+/u7ubYsWOMjIxw4sQJGhsbURQFi8Wy5TcPv8bQCKlehdq/fz92ux1VVfX9yv79+wkGgxw5coSurq665oGfwbALM9ULMNUrVaVS6W8n9k6nU6+NVofIFrOhfcOE/AaY/w3xTzCF1GAKqcEUUoMppAZTSA2mkBpMITVstnT/9WvpLcaMkBpMITWYQmowhdRgCqnBFFLDn5fYjiWtBHE5AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MVISc1SpAo_N"
      },
      "source": [
        "For every pixel position, we want to compute the average over all the images of the intensity of that pixel. To do this we first combine all the images in this list into a single three-dimensional tensor. The most common way to describe such a tensor is to call it a *rank-3 tensor*. We often need to stack up individual tensors in a collection into a single tensor. Unsurprisingly, PyTorch comes with a function called `stack` that we can use for this purpose.\n",
        "\n",
        "Some operations in PyTorch, such as taking a mean, require us to *cast* our integer types to float types. Since we'll be needing this later, we'll also cast our stacked tensor to `float` now. Casting in PyTorch is as simple as typing the name of the type you wish to cast to, and treating it as a method.\n",
        "\n",
        "Generally when images are floats, the pixel values are expected to be between 0 and 1, so we will also divide by 255 here:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "em4pFaPTAo_N"
      },
      "source": [
        "# Calculate the stacked tensor for each of the digit and store that tensor in a dictionary index by digit\n",
        "stacked_tensors_dict = {}\n",
        "for digit, img_tensor in tensors_dict.items():\n",
        "    stacked_tensors_dict[digit] = torch.stack(img_tensor).float()/255"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dvddIlsBAo_N"
      },
      "source": [
        "Perhaps the most important attribute of a tensor is its *shape*. This tells you the length of each axis. In this case, we can see that we have around 6,000 images for each digit, each image of size 28×28 pixels. There is nothing specifically about this tensor that says that the first axis is the number of images, the second is the height, and the third is the width—the semantics of a tensor are entirely up to us, and how we construct it. As far as PyTorch is concerned, it is just a bunch of numbers in memory."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HR_70dP0CDmt",
        "outputId": "8f8776e4-8f7b-4587-adb1-2c0c23f8e69b"
      },
      "source": [
        "print('Shapes of image tensor for each digit:')\n",
        "for digit, img_tensor in stacked_tensors_dict.items():\n",
        "    print('   ', digit, ': ', stacked_tensors_dict[digit].shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shapes of image tensor for each digit:\n",
            "    0 :  torch.Size([5923, 28, 28])\n",
            "    1 :  torch.Size([6742, 28, 28])\n",
            "    2 :  torch.Size([5958, 28, 28])\n",
            "    3 :  torch.Size([6131, 28, 28])\n",
            "    4 :  torch.Size([5842, 28, 28])\n",
            "    5 :  torch.Size([5421, 28, 28])\n",
            "    6 :  torch.Size([5918, 28, 28])\n",
            "    7 :  torch.Size([6265, 28, 28])\n",
            "    8 :  torch.Size([5851, 28, 28])\n",
            "    9 :  torch.Size([5949, 28, 28])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eioTreEvAo_O"
      },
      "source": [
        "Finally, we can compute what the ideal digit image looks like. We calculate the mean of all the image tensors by taking the mean along dimension 0 of our stacked, rank-3 tensor. This is the dimension that indexes over all the images.\n",
        "\n",
        "In other words, for every pixel position, this will compute the average of that pixel over all images. The result will be one value for every pixel position, or a single image. Here it is:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "imwKFV7kAo_P",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 697
        },
        "outputId": "f28ee594-f276-450e-d752-82694bc75dff"
      },
      "source": [
        "means_dict = {}\n",
        "for digit, tnsr in stacked_tensors_dict.items():\n",
        "    means_dict[digit] = stacked_tensors_dict[digit].mean(0)\n",
        "    show_image(means_dict[digit])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAItElEQVR4nO2baW/aWheFl2eMbYwhobRRVLX//4+1UsrgGU/vh6u138Op07TBJL1XbAlhwuTzeO3xEGMYBtzs/2a+9wn8bXYDotkNiGY3IJrdgGhmv/D8fzkFGWN/vClEs5cUMqlNUfMYxuiFncyuDkSHoD5+7lj9mw6Aj5+7v9SuAmQMwnO3vu/lnse80QzDgGmacq/fDMM4A3MJnKsqhIt6CULXdei6Dm3bouu6MzBcoGVZME0TjuPAsizYti2frwLj970WyuRAdAgARgH0fY+2bXE6neRWlqUc8zVcrOd5cBwHQRCc3RMQcA5GhfUnNimQ5+KArg5CaZoGTdPgdDqhKApUVYW6rlGWpajGtm2YpinvdV0XhmGg6zpYlnX22X+lQgCMAlCVcTqd0DQNqqpCWZbIsgxFUeB4PKIoChRFIUB834fjOIjjGEEQwHVdmKb5k2uNgXmNTQbkOXWox8MwyEKpjLquRRWEUVWVvKfrOnELxhHeqwH1r80yYy6ixwwCSNMUeZ7jx48fSNMUaZridDqhbVsBYFkWPM/DfD7HbDaTe9d1Yds2LMs6g3IpmKtWqmqAVbOJqo6yLCV2MJgOwwDLsuC6rkDwPE9AOI4jsUUNpFOoZBKF/KruIIi2bdE0Deq6Rp7nyLIMu90Ox+MRu90OVVWhqipZ6Gw2QxRFuLu7QxRFWC6X8H0f8/lc1EH3eU4hrwE0qULGYoYaO1RlMLOUZYm6rkUZhmHAcRz4vo8wDDGfz+H7PjzPE3WoMYT2r4ghanoliKIoRB273Q5FUSDPc3mv4zgIwxDr9RpJkmC1WmE+nyMMwzNXGQuol6oDuFIMGYPSdZ0UXWo2YdwAANu2MZvNEIYhwjBEEATwPA+e50kAvUZmUW3ywkyvP5hZqqo6ix2HwwFpmsrzzB7L5RKbzQZJkkjtMZvNRjMK8C9o7nQobduepds8z5HnuaiDccd1XXGNIAjg+77EDLVPUb9nzC4FM2lhpsNgac7YcTgcsN/vcTgcJHbYtg3XdeH7PpIkwXq9xnK5FDCqq/B7njMVxmsr1qsoRC3V27aVajTLMmRZJpml73uYpinqYGplI6f2Jn3fj34f3Yf9DsGxwXv35m4su7BPYd1xPB7PmrcgCJAkCZIkQRRFmM/n4ioABIZa6HGhanc7xUxkcpfhsQqEDVye5yiKAqfTSWYcnuchiiKEYSjB0zAMiT/6DIVGEHy9moF4Dq9RycVAdBCquxDGfr+XzJLnOcqylEKLsYPK4ALbthUoVJM64yAA13WlzKeiVDDv5jJj2YXplk1cnudSlbI8930fvu/LkKdpGgnI/Iymac4qWYJwHOdMVSzaCOVdgdCGYZBUy9rjeDwiTVNkWSbPEUgQBIiiCLZtC4iu66RwY3lP1XmeB8uypHKNogie58EwjDOVMGDznH4XzOQKoTo4AMrzHGmaygIpd1alnHpVVYWu62RotN/vkWWZdMJc0Gw2g+M4qKoKvu+Le7muCwByPxZs3wyIPkdl/FDVURQF6rqGbduSVjkNG4ZB5iNPT0/Y7XYChK7D2QgLtrquEQQBLMtC13WYzWYA/nE5AKI4uuKbAtFhMLswblD2TdPAtm25maaJ0+kkwZbDov1+L+/hZ9NVmIHyPEff9wiCAIZhIAxDgfPcrPVNgfDE1YBKGCzVm6YRyXNxBEIQVAeDKV/b970Ua6xfCIZgbdsWNemjiHeJIXpDp847mD0AyFWu6xpVVaHveynr8zxH27awbRuO40h61rtdumVVVXBdV9L02LDqXWOI3sNwGNQ0zVkdQdfi84fDAYfDQeoOx3GkpPc87wwEM5lhGOKerFXUSfxrbPKpO1XCEyUcdVeOV7coCnkdXYJ1RRAEAsO2bRk+Mxbxc9TdvSnmq1fpZXi12NwRhj4SqKpKUjSnZSzU4jhGGIYSfNM0lZRMGLq9NEX7HZsUiH5l1KaMV5euAEBSomma8H0fpmlK28/ehgrj6JH1DFMu07gaa1i5qjPX37WrjBD1uYTa/TKuMHboI4AwDLFYLGRIpAbQsixl/5ewGXwJYmzM+C5pV/VhXjU1xXZdhzRN5YonSQLDMKSfse1/TuV0OiHLMhyPRwzDIDUKaxMOmF3XRRiGiOMYSZKcTdn0zvdPbBIg6pWgjNUrx73Yuq5FMYTGnX01GA/DIAra7XbIsgxpmqIsS0RRBNd1pVPmzFUdN14yiJ5UIZZlSabgBCzPc4RhKBvYeZ7jcDjIIheLBZbLJVzXhed5kq3oVizq+NMHutR2u8X9/T3u7+9lGD02nee5vSkQPe2xoOLVo+sMwyDFFLMQF+55Hnzfl4zExo6PV6uVqIIQkyRBGIbiKr/as3lTIITCknk+n6Pve3z69AkAcDgcYJomdrsdnp6epK3nlgRdSx0m8ziOY6xWKzw+PiJJEnz9+hUfPnzAly9fEMfx2RxW/YXAu9Uh+m6ZrpDVaoXVaoU8z7Fer1FVFUzTRNM0stHN93FBtm3LIj3PE0Xc3d1hu91iu91iuVxK8abCvGRaNgkQHQYA+ZXPMAwyDdtsNoiiCN++fcPDwwOenp7w/ft36XsIg7t22+0Wi8UCHz9+xHq9xufPn7HZbHB/f48wDM+Cq/4DvNfCmAyIOojhlabrAMB6vQYACY593yMMQ7iue7Y/Y9s2kiQRNSRJgsfHR2w2Gzw8PCCOY8RxLOpRd/OmgAEAxgtN0B91SGo/w+qUP6Gqqkom72ptwR09LohuwIUvFgvJWuruvwoCeNWW5ugLJwUC/Nz5qr0NN7u5jclU3DSNZAS6AWsLNntqjaH+FOICVbwNEHmjNlbU91dYiKmvBc4r3rFjPZVe4B5vC+TsQ7TplX48dg6/6lgn2ul/PyA/fegfDm+u8TsQPAPkTf8bgnalBU5it/+X0ewGRLMbEM1uQDS7AdHsBkSzl9Lu35sfr2Q3hWh2A6LZDYhmNyCa3YBodgOi2f8AB/Frf08MJSUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hel27ng0Ao_P"
      },
      "source": [
        "According to this dataset, these are the ideal images for each of the digits"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "an-Fs1vpAo_P"
      },
      "source": [
        "Let's now pick an arbitrary 3 and measure its *distance* from our \"ideal digits.\"\n",
        "\n",
        "> **Stop and Think!**: How would you calculate how similar a particular image is to each of our ideal digits? Remember to step away from this book and jot down some ideas before you move on! Research shows that recall and understanding improves dramatically when you are engaged with the learning process by solving problems, experimenting, and trying new ideas yourself"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VTy3L40JsL0g"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lp5ha0ANCoSr"
      },
      "source": [
        "Here's a sample image of one digit:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ICZFvZHHAo_P",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "1876d39f-7d55-48df-e3fd-581fae1d0fcd"
      },
      "source": [
        "selected_digit = 3\n",
        "img = stacked_tensors_dict[selected_digit][2]\n",
        "show_image(img);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ypkq4CqSAo_P"
      },
      "source": [
        "Let's compare again our Mean Absolute Error (MAE) and Mean Square Error (MSE)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UTs8ufStAo_Q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3dd2452a-75b8-4526-dcbb-c87a5547e56a"
      },
      "source": [
        "dist_3_mae = (img - means_dict[3]).abs().mean()\n",
        "dist_3_mse = ((img - means_dict[3])**2).mean().sqrt()\n",
        "dist_3_mae, dist_3_mse"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.1100), tensor(0.1980))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xt4MbXJ-Ao_Q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5569a7ad-4547-4b2b-de71-c9eb26053553"
      },
      "source": [
        "dist_7_mae = (img - means_dict[7]).abs().mean()\n",
        "dist_7_mse = ((img - means_dict[7])**2).mean().sqrt()\n",
        "dist_7_mae, dist_7_mse"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.1541), tensor(0.2974))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6quCmrdveh5n"
      },
      "source": [
        "Let's visualize what these distances mean:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 379
        },
        "id": "KXN1-_VDRT_G",
        "outputId": "9d63bb49-98dc-436d-a3fc-8464cf9357d1"
      },
      "source": [
        "digit = 4\n",
        "img = stacked_tensors_dict[digit][10]\n",
        "\n",
        "fig, axs = plt.subplots(nrows=1, ncols=11, figsize=(18,5))\n",
        "for i in range(10):\n",
        "    show_image(means_dict[i], title=f\"Mean {i}\", ax=axs[i+1])\n",
        "show_image(img, title='Image to compare', ax=axs[0])\n",
        "plt.show()\n",
        "\n",
        "print('\\nSimple Difference:')\n",
        "fig, axs = plt.subplots(nrows=1, ncols=11, figsize=(18,5))\n",
        "for i in range(10):\n",
        "    show_image((img - means_dict[i]), title=f'with {i}', ax=axs[i+1])\n",
        "show_image(img, title='Image to compare', ax=axs[0])\n",
        "plt.show()\n",
        "\n",
        "print('\\nMAE - Mean Absolute Error:')\n",
        "fig, axs = plt.subplots(nrows=1, ncols=11, figsize=(18,5))\n",
        "for i in range(10):\n",
        "    show_image((img - means_dict[i]).abs(), title=f'with {i}', ax=axs[i+1])\n",
        "show_image(img, title='Image to compare', ax=axs[0])\n",
        "plt.show()\n",
        "\n",
        "print('\\nMSE - Mean Squared Error:')\n",
        "fig, axs = plt.subplots(nrows=1, ncols=11, figsize=(18,5))\n",
        "for i in range(10):\n",
        "    show_image((img - means_dict[i]).square(), title=f'with {i}', ax=axs[i+1])\n",
        "show_image(img, title='Image to compare', ax=axs[0])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1296x360 with 11 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Simple Difference:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1296x360 with 11 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "MAE - Mean Absolute Error:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1296x360 with 11 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "MSE - Mean Squared Error:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1296x360 with 11 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KhRFcuqwAo_Q"
      },
      "source": [
        "PyTorch already provides both of these as *loss functions*. You'll find these inside `torch.nn.functional`, which the PyTorch team recommends importing as `F` (and is available by default under that name in fastai):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E2aPZy-3Ao_Q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "977adaba-6da0-41aa-ce58-c67dead68e48"
      },
      "source": [
        "F.l1_loss(img.float(),means_dict[7]), F.mse_loss(img, means_dict[7]).sqrt()  "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.1161), tensor(0.2299))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Av_zS0apAo_R"
      },
      "source": [
        "Here `mse` stands for *mean squared error*, and `l1` refers to the standard mathematical jargon for *mean absolute value* (in math it's called the *L1 norm*)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "72-jn9W-Ao_Y"
      },
      "source": [
        "So, is our baseline model any good? To quantify this, we must define a metric."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_hE2D-d4Ao_Y"
      },
      "source": [
        "c over a *validation set*. This is so that we don't inadvertently overfit—that is, train a model to work well only on our training data. This is not really a risk with the pixel similarity model we're using here as a first try, since it has no trained components, but we'll use a validation set anyway to follow normal practices and to be ready for our second try later.\n",
        "\n",
        "To get a validation set we need to remove some of the data from training entirely, so it is not seen by the model at all. As it turns out, the creators of the MNIST dataset have already done this for us. Do you remember how there was a whole separate directory called *valid*? That's what this directory is for!\n",
        "\n",
        "So to start with, let's create tensors for our 3s and 7s from that directory. These are the tensors we will use to calculate a metric measuring the quality of our first-try model, which measures distance from an ideal image:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KJVX90_NHIui"
      },
      "source": [
        "### Create validation set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5S4A7eEjAo_Z",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cdad8a0c-6e18-413c-e956-25c8fc3013d5"
      },
      "source": [
        "valid_tensors_dict = {}\n",
        "\n",
        "for digit, tnrs in stacked_tensors_dict.items():\n",
        "    valid_tensors_dict[digit] = torch.stack([tensor(Image.open(o)) \n",
        "                                             for o in (path/'testing'/f\"{digit}\").ls()])\n",
        "    valid_tensors_dict[digit] = valid_tensors_dict[digit].float()/255\n",
        "    print('shape for',digit, ':', valid_tensors_dict[digit].shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "shape for 0 : torch.Size([980, 28, 28])\n",
            "shape for 1 : torch.Size([1135, 28, 28])\n",
            "shape for 2 : torch.Size([1032, 28, 28])\n",
            "shape for 3 : torch.Size([1010, 28, 28])\n",
            "shape for 4 : torch.Size([982, 28, 28])\n",
            "shape for 5 : torch.Size([892, 28, 28])\n",
            "shape for 6 : torch.Size([958, 28, 28])\n",
            "shape for 7 : torch.Size([1028, 28, 28])\n",
            "shape for 8 : torch.Size([974, 28, 28])\n",
            "shape for 9 : torch.Size([1009, 28, 28])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QQylH3NjHWcs"
      },
      "source": [
        "It's good to get in the habit of checking shapes as you go. Here we see 10 tensors, each representing one digit validation set of about 1,000 images of size 28×28. Total number of validation images is 10,000."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RzgqkBhoHXET",
        "outputId": "0ac0b275-d688-493f-f876-99de9180159c"
      },
      "source": [
        "print('Shapes of image tensor for each digit:')\n",
        "for digit, tnrs in valid_tensors_dict.items():\n",
        "    print(' shape for',digit, ':', valid_tensors_dict[digit].shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shapes of image tensor for each digit:\n",
            " shape for 0 : torch.Size([980, 28, 28])\n",
            " shape for 1 : torch.Size([1135, 28, 28])\n",
            " shape for 2 : torch.Size([1032, 28, 28])\n",
            " shape for 3 : torch.Size([1010, 28, 28])\n",
            " shape for 4 : torch.Size([982, 28, 28])\n",
            " shape for 5 : torch.Size([892, 28, 28])\n",
            " shape for 6 : torch.Size([958, 28, 28])\n",
            " shape for 7 : torch.Size([1028, 28, 28])\n",
            " shape for 8 : torch.Size([974, 28, 28])\n",
            " shape for 9 : torch.Size([1009, 28, 28])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Nt2VHIgKQqq"
      },
      "source": [
        "### Loss - Metric"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UMxFeeiwAo_Z"
      },
      "source": [
        "We ultimately want to write a function, `evaluate_digit()`, that will return the most probable digit for one inage we pass to the function.\n",
        "\n",
        "**STOP AND THINK**:\n",
        "\n",
        "- How would you extrapolate the approach for used in the sample MNIST case, when we only had two digits? \n",
        "- In this casem you cannot use the same method because we have more than two digits this time. \n",
        "- A function `is_3` as `True` or `False` is not enough. \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tk1bac__Lthw"
      },
      "source": [
        "Hint for one possible solution: \n",
        "- compare the distances between one image and each of the mean images, then assume that the image corresponds to the digit with the smallest distance."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5F0iV2cFUxc-"
      },
      "source": [
        "Code for this approach:\n",
        "\n",
        "1. We keep the same distance as before, that is MAE:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3ViXqzG1Ao_Z",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 236
        },
        "outputId": "b3b641b9-0256-47ed-a48c-0683f8ce25d1"
      },
      "source": [
        "def mnist_distance(a, b): \n",
        "    return (a - b).abs().mean((-1, -2))\n",
        "\n",
        "mnist_distance(img, means_dict[7])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-6-91d44ba7718d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mmnist_distance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmeans_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m: name 'img' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kXZl2iB5O72Q"
      },
      "source": [
        "2. We compute the distance to each digit mean"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "F8mgpjNbPA0g",
        "outputId": "0d800f11-b77d-4898-d892-a10dea79c2ad"
      },
      "source": [
        "# Select an image to compate\n",
        "img_tnsr = valid_tensors_dict[8][559]\n",
        "show_image(img_tnsr)\n",
        "plt.show()\n",
        "\n",
        "for i in range(10):\n",
        "    print(f\"Distance between image and {i} is {mnist_distance(img_tnsr, means_dict[i])} \")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-5-67e9e72fa799>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Select an image to compate\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mimg_tnsr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalid_tensors_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m559\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mshow_image\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg_tnsr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'valid_tensors_dict' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "reRtNDT8PbXg"
      },
      "source": [
        "The smallest distance should represent the correct digit. In this case it is correct."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YXj4B1VyPia6"
      },
      "source": [
        "With broadcasting, we also can apply the distance to all the images of one class/digit at the same time. `mnist_distance` should return a tensor with the distances for all the images in the batch."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "hYjPk8OEJP6R",
        "outputId": "70874e0b-e743-46c0-a679-82cde688d0e3"
      },
      "source": [
        "# Select a batch with all the images representing one digit\n",
        "img_tnsr = stacked_tensors_dict[8]\n",
        "\n",
        "distances = mnist_distance(img_tnsr, means_dict[7])\n",
        "display(distances.shape)\n",
        "display(distances)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-4-65b112a80dbf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Select a batch with all the images representing one digit\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mimg_tnsr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstacked_tensors_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mdistances\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmnist_distance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg_tnsr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmeans_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'stacked_tensors_dict' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "5jfV1_NGKFf5",
        "outputId": "91eff4f0-8d99-4a30-ee35-9f8787da09b5"
      },
      "source": [
        "# Show distances to all the digits\n",
        "img_tnsr = stacked_tensors_dict[8]\n",
        "\n",
        "for i in range(10):\n",
        "    display(mnist_distance(img_tnsr, means_dict[i]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-3-12c9f31be37b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Show distances to all the digits\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mimg_tnsr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstacked_tensors_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmnist_distance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg_tnsr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmeans_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'stacked_tensors_dict' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KbYXojz7Pvn_"
      },
      "source": [
        "Let's see how are can compute all the distances from one image tensor batch to each of the digit means in a few operations only. \n",
        "\n",
        "1. Let's see what we have to start with:\n",
        "    - we start from a batch of image tensors `image_tensor_batch` of shape `(nbr_img, 28, 28)`\n",
        "    - `mnist_distance(image_tensor_batch)` returns a tensor of shape `(nbr_img)`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "1fwOHGVDQ4WI",
        "outputId": "e280eb2e-64de-4f35-a1ea-aa56e2ca2b30"
      },
      "source": [
        "img_batch_tnsr = stacked_tensors_dict[8]\n",
        "print('Shape of batch_tnsr:', img_batch_tnsr.shape)\n",
        "\n",
        "distances = mnist_distance(img_tnsr, means_dict[0])\n",
        "print('Shape of distances: ', distances.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-2-838fc8bdfa28>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mimg_batch_tnsr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstacked_tensors_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Shape of batch_tnsr:'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mimg_batch_tnsr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mdistances\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmnist_distance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg_tnsr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmeans_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Shape of distances: '\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdistances\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'stacked_tensors_dict' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w3UXMvExSBJB"
      },
      "source": [
        "2. Now we want to have all distances for all digits in a dimension-2 tensor of shape `(nbr of images, 10)`. That is a tensor with the same number of samples/images as the batch and a distance to each digit. Using tensors instead of list or other data sructure will allow us to use fast tensor calculation to easily extract which digit corresponds to each image, as opposed to slow Python loop through all the images in Python. One way to do it:\n",
        "    - use the `torch.stack` function to stack the distances tensors for each of the digits into one single tensor"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 253
        },
        "id": "9KvjgyhRMlp_",
        "outputId": "21918318-2d06-44f4-8afa-c69f586883ed"
      },
      "source": [
        "distances = torch.stack([mnist_distance(img_tnsr, m) for m in means_dict.values()], dim=1)\n",
        "display(distances)\n",
        "distances.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-1-8e72dcefce00>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdistances\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmnist_distance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg_tnsr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mm\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mmeans_dict\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mdistances\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'torch' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MSxvds2rVZyB"
      },
      "source": [
        "\"decrypting\" code above: `torch.stack([mnist_distance(img_tnsr, m) for m in means_dict.values()], dim=1)`\n",
        "- Signature of stack: `torch.stack(tensors, dim=0)` [doc](https://pytorch.org/docs/stable/generated/torch.stack.html):\n",
        "    - `tensors` is a sequence of tensors to concatenate, for instance a list of tensors\n",
        "    - `dim` is the dimension to insert. Has to be between 0 and the number of dimensions of concatenated, In our case, `dim` is 1 as we want to stack the 10 values for each images. You can try other values and see what it gives.\n",
        "- `[mnist_distance(img_tnsr, m) for m in means_dict.values()]`:\n",
        "    - list comprehension to get a list of the 10 distances, one for each digit. Remember that means_dict keeps the ten mean images reporesenting the \"ideal\" difit. The list comprehension is equivalent to:\n",
        "    ```python\n",
        "        tensor_list = []\n",
        "        for mean in means_dict.values():\n",
        "            tensor_list.append(mnist_distance(img_tnsr, m))\n",
        "    ```\n",
        "\n",
        "The code is passing a list of 10 dimension-1 tensors (shape = `(number of images in the batch)`) to `torch.stack`, to create a dimension-2 tensor of shape `(number of images in the batch, 10)`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8uWfanTIVsdJ"
      },
      "source": [
        "Now we have a tensor `distances` with the distance of each image to the ten means. We can index it to get the distances of any image to the ten means."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "id": "wS5chZmwVxOo",
        "outputId": "aeb93f17-96ea-4341-bce1-dc467f66f2c2"
      },
      "source": [
        "distances[120:125, :]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-2-7d0f539f5047>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdistances\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m120\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m125\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m: name 'distances' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SnP8007KXcMA"
      },
      "source": [
        "3. Select the class/digit for each image in the batch: pick the minimum distance. We will use the method tensor `argmin()` to pick the index with minimum distance, which is the digit corresponding to the minumum distance and therefore our class as we defined it in our approach.\n",
        "\n",
        "> See how `argmin` works with a single image. We pick one image tensor and show it. We also pick the corresponding distances to the ten digit, i.e. a tensor of shape (10). `argmin()` returns the index of the minimum distance, in this case 8, which corresponds to digit 8."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 120
        },
        "id": "PVB0WQHLYlk2",
        "outputId": "33a5fde7-ded6-4c4c-fdd0-439f8f1569a1"
      },
      "source": [
        "img_nbr = 25\n",
        "show_image(stacked_tensors_dict[8][img_nbr])\n",
        "plt.show()\n",
        "\n",
        "distances_for_one_img = distances[img_nbr]\n",
        "display(distances_for_one_img)\n",
        "distances_for_one_img.argmin()\n",
        "distances_for_one_img[8]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "tensor([0.1650, 0.1222, 0.1467, 0.1261, 0.1344, 0.1259, 0.1477, 0.1398, 0.1143, 0.1293])"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.1143)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yKEouuQ1agEO"
      },
      "source": [
        "When we apply to a batch of images, we need to tell pytorch along which direction the minimum must be seeked. In our case `dim=1`.  It returns a tensor of dimension 1, with shape = `(nbr_img)`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TGU_rT7JOibR",
        "outputId": "2030de31-f176-4a95-ef1e-66f88f8ee961"
      },
      "source": [
        "digits = distances.argmin(dim=1)\n",
        "digits.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5851])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-O79XYgwjmlx"
      },
      "source": [
        "```\n",
        "argmin(input, dim, keepdim=False) -> LongTensor\n",
        "\n",
        "Returns the indices of the minimum values of a tensor across a dimension.\n",
        "\n",
        "This is the second value returned by :meth:`torch.min`. See its\n",
        "documentation for the exact semantics of this method.\n",
        "\n",
        "Args:\n",
        "    input (Tensor): the input tensor.\n",
        "    dim (int): the dimension to reduce. If ``None``, the argmin of the flattened input is returned.\n",
        "    keepdim (bool): whether the output tensor has :attr:`dim` retained or not. Ignored if ``dim=None``.\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EVrnf9mra5xt"
      },
      "source": [
        "Using `argmin()` allows us to compute the mimimun for all images, in one step, and with no Python loop."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LLsY0kBWj1me"
      },
      "source": [
        "### Pixel Similarity Classifier"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zc4xy7bbX8Ad"
      },
      "source": [
        "Now we can build our classifier as a function `evaluate_digit` to which we pass an image tensor or a batch of image tensors and which will return a class/digit"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yP_X__waAo_a"
      },
      "source": [
        "def evaluate_digit(x): \n",
        "    if x.ndim < 3:\n",
        "        x = x.unsqueeze(dim=0)\n",
        "    distances = torch.stack([mnist_distance(x, m) for m in means_dict.values()], dim=1)\n",
        "    return distances.argmin(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jr2RPxqlbYLF"
      },
      "source": [
        ">Note: we unsqueeze the tensor when a single image is given instead of a batch, because we expect a batch. Unsqueezing is like translforming a single image into a batch with a single image:\n",
        "```python\n",
        "    if x.ndim < 3:\n",
        "        x = x.unsqueeze(dim=0)\n",
        "```\n",
        "\n",
        "See the difference below"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jWWpkaZlbuF5",
        "outputId": "e11e6f04-1a3a-44c3-9f3d-4213a70b80bc"
      },
      "source": [
        "img.shape, img.unsqueeze(dim=0).shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([28, 28]), torch.Size([1, 28, 28]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CLmCNNLXcFFO"
      },
      "source": [
        "Let's test our classifier with a single image:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vCTbUcKLYVRD"
      },
      "source": [
        "tnsr = stacked_tensors_dict[8][58]\n",
        "show_image(tnsr)\n",
        "plt.show()\n",
        "\n",
        "evaluate_digit(tnsr)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p4JMkpShcWat"
      },
      "source": [
        "Let's test our classifier with a small image batch:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R222MSdca9UA",
        "outputId": "48f5564d-9ca7-4669-d1dc-1e90b2336fc4"
      },
      "source": [
        "tnsr = stacked_tensors_dict[8][58:87]\n",
        "print('Nbr images: ', tnsr.shape[0])\n",
        "\n",
        "evaluate_digit(tnsr)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Nbr images:  29\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([8, 8, 1, 1, 9, 1, 8, 9, 1, 8, 1, 1, 8, 8, 1, 9, 9, 9, 1, 8, 3, 8, 1, 1, 8, 1, 8, 1, 8])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kJUtTINZbs_q"
      },
      "source": [
        "We can see that the model is not that great ! Some images are correctly evaluated and some are not."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_a0JkHtpbV4h"
      },
      "source": [
        "### Evaluation of the classifier\n",
        "Let's compute the accuracy for the train and the validation set for each class/digit\n",
        "1. For each class, we evaluate the digit for the full dataset (training and validation)\n",
        "2. We compute how many are correct and how many are not correct"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zdkODv0fcGOa",
        "outputId": "d3c226ae-0e8b-42bb-bcb2-6f1a3b1285d0"
      },
      "source": [
        "# One class at the time\n",
        "digit = 5\n",
        "tnsr = stacked_tensors_dict[digit]\n",
        "preds = evaluate_digit(tnsr) \n",
        "correct = torch.eq(preds, digit).sum()\n",
        "incorrect = torch.ne(preds, digit).sum()\n",
        "correct.item(), incorrect.item(), (correct / preds.shape[0]).item()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1627, 3794, 0.30012911558151245)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zm5e38QUAo_b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e895227d-b7c3-495f-a69d-7b4c3dea9340"
      },
      "source": [
        "# All digits for training set\n",
        "for digit in range(10):\n",
        "    tnsr = stacked_tensors_dict[digit]\n",
        "    preds = evaluate_digit(tnsr) \n",
        "    correct = torch.eq(preds, digit).sum()\n",
        "    # print(f\" - {correct.item():,d} correct digits out or {preds.shape[0]}\")\n",
        "    print(f\"Accuracy for {digit}: {(correct / preds.shape[0]).item():1.4f}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy for 0: 0.8141\n",
            "Accuracy for 1: 0.9981\n",
            "Accuracy for 2: 0.4329\n",
            "Accuracy for 3: 0.5836\n",
            "Accuracy for 4: 0.6648\n",
            "Accuracy for 5: 0.3001\n",
            "Accuracy for 6: 0.7454\n",
            "Accuracy for 7: 0.7778\n",
            "Accuracy for 8: 0.3958\n",
            "Accuracy for 9: 0.7163\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IR9gSAyWgDRb",
        "outputId": "545e2876-3144-48ef-e2ad-13af6cb6db38"
      },
      "source": [
        "# All digits for validation set\n",
        "for digit in range(10):\n",
        "    tnsr = valid_tensors_dict[digit]\n",
        "    preds = evaluate_digit(tnsr) \n",
        "    correct = torch.eq(preds, digit).sum()\n",
        "    # print(f\" - {correct.item():,d} correct digits out or {preds.shape[0]}\")\n",
        "    print(f\"Accuracy for {digit}: {(correct / preds.shape[0]).item():1.4f}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy for 0: 0.8153\n",
            "Accuracy for 1: 0.9982\n",
            "Accuracy for 2: 0.4234\n",
            "Accuracy for 3: 0.6089\n",
            "Accuracy for 4: 0.6680\n",
            "Accuracy for 5: 0.3262\n",
            "Accuracy for 6: 0.7871\n",
            "Accuracy for 7: 0.7646\n",
            "Accuracy for 8: 0.4425\n",
            "Accuracy for 9: 0.7760\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Wl3rqr3Ao_c"
      },
      "source": [
        "Although this is not awfull, the performance varies a lot for each of the digit. 0 and 1 are well classified byt 5 and 8 are not, for example.\n",
        "\n",
        "Can we do better if we use another metric? We uses MAE, let's do the same but using RMSE:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zSqPZmeYLCqC"
      },
      "source": [
        "# Define a new loss/distance function: mnist_rmse\n",
        "def mnist_rmse(a, b):\n",
        "    return ((a - b) ** 2 ).mean((-1, -2)).sqrt()\n",
        "\n",
        "# Our new classifier will use rmse to compute the distances and pick the minimum\n",
        "def evaluate_digit_rmse(x): \n",
        "    if x.ndim < 3:\n",
        "        x = x.unsqueeze(dim=0)\n",
        "    distances = torch.stack([mnist_rmse(x, m) for m in means_dict.values()], dim=1)\n",
        "    return distances.argmin(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zZ--Vx6wNEp5"
      },
      "source": [
        "Now we can evaluate the performance of this new classifer with the validation set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZxAezLXGMTix",
        "outputId": "17890b47-8ec2-4173-d8d7-70863886cd08"
      },
      "source": [
        "# All digits for validation set\n",
        "for digit in range(10):\n",
        "    tnsr = valid_tensors_dict[digit]\n",
        "    preds = evaluate_digit_rmse(tnsr) \n",
        "    correct = torch.eq(preds, digit).sum()\n",
        "    # print(f\" - {correct.item():,d} correct digits out or {preds.shape[0]}\")\n",
        "    print(f\"Accuracy for {digit}: {(correct / preds.shape[0]).item():1.4f}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy for 0: 0.8959\n",
            "Accuracy for 1: 0.9621\n",
            "Accuracy for 2: 0.7568\n",
            "Accuracy for 3: 0.8059\n",
            "Accuracy for 4: 0.8259\n",
            "Accuracy for 5: 0.6861\n",
            "Accuracy for 6: 0.8633\n",
            "Accuracy for 7: 0.8327\n",
            "Accuracy for 8: 0.7372\n",
            "Accuracy for 9: 0.8067\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tCc7STRUNQz3"
      },
      "source": [
        "We see that the accuracy increases for almost all the digits. \n",
        "\n",
        "The base line is not bad, but all in all, it still shows some relativaly low accuracy compared to real model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0VpRly6QAo_c"
      },
      "source": [
        "## Stochastic Gradient Descent (SGD)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 124
        },
        "id": "OzVuXe_E-GtE",
        "outputId": "ef97e9bf-4c04-439a-aeca-3d26915ef5a2"
      },
      "source": [
        "gv('''\n",
        "\"1. init\"->\"2. predict\"->\"3. loss\"->\"4. gradient\"->\"5. step\"->\"7. stop\"\n",
        "\"5. step\"->\"2. predict\"[label=\"6. repeat\"]\n",
        "''')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kAlUoNRzOafQ"
      },
      "source": [
        "Steps that we are going to require, to turn a function into a machine learning classifier:\n",
        "\n",
        "1. *Initialize* the weights.\n",
        "1. For each image, use these weights to *predict* whether it appears to be a 3 or a 7.\n",
        "1. Based on these predictions, calculate how good the model is (its *loss*).\n",
        "1. Calculate the *gradient*, which measures for each weight, how changing that weight would change the loss\n",
        "1. *Step* (that is, change) all the weights based on that calculation.\n",
        "1. Go back to the step 2, and *repeat* the process.\n",
        "1. Iterate until you decide to *stop* the training process (for instance, because the model is good enough or you don't want to wait any longer)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e75BvXjsQW2X"
      },
      "source": [
        "#### Prepare datasets and dataloaders"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9bxXKzVvQ952"
      },
      "source": [
        "`train_x` is the set of independant variables (inputs), that is our images. We create  `train_x` tensor by concatenating all the tensors for each digit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7eVXaIMnQ954"
      },
      "source": [
        "train_x = torch.cat([stacked_tensors_dict[i] for i in range(0,10)]).view(-1, 28*28)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kENaWxHARETG",
        "outputId": "59884970-e266-47fd-f0af-ead75befa778"
      },
      "source": [
        "train_x.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([60000, 784])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AbuZLyURQ955"
      },
      "source": [
        "As expected, it is a set of 60,000 images represented as a flat one dimension vector of shape 28 x 28 = 784"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8U3evtmMQ957"
      },
      "source": [
        "We need a label for each image, 0 to 9, depending on the digit the image represent. It is not as simple as for the basic MNIST case, as we have more than two classes and the number of images in each class is not equal. There is probably an easier way than the one below !"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IImhF4RwQ958"
      },
      "source": [
        "# Returns a list of 10 sublists, where each sublist consists of as many times digit as the number of image in the category\n",
        "l = [ [i] * stacked_tensors_dict[i].shape[0] for i in range(0,10)]\n",
        "\n",
        "# check the the total number of labels is equal to the numer of images\n",
        "assert sum([len(sublist) for sublist in l]) == train_x.shape[0] "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_CgSzj67Q959",
        "outputId": "9e68e680-ce14-4fdc-8882-4adee0cd0e0c"
      },
      "source": [
        "# Create a tensor based on the list of labels\n",
        "label_list = []\n",
        "for i in range(10):\n",
        "    label_list.extend(l[i])\n",
        "assert len(label_list) == train_x.shape[0]\n",
        "\n",
        "train_y = torch.tensor(label_list).unsqueeze(1)\n",
        "train_x.shape,train_y.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([60000, 784]), torch.Size([60000, 1]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JVwaZsHSRrnS"
      },
      "source": [
        "The shapes of `train_x` and `train_y` are as expected"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "67Prd18yQ95_"
      },
      "source": [
        "A `Dataset` in PyTorch is required to return a tuple of `(x,y)` when indexed. Python provides a `zip` function which, when combined with `list`, provides a simple way to get this functionality:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hnmy7VORQ96A",
        "outputId": "f9a9283c-4db6-4572-dd6c-fac5ae7a4fc6"
      },
      "source": [
        "from random import shuffle\n",
        "\n",
        "dset = list(zip(train_x,train_y))\n",
        "\n",
        "# Shuffle the dset so that digits are mixed\n",
        "shuffle(dset)\n",
        "\n",
        "\n",
        "x, y = dset[0]\n",
        "x.shape,y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784]), tensor([5]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bgyrNSXsBcyH"
      },
      "source": [
        "Now we do the same for the validation sets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QJmLpADmQ96A",
        "outputId": "7609ef34-4fb3-40bd-8d3a-6506c24b523b"
      },
      "source": [
        "valid_x = torch.cat([valid_tensors_dict[i] for i in range(0,10)]).view(-1, 28*28)\n",
        "\n",
        "# Returns a list of 10 sublists, where each sublist consists of a as many times digit as the number of image in the category\n",
        "l = [ [i] * valid_tensors_dict[i].shape[0] for i in range(0,10)]\n",
        "\n",
        "# check the the total number of labels is equal to the numer of images\n",
        "assert sum([len(sublist) for sublist in l]) == valid_x.shape[0] \n",
        "print(valid_x.shape)\n",
        "\n",
        "# Create a tensor based on the list of labels\n",
        "label_list = []\n",
        "for i in range(10):\n",
        "    label_list.extend(l[i])\n",
        "assert len(label_list) == valid_x.shape[0]\n",
        "\n",
        "valid_y = torch.tensor(label_list).unsqueeze(1)\n",
        "print(valid_y.shape)\n",
        "\n",
        "valid_dset = list(zip(valid_x,valid_y))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([10000, 784])\n",
            "torch.Size([10000, 1])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lo1sINyOQ96A"
      },
      "source": [
        "Datasets are ready. Now we prepare the dataloaders to feed the training loop."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ppJHdq70Yxb2"
      },
      "source": [
        "dl = DataLoader(dset, batch_size=256)\n",
        "valid_dl = DataLoader(valid_dset, batch_size=5)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hAj5qWL1Ao_k"
      },
      "source": [
        "#### Define the model architecture and parameters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U3_b3NRtDZFl"
      },
      "source": [
        "Model is defined by creating functions to compute each of the 7 steps listed above"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p--DimUkCqhc"
      },
      "source": [
        "##### Parameters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zpK6kbbRSOMp"
      },
      "source": [
        "In our model, we need to evaluate the distance from one image (input) to each of the possible classes (0 - 9). So we need to predict 10 values, out of which we will pick the minimum value to predict the correpsonding digit.\n",
        "\n",
        "In effect,**y** in **y=Wx+b** represents the `distances` between the image **x** and each of the digits. **y** is therefore a vector of shape `(10)`. The prediction is computed from an image **x** which is a vector of shape `(784)`. Therefore **W** must be of shape `(784, 10)`. And **b** must be of the same shape as the output, that is shape `(10)`.\n",
        "\n",
        "<img src=\"https://raw.githubusercontent.com/vtecftwy/fastbook/master/images/img_mnist_full_linear_layer.png\" height=\"400px\" />\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LzhbtgMGCVJS"
      },
      "source": [
        "Define a function to create random parameters, and then create **W** and **b** with the correct shapes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Qn2XEth3Qs2X",
        "outputId": "57ddd64d-96dd-4790-9585-3778f39f78ce"
      },
      "source": [
        "def init_params(size, std=1.0): \n",
        "    return (torch.randn(size)*std).requires_grad_()\n",
        "\n",
        "weights = init_params((28*28, 10))\n",
        "bias = init_params(10)\n",
        "\n",
        "weights.shape, bias.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784, 10]), torch.Size([10]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G6Ybt963Ao_l"
      },
      "source": [
        "##### Define functions to calculate the predictions. \n",
        "\n",
        "The output of the linear layer is a distance. If we apply `softmax`, we get a sort of probability (sum of values = 1), which is what we want. Also, we can use `softmax` or `log_sofmax`. But it is useful to use `log_softmax` for several reasons, including the fact that larger errors are more penalized then small errors and the fact that it allows some computation stability in the network (see [here](https://deepdatascience.wordpress.com/2020/02/27/log-softmax-vs-softmax/)). \n",
        "\n",
        "See pytorch documentation: [`softmax`](https://pytorch.org/docs/stable/nn.functional.html?highlight=softmax#softmax) and [`log_softmax`](https://pytorch.org/docs/stable/generated/torch.nn.LogSoftmax.html?highlight=softmax#logsoftmax)\n",
        "\n",
        "Note: **`torch.nn.functional`** can be shorted as **`F`**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g_xOqHw_Tioi"
      },
      "source": [
        "def linear(xb):\n",
        "    outputs =  xb @ weights + bias\n",
        "    probs = F.log_softmax(outputs, dim=1)\n",
        "    return probs\n",
        "\n",
        "def evaluate_preds(xb):\n",
        "    probs = linear(xb)\n",
        "    return probs.argmax(dim=1).unsqueeze(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0HHF3tn7Ao_m"
      },
      "source": [
        "##### Define a function to calculate the loss\n",
        "\n",
        "As we have 10 classes, the loss function should be **cross entropy**. In PyTorch, there is a function `cross_entropy` ([`doc`](https://pytorch.org/docs/stable/nn.functional.html#cross-entropy)) and a layer `CrossEntropyLoss`([`doc`](https://pytorch.org/docs/stable/nn.functional.html#cross-entropy)). It happens to be a combination of `log_softmax` ([`doc`](https://pytorch.org/docs/stable/nn.functional.html#log-softmax)), which we have applied already in the linear layer, and `nll_loss` ([`doc`](https://pytorch.org/docs/stable/nn.functional.html#nll-loss)). `nll_loss` stands for *negative log likelihood loss*\n",
        "\n",
        "So, let's apply `nll_loss` to the output of linear layer.\n",
        "\n",
        "More on negative log likelihood loss [here](https://medium.com/deeplearningmadeeasy/negative-log-likelihood-6bd79b55d8b6) and cross entropy [here](https://machinelearningmastery.com/cross-entropy-for-machine-learning/)\n",
        "\n",
        "Other links: \n",
        "- https://glassboxmedicine.com/2019/12/07/connections-log-likelihood-cross-entropy-kl-divergence-logistic-regression-and-neural-networks/\n",
        "- https://gombru.github.io/2018/05/23/cross_entropy_loss/"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ww5kD8caAo_k"
      },
      "source": [
        "loss_fct = F.nll_loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xQLwzJCBAo_n"
      },
      "source": [
        "##### Define a function to calculate the gradients"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ILZAptP-ZP9O"
      },
      "source": [
        "def calc_grad(xb, yb, model):\n",
        "    preds = model(xb)\n",
        "    loss = loss_fct(preds, yb.squeeze())\n",
        "    # print(loss)\n",
        "    loss.backward()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cv3lJG7cQB1v"
      },
      "source": [
        "# xb, yb = first(dl)\n",
        "# display(xb.shape, yb.shape)\n",
        "# probs = linear(xb)\n",
        "# display(probs.shape)\n",
        "# evaluate_preds(xb)\n",
        "# display(yb)\n",
        "# loss_fct(probs, yb.squeeze())\n",
        "# calc_grad(xb, yb, linear)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BSi9WAxUAo_q"
      },
      "source": [
        "##### Define a function performing one step/one epoch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jImqcs7aZlYp"
      },
      "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_()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6W7gQ4jEAo_r"
      },
      "source": [
        "##### Define a function to evaluate the validation accurary"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WsS8le8QD8To"
      },
      "source": [
        "def batch_accuracy(xb, yb):\n",
        "    \"\"\"Determines how many of the predictions are actually correct\"\"\"\n",
        "    accuracy = torch.eq(xb, yb).sum() / xb.shape[0]\n",
        "    return accuracy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "asUH98GjAj5U"
      },
      "source": [
        "# preds.unsqueeze(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k887jKBsD8OZ"
      },
      "source": [
        "def validate_epoch(model):\n",
        "    \"\"\"Collects the accuracy from each element in the dataloader and displays it\"\"\"\n",
        "    accs = [batch_accuracy(model(xb), yb) for xb, yb in valid_dl]\n",
        "    return round(torch.stack(accs).mean().item(), 4)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "51Bt7YLMEwR6"
      },
      "source": [
        "#### Bringing it all together and run training loop"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OpengN_UD8HK"
      },
      "source": [
        "weights = init_params((28*28, 10))\n",
        "bias = init_params(10)\n",
        "\n",
        "lr = 1\n",
        "params = weights, bias\n",
        "\n",
        "train_epoch(linear, lr, params)\n",
        "\n",
        "train_epoch(linear, lr, params)\n",
        "validate_epoch(evaluate_preds)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nEwfyQIyvaVq"
      },
      "source": [
        "Run 20 epochs and see the accuracy for each epoch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nET2H9YQD79j",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f13af870-b0c7-4f84-c17e-651d7970b503"
      },
      "source": [
        "n_epochs = 20\n",
        "for i in range(n_epochs):\n",
        "    train_epoch(linear, lr, params)\n",
        "    print(f\"{i}:{validate_epoch(evaluate_preds):1.4f}\", end=' ')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0:0.8765 1:0.8829 2:0.8858 3:0.8893 4:0.8915 5:0.8942 6:0.8969 7:0.8997 8:0.9010 9:0.9024 10:0.9037 11:0.9044 12:0.9055 13:0.9069 14:0.9075 15:0.9071 16:0.9079 17:0.9091 18:0.9098 19:0.9100 "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ccn3Q175vc0c"
      },
      "source": [
        "Run another 20/200/2000 epochs several times and see the evolution of the accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UNsiOf5lE01F",
        "outputId": "32e5cef1-ea0b-4bd8-da86-fa29e92f856e"
      },
      "source": [
        "n_epochs = 20\n",
        "for i in range(n_epochs):\n",
        "    train_epoch(linear, lr, params)\n",
        "    print(f\"{i}:{validate_epoch(evaluate_preds):1.4f}\", end=' ')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0:0.9107 1:0.9112 2:0.9119 3:0.9121 4:0.9124 5:0.9127 6:0.9129 7:0.9131 8:0.9132 9:0.9130 10:0.9132 11:0.9137 12:0.9139 13:0.9141 14:0.9142 15:0.9144 16:0.9144 17:0.9145 18:0.9150 19:0.9149 "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hFy5_mq-FBJi",
        "outputId": "80bc921f-b5ce-46af-a601-f7c2f951bb10"
      },
      "source": [
        "n_epochs = 20\n",
        "for i in range(n_epochs):\n",
        "    train_epoch(linear, lr, params)\n",
        "    print(f\"{i}:{validate_epoch(evaluate_preds):1.4f}\", end=' ')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0:0.9152 1:0.9157 2:0.9161 3:0.9166 4:0.9171 5:0.9177 6:0.9181 7:0.9184 8:0.9184 9:0.9186 10:0.9190 11:0.9193 12:0.9191 13:0.9191 14:0.9190 15:0.9194 16:0.9198 17:0.9197 18:0.9197 19:0.9197 "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NnYVAx1MFNLq",
        "outputId": "cf1ce4f8-9d61-40df-fe4d-5a6762a37421"
      },
      "source": [
        "n_epochs = 200\n",
        "for i in range(n_epochs):\n",
        "    train_epoch(linear, lr, params)\n",
        "    if i%10 == 0:\n",
        "        print(f\"{i}:{validate_epoch(evaluate_preds):1.4f}\", end=' ')\n",
        "print(validate_epoch(evaluate_preds))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0:0.9197 10:0.9197 20:0.9202 30:0.9205 40:0.9206 50:0.9212 60:0.9211 70:0.9218 80:0.9218 90:0.9218 100:0.9220 110:0.9224 120:0.9224 130:0.9224 140:0.9228 150:0.9227 160:0.9226 170:0.9224 180:0.9222 190:0.9221 0.9221\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZcXT3ED0F7nC",
        "outputId": "198d97e4-1add-4ead-8f12-4403798ce4ef"
      },
      "source": [
        "n_epochs = 200\n",
        "for i in range(n_epochs):\n",
        "    train_epoch(linear, lr, params)\n",
        "    if i%10 == 0:\n",
        "        print(f\"{i}:{validate_epoch(evaluate_preds):1.4f}\", end=' ')\n",
        "print(validate_epoch(evaluate_preds))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0:0.9221 10:0.9224 20:0.9226 30:0.9227 40:0.9227 50:0.9229 60:0.9229 70:0.9231 80:0.9232 90:0.9233 100:0.9234 110:0.9232 120:0.9231 130:0.9229 140:0.9228 150:0.9227 160:0.9228 170:0.9228 180:0.9228 190:0.9229 0.9229\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G6puUR2RGFUS"
      },
      "source": [
        "n_epochs = 2000\n",
        "for i in range(n_epochs):\n",
        "    train_epoch(linear, lr, params)\n",
        "    if i%100 == 0:\n",
        "        print(f\"{i}:{validate_epoch(evaluate_preds):1.4f}\", end=' ')\n",
        "print(validate_epoch(evaluate_preds))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r-b6pqY3GfSo",
        "outputId": "b2a22eac-b743-48a5-c17f-3945444f6dbf"
      },
      "source": [
        "print(validate_epoch(evaluate_preds))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.9184\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "1RQ09gHxQeZH",
        "outputId": "2425ab61-2f48-4ea0-d455-09ae56c06d08"
      },
      "source": [
        "img = valid_tensors_dict[8][49]\n",
        "show_image(img)\n",
        "plt.show()\n",
        "evaluate_preds(img.view(28*28).unsqueeze(dim=0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "Y-Xceh_zv8l9",
        "outputId": "6d18aa10-fe75-480d-eda2-4d5a2cd13be4"
      },
      "source": [
        "img = valid_tensors_dict[2][159]\n",
        "show_image(img)\n",
        "plt.show()\n",
        "evaluate_preds(img.view(28*28).unsqueeze(dim=0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[2]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "mKAD5umvv8cD",
        "outputId": "de690635-6909-427b-abe8-98f986d1bddb"
      },
      "source": [
        "img = valid_tensors_dict[7][957]\n",
        "show_image(img)\n",
        "plt.show()\n",
        "evaluate_preds(img.view(28*28).unsqueeze(dim=0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[7]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ddlCEUDyux37"
      },
      "source": [
        "## Improve model by introducing ReLu and two layers"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5AKIgUMKvAXc",
        "outputId": "f3a75758-63cc-456a-b8f3-675948dd58f0"
      },
      "source": [
        "def init_params(size, std=1.0): \n",
        "    return (torch.randn(size)*std).requires_grad_()\n",
        "\n",
        "w1 = init_params((28*28, 100))\n",
        "b1 = init_params(100)\n",
        "\n",
        "w2 = init_params((100, 10))\n",
        "b2 = init_params(10)\n",
        "\n",
        "w1.shape, b1.shape, w2.shape, b2.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784, 100]),\n",
              " torch.Size([100]),\n",
              " torch.Size([100, 10]),\n",
              " torch.Size([10]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PX9mzfQCvAXe"
      },
      "source": [
        "##### Define functions to calculate the predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SR6J5TNEvAXf"
      },
      "source": [
        "activ1 = nn.ReLU()\n",
        "\n",
        "def linear1(xb):\n",
        "    outputs =  xb @ w1 + b1\n",
        "    return activ1(outputs)\n",
        "\n",
        "def linear2(xb):\n",
        "    outputs =  xb @ w2 + b2\n",
        "    probs = F.log_softmax(outputs, dim=1)\n",
        "    return probs\n",
        "\n",
        "def model(xb):\n",
        "    xb = linear1(xb)\n",
        "    xb = linear2(xb)\n",
        "    return xb\n",
        "\n",
        "def classifier(xb):\n",
        "    xb = model(xb)\n",
        "    return xb.argmax(dim=1).unsqueeze(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zkif8_INwhnU"
      },
      "source": [
        "# # Testing layer by layer\n",
        "# xb, yb = first(dl)\n",
        "# display(xb.shape, yb.shape)\n",
        "# display(linear1(xb).shape)\n",
        "# display(linear2(linear1(xb)).shape)\n",
        "# display(model(xb))\n",
        "# classifier(xb)[0:3]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DYA40BUgvAXf"
      },
      "source": [
        "##### Define a function to calculate the loss"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TaNy5A5OvAXg"
      },
      "source": [
        "loss_fct = F.nll_loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HNSqQxstvAXg"
      },
      "source": [
        "##### Define a function to calculate the gradients"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G7Ac3w6JvAXg"
      },
      "source": [
        "def calc_grad(xb, yb, model):\n",
        "    preds = model(xb)\n",
        "    loss = loss_fct(preds, yb.squeeze())\n",
        "    # print(loss)\n",
        "    loss.backward()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xhCBXbTyvAXh"
      },
      "source": [
        "# # Testing function\n",
        "# xb, yb = first(dl)\n",
        "# display(xb.shape, yb.shape)\n",
        "# probs = model(xb)\n",
        "# display(probs.shape)\n",
        "# # display(yb)\n",
        "# loss_fct(probs, yb.squeeze())\n",
        "# calc_grad(xb, yb, model)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3oWpDgcWvAXh"
      },
      "source": [
        "##### Define a function performing one step/one epoch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qkDQTt8yvAXi"
      },
      "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_()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6J6GFo3jvAXi"
      },
      "source": [
        "##### Define a function to evaluate the validation accurary"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-d3hPWfyvAXi"
      },
      "source": [
        "#Determines how many of the predictions are actually correct \n",
        "def batch_accuracy(xb, yb):\n",
        "    accuracy = torch.eq(xb, yb).sum() / xb.shape[0]\n",
        "    return accuracy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UVgQz70VvAXi"
      },
      "source": [
        "# preds.unsqueeze(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AADwAdXTvAXi"
      },
      "source": [
        "#Collects the accuracy from each element in the dataloader and displays it\n",
        "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)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yaqhJzDevAXi"
      },
      "source": [
        "#### Bringing it all together and run training loop"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aBuIeTLGPYI4"
      },
      "source": [
        "Create a function to run `n` epochs and display results."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WIeimeJl78K1"
      },
      "source": [
        "from math import log10\n",
        "\n",
        "def run_n_epochs(model, lr, params, n_epochs):\n",
        "    trigger = 10**(int(log10(n_epochs))-1)\n",
        "    cols = 10\n",
        "    starting_i = metric_results['epochs'][-1] + 1\n",
        "    for i in range(starting_i, starting_i + n_epochs):\n",
        "        train_epoch(model, lr, params)\n",
        "        if i%trigger == 0:\n",
        "            v = validate_epoch(classifier)\n",
        "\n",
        "            metric_results['epochs'].append(i)\n",
        "            metric_results['values'].append(v)\n",
        "            \n",
        "            end_str = '\\n' if i//trigger%cols == 0 else ' ' \n",
        "            print(f\"{i:3d}:{v:1.4f}\", end=end_str)\n",
        "    print(f\"\\nLast:{v:1.4f}\")\n",
        "    fig, ax = plt.subplots(1, 1, figsize=(12,4))\n",
        "    ax.scatter(metric_results['epochs'], metric_results['values'])\n",
        "    return metric_results"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PbcQyVqtPgro"
      },
      "source": [
        "Shuffle data, initalize parameters, run one epoch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TyFqswY8vAXj",
        "outputId": "4537717a-5e00-43b0-a1c9-7e11fc378000"
      },
      "source": [
        "shuffle(dset)\n",
        "dl = DataLoader(dset, batch_size=256)\n",
        "valid_dl = DataLoader(valid_dset, batch_size=5)\n",
        "\n",
        "w1 = init_params((28*28, 100))\n",
        "b1 = init_params(100)\n",
        "w2 = init_params((100, 10))\n",
        "b2 = init_params(10)\n",
        "\n",
        "lr = 1\n",
        "params = w1, b1, w2, b2\n",
        "\n",
        "metric_results = {}\n",
        "metric_results['epochs'] = [0]\n",
        "metric_results['values'] = [0]\n",
        "\n",
        "train_epoch(model, lr, params)\n",
        "validate_epoch(classifier)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7373"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "wnLgh5gXAj1T",
        "outputId": "20c5faba-6e7d-466e-b760-df172780253a"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  1:0.8175   2:0.8432   3:0.8719   4:0.8884   5:0.8970   6:0.9010   7:0.9027   8:0.9068   9:0.9101  10:0.9107\n",
            " 11:0.9127  12:0.9153  13:0.9168  14:0.9176  15:0.9190  16:0.9196  17:0.9226  18:0.9235  19:0.9238  20:0.9253\n",
            "\n",
            "Last:0.9253\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "QIXGZWGZ8TzL",
        "outputId": "b980d1c9-38bb-48c3-c7d4-74456de6ea63"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 21:0.9257  22:0.9267  23:0.9274  24:0.9284  25:0.9296  26:0.9299  27:0.9302  28:0.9299  29:0.9301  30:0.9306\n",
            " 31:0.9310  32:0.9306  33:0.9300  34:0.9306  35:0.9306  36:0.9301  37:0.9307  38:0.9310  39:0.9315  40:0.9326\n",
            "\n",
            "Last:0.9326\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsIAAAD4CAYAAADmbIA7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAToUlEQVR4nO3dcayd510f8O+vdgJWKRgaD1E7wR6YgNWyBN1lRam2rJTFAZSEwlCiIXVShDeJTJ3WZXO2qXOzoaaLoOyPDM2MrhEahFAyz6KeDGrCNqG1y80cGpLMzEvbxbddY9q6Y8Jt4vTZH/c43Nzea5/rc67fc/18PlLk8z7nec77u08e3/fr97znPdVaCwAA9OZ1QxcAAABDEIQBAOiSIAwAQJcEYQAAuiQIAwDQpc1D7fiqq65qO3fuHGr3AAB04sknn/zj1tq25e2DBeGdO3dmfn5+qN0DANCJqvrMSu0ujQAAoEuCMAAAXRKEAQDokiAMAECXBGEAALo02F0jAADYGA4dW8gDR4/ns6fP5E1bt+Sem6/N7ddvX/ex600QBmBVkx7Ahjp4bsSxG7Vu83X5/8yHji3k3kefzpmXX0mSLJw+k3sffTpJLjh+krGXwqYDBw4MsuODBw8e2Ldv3yD7Bvp16NhC7npoPv/8t5/Nb86fzBtff2W+9zu+ed3HDrnvix177gD2xT99KUnyJ185m//0R6ey41u3rPv43sZu1LrNVx8/810Pzb867pyzX2t5euHLuettu9Zt7DS9733v+9yBAwcOLm93jTBw0Q4dW8iN9z+WXfs/mhvvfyyHji3M9NhzB4KF02fS8mdnJsYZP8nYIfc9ydgHjh5/9SzOOWdefiUPHD1+wbGTju9t7JD73ohjh9x3jz/zZ0+fWVP7tMZeCoIwzICNFijPje0p2G3UA9hQB79Jx/c2dsh9b8SxQ+67x5/5TVu3rKl9WmMvBUEYRiYJhZOM34iBMukv2G3UA9hQB79Jx/c2dsh9b8SxQ+67x5/5npuvzZYrNr2mbcsVm3LPzdeu69hLQRDmsjJEGJ10/EYMlEl/wW6jHsCGOvhNOr63sUPueyOOHXLfPf7Mt1+/Pe9/51uyfeuWVJLtW7fk/e98y1gfdptk7KXgrhGsi432qdbzhcJx9j3J+I0YKJPFILWwQt9xw9kQY++5+drXrJFkbQeRix075L4nGXtu7V7s3+VJxvc2dqPWbb76+JnPjb/Y8DrJ2PVWrbVBdjw3N9fm5+cH2TfjmVYgTRYPvOP8C3CSsTfe/9iKAWn71i35/f1vP+/YXfs/mpX+JlSST93/o+cdO+n4Seoeamwy3P/nScaeG9/TbY+mUTfARldVT7bW5pa3OyPMioY6uzrUmdVJzjJOOn4jnilMNvYZlaHOagy171k+GwMwJEH4MjbJWaCN+Fb/UGF00vEbNVCeew3BDoCNShC+TE36TS5DBdKhwuyQ122dGy9QAsClJQhfpib98NdGfKt/yDA6jfEAwKUlCM+4i728YdI7AmzEt/rPjRdGAYBxCMIzbJLLGyb98NdGfasfAGBcgvAMm+Tyhkk//JUIpADA5U0QnmGTXN4wjTsCAABczgThGTaNyxsEXwCAlb1u6AJY3aTfSQ4AwOqcEb4ELvbODy5vAABYP4LwOpv0iy1c3gAAsD5cGrHOznfnBwAAhiMIr7NJv9gCAID1IQivs9Xu8DDunR8AAFgfgvA6c+cHAIDZ5MNyY3LnBwCAy4sgPAZ3fgAAuPy4NGIM7vwAAHD5GSsIV9XeqjpeVSeqav8Kz19TVY9X1bGq+mRV/cj0Sx2OOz8AAFx+LhiEq2pTkgeT3JJkT5I7q2rPsm7/JMkjrbXrk9yR5F9Nu9AhufMDAMDlZ5wzwjckOdFae7619lKSh5PctqxPS/LNo8ffkuSz0ytxeO78AABw+Rnnw3Lbk7ywZPtkkr+0rM+BJL9TVX8nyeuTvGOlF6qqfUn2Jck111yz1loH484PAACXn2ndNeLOJB9urf18Vf1gkl+tqje31r62tFNr7WCSg0kyNzfXprTvS8KdHwAALi/jXBqxkOTqJds7Rm1L3ZXkkSRprf3XJN+Y5KppFAgAAOthnCD8RJLdVbWrqq7M4ofhDi/r87+T/FCSVNX3ZTEIn5pmoQAAME0XDMKttbNJ7k5yNMlzWbw7xDNVdV9V3Trq9p4kP1NVf5Dk15P8zdbahrr0AQCAvox1jXBr7UiSI8va3rvk8bNJbpxuaQAAsH58sxwAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOjSWEG4qvZW1fGqOlFV+1fp81NV9WxVPVNVvzbdMgEAYLo2X6hDVW1K8mCSH05yMskTVXW4tfbskj67k9yb5MbW2peq6s+tV8EAADAN45wRviHJidba8621l5I8nOS2ZX1+JsmDrbUvJUlr7cXplgkAANM1ThDenuSFJdsnR21LfU+S76mq36+qj1fV3pVeqKr2VdV8Vc2fOnXq4ioGAIApmNaH5TYn2Z3kpiR3Jvnlqtq6vFNr7WBrba61Nrdt27Yp7RoAANZunCC8kOTqJds7Rm1LnUxyuLX2cmvtU0n+KIvBGAAAZtI4QfiJJLuraldVXZnkjiSHl/U5lMWzwamqq7J4qcTzU6wTAACm6oJBuLV2NsndSY4meS7JI621Z6rqvqq6ddTtaJIvVNWzSR5Pck9r7QvrVTQAAEyqWmuD7Hhubq7Nz88Psm8AAPpRVU+21uaWt/tmOQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALo0VhCuqr1VdbyqTlTV/vP0+4mqalU1N70SAQBg+i4YhKtqU5IHk9ySZE+SO6tqzwr93pDk3Uk+Me0iAQBg2sY5I3xDkhOttedbay8leTjJbSv0+2dJPpDkK1OsDwAA1sU4QXh7kheWbJ8ctb2qqn4gydWttY+e74Wqal9VzVfV/KlTp9ZcLAAATMvEH5arqtcl+YUk77lQ39bawdbaXGttbtu2bZPuGgAALto4QXghydVLtneM2s55Q5I3J/m9qvp0krcmOewDcwAAzLJxgvATSXZX1a6qujLJHUkOn3uytfbl1tpVrbWdrbWdST6e5NbW2vy6VAwAAFNwwSDcWjub5O4kR5M8l+SR1tozVXVfVd263gUCAMB62DxOp9bakSRHlrW9d5W+N01eFgAArC/fLAcAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXxgrCVbW3qo5X1Ymq2r/C83+vqp6tqk9W1ceq6junXyoAAEzPBYNwVW1K8mCSW5LsSXJnVe1Z1u1YkrnW2vcn+UiSfzHtQgEAYJrGOSN8Q5ITrbXnW2svJXk4yW1LO7TWHm+t/elo8+NJdky3TAAAmK5xgvD2JC8s2T45alvNXUn+4yRFAQDAets8zRerqp9OMpfkr6zy/L4k+5LkmmuumeauAQBgTcY5I7yQ5Ool2ztGba9RVe9I8o+T3Npa++pKL9RaO9ham2utzW3btu1i6gUAgKkYJwg/kWR3Ve2qqiuT3JHk8NIOVXV9kn+dxRD84vTLBACA6bpgEG6tnU1yd5KjSZ5L8khr7Zmquq+qbh11eyDJNyX5zap6qqoOr/JyAAAwE8a6Rri1diTJkWVt713y+B1TrgsAANaVb5YDAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdEoQBAOiSIAwAQJcEYQAAuiQIAwDQJUEYAIAuCcIAAHRJEAYAoEuCMAAAXRKEAQDokiAMAECXBGEAALokCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6JIgDABAlwRhAAC6JAgDANAlQRgAgC4JwgAAdEkQBgCgS4IwAABdGisIV9XeqjpeVSeqav8Kz39DVf3G6PlPVNXOaRc6DYeOLeTG+x/Lrv0fzY33P5ZDxxaGLgkAgIFcMAhX1aYkDya5JcmeJHdW1Z5l3e5K8qXW2ncn+WCSD0y70EkdOraQex99Ogunz6QlWTh9Jvc++rQwDADQqXHOCN+Q5ERr7fnW2ktJHk5y27I+tyV5aPT4I0l+qKpqemVO7oGjx3Pm5Vde03bm5VfywNHjA1UEAMCQxgnC25O8sGT75KhtxT6ttbNJvpzkjctfqKr2VdV8Vc2fOnXq4iq+SJ89fWZN7QAAXN4u6YflWmsHW2tzrbW5bdu2Xcpd501bt6ypHQCAy9s4QXghydVLtneM2lbsU1Wbk3xLki9Mo8Bpuefma7Plik2vadtyxabcc/O1A1UEAMCQxgnCTyTZXVW7qurKJHckObysz+Ek7xo9/skkj7XW2vTKnNzt12/P+9/5lmzfuiWVZPvWLXn/O9+S269ffpUHAAA92HyhDq21s1V1d5KjSTYl+VBr7Zmqui/JfGvtcJJfSfKrVXUiyRezGJZnzu3Xbxd8AQBIMkYQTpLW2pEkR5a1vXfJ468k+evTLQ0AANaPb5YDAKBLgjAAAF0ShAEA6JIgDABAl2qou5xV1akknxlk58lVSf54oH1vROZrbczX2pivtTFfa2O+1sZ8rY35Wpsh5+s7W2tf921ugwXhIVXVfGttbug6NgrztTbma23M19qYr7UxX2tjvtbGfK3NLM6XSyMAAOiSIAwAQJd6DcIHhy5ggzFfa2O+1sZ8rY35WhvztTbma23M19rM3Hx1eY0wAAD0ekYYAIDOCcIAAHSpqyBcVXur6nhVnaiq/UPXM+uq6tNV9XRVPVVV80PXM4uq6kNV9WJV/eGStm+rqt+tqv85+vNbh6xxlqwyXweqamG0zp6qqh8ZssZZUVVXV9XjVfVsVT1TVe8etVtfKzjPfFlfq6iqb6yq/1ZVfzCas/eN2ndV1SdGx8rfqKorh651Fpxnvj5cVZ9assauG7rWWVFVm6rqWFX99mh75tZWN0G4qjYleTDJLUn2JLmzqvYMW9WG8Fdba9fN2n3/ZsiHk+xd1rY/ycdaa7uTfGy0zaIP5+vnK0k+OFpn17XWjlzimmbV2STvaa3tSfLWJD87+p1lfa1stflKrK/VfDXJ21trfyHJdUn2VtVbk3wgi3P23Um+lOSuAWucJavNV5Lcs2SNPTVciTPn3UmeW7I9c2urmyCc5IYkJ1prz7fWXkrycJLbBq6JDa619p+TfHFZ821JHho9fijJ7Ze0qBm2ynyxgtba51pr/330+E+yeDDZHutrReeZL1bRFv2/0eYVo/9akrcn+cio3RobOc98sYKq2pHkR5P8m9F2ZQbXVk9BeHuSF5Zsn4xfkhfSkvxOVT1ZVfuGLmYD+fbW2udGj/9Pkm8fspgN4u6q+uTo0glv9S9TVTuTXJ/kE7G+LmjZfCXW16pGb10/leTFJL+b5H8lOd1aOzvq4li5xPL5aq2dW2M/N1pjH6yqbxiwxFnyi0n+QZKvjbbfmBlcWz0FYdbuba21H8ji5SQ/W1V/eeiCNpq2eH9CZwzO75eSfFcW32r8XJKfH7ac2VJV35Tkt5L83dba/136nPX19VaYL+vrPFprr7TWrkuyI4vvnH7vwCXNtOXzVVVvTnJvFuftLyb5tiT/cMASZ0JV/ViSF1trTw5dy4X0FIQXkly9ZHvHqI1VtNYWRn++mOTfZ/GXJBf2+ar6jiQZ/fniwPXMtNba50cHl68l+eVYZ6+qqiuyGOr+XWvt0VGz9bWKlebL+hpPa+10kseT/GCSrVW1efSUY+UKlszX3tFlOa219tUk/zbWWJLcmOTWqvp0Fi9FfXuSf5kZXFs9BeEnkuwefWLxyiR3JDk8cE0zq6peX1VvOPc4yV9L8ofnH8XI4STvGj1+V5L/MGAtM+9cqBv58VhnSV69nu5XkjzXWvuFJU9ZXytYbb6sr9VV1baq2jp6vCXJD2fx2urHk/zkqJs1NrLKfP2PJf8wrSxe89r9Gmut3dta29Fa25nFvPVYa+1vZAbXVlffLDe6bc4vJtmU5EOttZ8buKSZVVV/PotngZNkc5JfM19fr6p+PclNSa5K8vkk/zTJoSSPJLkmyWeS/FRrzQfEsup83ZTFt61bkk8n+VtLroHtVlW9Lcl/SfJ0/uwau3+Uxetera9lzjNfd8b6WlFVfX8WP7C0KYsnxh5prd03+v3/cBbf5j+W5KdHZzu7dp75eizJtiSV5Kkkf3vJh+q6V1U3Jfn7rbUfm8W11VUQBgCAc3q6NAIAAF4lCAMA0CVBGACALgnCAAB0SRAGAKBLgjAAAF0ShAEA6NL/B57vdgysMXo/AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "mwMUwNjs90uc",
        "outputId": "e03698e9-a58a-4aec-9990-af7ecce87853"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 41:0.9332  42:0.9342  43:0.9348  44:0.9352  45:0.9359  46:0.9368  47:0.9375  48:0.9381  49:0.9380  50:0.9386\n",
            " 51:0.9384  52:0.9387  53:0.9390  54:0.9390  55:0.9398  56:0.9401  57:0.9394  58:0.9400  59:0.9402  60:0.9403\n",
            "\n",
            "Last:0.9403\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OtEoMIN_1Z50",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "outputId": "9f57ae49-a4ec-484d-cec3-13ac587c1b98"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 50)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 61:0.9403  62:0.9411  63:0.9408  64:0.9416  65:0.9418  66:0.9419  67:0.9417  68:0.9426  69:0.9420  70:0.9428\n",
            " 71:0.9424  72:0.9417  73:0.9423  74:0.9421  75:0.9430  76:0.9433  77:0.9442  78:0.9438  79:0.9443  80:0.9441\n",
            " 81:0.9440  82:0.9440  83:0.9441  84:0.9440  85:0.9438  86:0.9444  87:0.9449  88:0.9444  89:0.9444  90:0.9447\n",
            " 91:0.9445  92:0.9450  93:0.9450  94:0.9448  95:0.9450  96:0.9447  97:0.9456  98:0.9447  99:0.9448 100:0.9451\n",
            "101:0.9456 102:0.9449 103:0.9446 104:0.9455 105:0.9451 106:0.9450 107:0.9450 108:0.9457 109:0.9456 110:0.9452\n",
            "\n",
            "Last:0.9452\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xzbnd9At1gpU"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 50)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TBposkA4Ditj"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/5, params, 80)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bPlz0M76DjTO"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "3mXfRZW3-IZk",
        "outputId": "08b9ffba-a755-4910-ef14-f7be6a9f2145"
      },
      "source": [
        "img = valid_tensors_dict[8][49]\n",
        "show_image(img)\n",
        "plt.show()\n",
        "classifier(img.view(28*28).unsqueeze(dim=0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "G7DbB7ha-IZr",
        "outputId": "063fbe7a-53ea-465c-d5fc-465cc95f0b3e"
      },
      "source": [
        "img = valid_tensors_dict[2][159]\n",
        "show_image(img)\n",
        "plt.show()\n",
        "\n",
        "classifier(img.view(28*28).unsqueeze(dim=0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[5]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "YIrEcrwl-IZr",
        "outputId": "853dee8a-5b67-4306-a198-7c770ae8651b"
      },
      "source": [
        "img = valid_tensors_dict[7][957]\n",
        "show_image(img)\n",
        "plt.show()\n",
        "\n",
        "classifier(img.view(28*28).unsqueeze(dim=0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 72x72 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[7]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9oI2FvUN-Cgz"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yNjM1Ml31_0E"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "181oE9ezELNy"
      },
      "source": [
        "## Improvement 2 model by introducing ReLu and three layers"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8Mej-i-JELNz",
        "outputId": "b32bfcb4-66a0-40cf-c57d-05437f465773"
      },
      "source": [
        "def init_params(size, std=1.0): \n",
        "    return (torch.randn(size)*std).requires_grad_()\n",
        "\n",
        "w1 = init_params((28*28, 250))\n",
        "b1 = init_params(250)\n",
        "\n",
        "w2 = init_params((250, 100))\n",
        "b2 = init_params(100)\n",
        "\n",
        "w3 = init_params((100, 10))\n",
        "b3 = init_params(10)\n",
        "\n",
        "w1.shape, b1.shape, w2.shape, b2.shape, w3.shape, b3.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784, 250]),\n",
              " torch.Size([250]),\n",
              " torch.Size([250, 100]),\n",
              " torch.Size([100]),\n",
              " torch.Size([100, 10]),\n",
              " torch.Size([10]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gB-4uG4IELN0"
      },
      "source": [
        "##### Define functions to calculate the predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LabWssUNELN1"
      },
      "source": [
        "activ1 = nn.ReLU()\n",
        "\n",
        "def linear1(xb):\n",
        "    outputs =  xb @ w1 + b1\n",
        "    return activ1(outputs)\n",
        "\n",
        "def linear2(xb):\n",
        "    outputs =  xb @ w2 + b2\n",
        "    return activ1(outputs)\n",
        "\n",
        "def linear3(xb):\n",
        "    \"\"\"https://pytorch.org/docs/stable/nn.functional.html#torch.nn.functional.log_softmax\"\"\"\n",
        "    outputs =  xb @ w3 + b3\n",
        "    probs = torch.log_softmax(outputs, dim=1)\n",
        "    return probs\n",
        "\n",
        "def model(xb):\n",
        "    xb = linear1(xb)\n",
        "    xb = linear2(xb)\n",
        "    xb = linear3(xb)\n",
        "    return xb\n",
        "\n",
        "def classifier(xb):\n",
        "    xb = model(xb)\n",
        "    return xb.argmax(dim=1).unsqueeze(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a359RvWkELN1"
      },
      "source": [
        "# # Testing layer by layer\n",
        "# xb, yb = first(dl)\n",
        "# display(xb.shape, yb.shape)\n",
        "# display(linear1(xb).shape)\n",
        "# display(linear2(linear1(xb)).shape)\n",
        "# display(linear3(linear2(linear1(xb))).shape)\n",
        "# display(model(xb))\n",
        "# classifier(xb)[0:3]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "llDIsX4KELN2"
      },
      "source": [
        "##### Define a function to calculate the loss"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2c9pQh2PELN2"
      },
      "source": [
        "loss_fct = F.nll_loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "imw0hvlqELN3"
      },
      "source": [
        "##### Define a function to calculate the gradients"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jZydlieWELN3"
      },
      "source": [
        "def calc_grad(xb, yb, model):\n",
        "    preds = model(xb)\n",
        "    loss = loss_fct(preds, yb.squeeze())\n",
        "    # print(loss)\n",
        "    loss.backward()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o7j3EL5OELN4"
      },
      "source": [
        "# # Testing function\n",
        "# xb, yb = first(dl)\n",
        "# display(xb.shape, yb.shape)\n",
        "# probs = model(xb)\n",
        "# display(probs.shape)\n",
        "# # display(yb)\n",
        "# loss_fct(probs, yb.squeeze())\n",
        "# calc_grad(xb, yb, model)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hMEf8gBPELN4"
      },
      "source": [
        "##### Define a function performing one step/one epoch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ythX26KAELN5"
      },
      "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_()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_vOlDoGnELN5"
      },
      "source": [
        "##### Define a function to evaluate the validation accurary"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O9ntDGtqELN7"
      },
      "source": [
        "#Determines how many of the predictions are actually correct \n",
        "def batch_accuracy(xb, yb):\n",
        "    accuracy = torch.eq(xb, yb).sum() / xb.shape[0]\n",
        "    return accuracy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KkpHxR5jELN8"
      },
      "source": [
        "# preds.unsqueeze(dim=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9iFwVrglELN8"
      },
      "source": [
        "#Collects the accuracy from each element in the dataloader and displays it\n",
        "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)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Co3xbdagELN9"
      },
      "source": [
        "#### Bringing it all together and run training loop"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Wt7YYg5ELN9"
      },
      "source": [
        "Create a function to run `n` epochs and display results."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BjnqFRyBELN9"
      },
      "source": [
        "from math import log10\n",
        "\n",
        "def run_n_epochs(model, lr, params, n_epochs):\n",
        "    trigger = 10**(int(log10(n_epochs))-1)\n",
        "    cols = 10\n",
        "    starting_i = metric_results['epochs'][-1] + 1\n",
        "    for i in range(starting_i, starting_i + n_epochs):\n",
        "        train_epoch(model, lr, params)\n",
        "        if i%trigger == 0:\n",
        "            v = validate_epoch(classifier)\n",
        "\n",
        "            metric_results['epochs'].append(i)\n",
        "            metric_results['values'].append(v)\n",
        "            \n",
        "            end_str = '\\n' if i//trigger%cols == 0 else ' ' \n",
        "            print(f\"{i:3d}:{v:1.4f}\", end=end_str)\n",
        "    print(f\"\\nLast:{v:1.4f}\")\n",
        "    fig, ax = plt.subplots(1, 1, figsize=(12,4))\n",
        "    ax.scatter(metric_results['epochs'], metric_results['values'])\n",
        "    return metric_results"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MzeqRUTNELN-"
      },
      "source": [
        "Shuffle data, initalize parameters, run one epoch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "38xKDG2fELN-",
        "outputId": "8746958b-79ee-4cf5-a998-203a72302c39"
      },
      "source": [
        "shuffle(dset)\n",
        "dl = DataLoader(dset, batch_size=256)\n",
        "valid_dl = DataLoader(valid_dset, batch_size=5)\n",
        "\n",
        "w1 = init_params((28*28, 250))\n",
        "b1 = init_params(250)\n",
        "w2 = init_params((250, 100))\n",
        "b2 = init_params(100)\n",
        "w3 = init_params((100, 10))\n",
        "b3 = init_params(10)\n",
        "\n",
        "lr = 1\n",
        "params = w1, b1, w2, b2\n",
        "\n",
        "metric_results = {}\n",
        "metric_results['epochs'] = [0]\n",
        "metric_results['values'] = [0]\n",
        "\n",
        "train_epoch(model, lr, params)\n",
        "validate_epoch(classifier)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.2884"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "7vb3sexJELN_",
        "outputId": "cdf65858-4dc8-42c1-9d33-e120cc9b29c4"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  1:0.3432   2:0.3574   3:0.3630   4:0.3939   5:0.4297   6:0.4517   7:0.4631   8:0.4663   9:0.4809  10:0.5085\n",
            " 11:0.5316  12:0.5307  13:0.5376  14:0.5375  15:0.5486  16:0.5588  17:0.5607  18:0.5021  19:0.4852  20:0.4854\n",
            "\n",
            "Last:0.4854\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "ViuA51I9ELN_",
        "outputId": "b68d387f-23ca-4540-c7c7-43fad0afe0bd"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 21:0.4977  22:0.5253  23:0.5194  24:0.5120  25:0.5184  26:0.5213  27:0.5087  28:0.5364  29:0.5601  30:0.6013\n",
            " 31:0.5643  32:0.5994  33:0.5914  34:0.6020  35:0.5796  36:0.5126  37:0.5282  38:0.5507  39:0.5483  40:0.4902\n",
            "\n",
            "Last:0.4902\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "Zqd0m-XGGLk4",
        "outputId": "25a46ebd-9f62-47a7-e8bd-466a7e5024b5"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 41:0.4232  42:0.5093  43:0.5523  44:0.5202  45:0.5218  46:0.5272  47:0.5283  48:0.4833  49:0.5261  50:0.5203\n",
            " 51:0.5246  52:0.5327  53:0.5393  54:0.5222  55:0.5914  56:0.5971  57:0.5539  58:0.6100  59:0.6073  60:0.5957\n",
            "\n",
            "Last:0.5957\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L0LrEYSx5E1i"
      },
      "source": [
        "Adjust the learning rate to have slower learning from here"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "IY3B6_N0GLeG",
        "outputId": "16849132-0532-4937-d843-116e67e93a72"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/2, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 61:0.6435  62:0.6539  63:0.6572  64:0.6605  65:0.6668  66:0.6696  67:0.6693  68:0.6698  69:0.6571  70:0.6666\n",
            " 71:0.6746  72:0.6757  73:0.6627  74:0.6650  75:0.6740  76:0.6753  77:0.6765  78:0.6806  79:0.6763  80:0.6837\n",
            "\n",
            "Last:0.6837\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "aerSw38SGLaR",
        "outputId": "749d9c94-98fe-4ec1-965b-8f7d67693c98"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/2, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 81:0.6771  82:0.6810  83:0.6805  84:0.6825  85:0.6815  86:0.6804  87:0.6791  88:0.6810  89:0.6817  90:0.6820\n",
            " 91:0.6840  92:0.6793  93:0.6826  94:0.6856  95:0.6799  96:0.6847  97:0.6869  98:0.6846  99:0.6881 100:0.6896\n",
            "\n",
            "Last:0.6896\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "0VtUybcaGjwd",
        "outputId": "bb09165c-033b-4847-a986-8935acc5d4e8"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/2, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "101:0.6863 102:0.6931 103:0.6862 104:0.6885 105:0.6917 106:0.6903 107:0.6901 108:0.6805 109:0.6788 110:0.6773\n",
            "111:0.6856 112:0.6888 113:0.6913 114:0.6882 115:0.6887 116:0.7115 117:0.6861 118:0.6913 119:0.6909 120:0.6935\n",
            "\n",
            "Last:0.6935\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "EEQmMBddGjs_",
        "outputId": "648d34ae-1db5-4caf-d53b-6af97b7d8a22"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/2, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "121:0.6871 122:0.6914 123:0.6899 124:0.6908 125:0.6903 126:0.6891 127:0.6898 128:0.6915 129:0.6897 130:0.6891\n",
            "131:0.6779 132:0.6884 133:0.6850 134:0.6816 135:0.6902 136:0.7214 137:0.6897 138:0.6840 139:0.6907 140:0.6878\n",
            "\n",
            "Last:0.6878\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WRirDqFh5siJ"
      },
      "source": [
        "Seems we are bouncing between two values and not improving. Further reduction of the learning rate for even slower training. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "id": "WjRUzdZPGjps",
        "outputId": "d2df478d-4faf-4195-abf6-6bd3ed794217"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/4, params, 20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "141:0.7315 142:0.7358 143:0.7328 144:0.7350 145:0.7383 146:0.7404 147:0.7412 148:0.7422 149:0.7408 150:0.7420\n",
            "151:0.7428 152:0.7425 153:0.7424 154:0.7451 155:0.7441 156:0.7434 157:0.7446 158:0.7393 159:0.7429 160:0.7449\n",
            "\n",
            "Last:0.7449\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "49ppCbLq6Cla"
      },
      "source": [
        "It worked, we managed to pass above 75% accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "yM_jEbbAGje0",
        "outputId": "a92c2c29-883f-44ce-eac5-b71796a058ff"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/4, params, 50)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "161:0.7447 162:0.7454 163:0.7451 164:0.7454 165:0.7438 166:0.7437 167:0.7435 168:0.7442 169:0.7451 170:0.7443\n",
            "171:0.7427 172:0.7435 173:0.7443 174:0.7458 175:0.7420 176:0.7431 177:0.7455 178:0.7440 179:0.7446 180:0.7450\n",
            "181:0.7440 182:0.7447 183:0.7451 184:0.7451 185:0.7443 186:0.7452 187:0.7469 188:0.7476 189:0.7408 190:0.7460\n",
            "191:0.7452 192:0.7465 193:0.7472 194:0.7473 195:0.7476 196:0.7462 197:0.7472 198:0.7484 199:0.7456 200:0.7483\n",
            "201:0.7436 202:0.7455 203:0.7456 204:0.7482 205:0.7462 206:0.7453 207:0.7459 208:0.7465 209:0.7449 210:0.7499\n",
            "\n",
            "Last:0.7499\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JjFn_eMx6JGi"
      },
      "source": [
        "Let's reduce even more the learning rate to try to reach higher accuracy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 322
        },
        "id": "RENoPJuzIkHk",
        "outputId": "04bafef8-f14c-401f-c708-ba09b9719eba"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/8, params, 100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "220:0.7573 230:0.7568 240:0.7568 250:0.7568 260:0.7571 270:0.7610 280:0.7613 290:0.7607 300:0.7633\n",
            "310:0.7616 \n",
            "Last:0.7616\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        },
        "id": "GpgXc1ZFIj9u",
        "outputId": "d335cb1c-cd65-4110-b26e-4715c09154ba"
      },
      "source": [
        "metric_results = run_n_epochs(model, lr/16, params, 500)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "320:0.7666 330:0.7674 340:0.7682 350:0.7669 360:0.7665 370:0.7679 380:0.7668 390:0.7674 400:0.7667\n",
            "410:0.7681 420:0.7681 430:0.7679 440:0.7677 450:0.7674 460:0.7678 470:0.7677 480:0.7684 490:0.7694 500:0.7684\n",
            "510:0.7694 520:0.7690 530:0.7697 540:0.7703 550:0.7699 560:0.7705 570:0.7683 580:0.7699 590:0.7701 600:0.7712\n",
            "610:0.7695 620:0.7685 630:0.7686 640:0.7687 650:0.7691 660:0.7685 670:0.7684 680:0.7689 690:0.7695 700:0.7688\n",
            "710:0.7694 720:0.7705 730:0.7708 740:0.7722 750:0.7718 760:0.7716 770:0.7721 780:0.7725 790:0.7730 800:0.7738\n",
            "810:0.7738 \n",
            "Last:0.7738\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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hmtVMvzjb8xojEdx105WlZ4zoJek9ZEOSJElnxiDc5ILXzB0pctH5o/zmz13Fp7ZcWWoe35OZbNk4zjsuX9m3OrmQhiRJ0mAYhOHUPL7TM6/2+o6NjvCJ915xasaGMtOhNYYyPPKtE32rmwtpSJIkDUapm+Ui4jrgs8AIcG9m7mrZ/yFgN9AY0PrfMvPePtZzoHpNg7Z731GenZ7htaPnnDYTRLNsOrYfXEhDkiRpcHoG4YgYAe4G3gUcBw5ExJ7MfLzl0Acy85YB1HHgOgXXV6dBq4fkbiG4+VrdplZrtemNF/PU8zM8Oz3DhWOjRMD0i7NcumKM7ZvXO4ewJEnSgJTpEb4aOJaZTwJExP3AjUBrEF62OgXXTtOg9brW9s3r5wToTsZXjHHfL759XteXJElSf5QZIzwOPNO0fbwoa/W+iPhGRDwUEZe1u1BEbIuIgxFx8MSJ/o2jXajtm9czNjoyp6zbNGidNIYybNk4fmr2iADG2qww57AHSZKk4erXzXJ/BqzJzDcDXwJ+v91BmXlPZk5k5sTKlf2bWWGhWoPr+Iqx0tOgtZ7TGMqwZeM4X9lxLZ/5uaug5Ta7AN731vpxm3btZ+2OL7Jp137nDJYkSVpEZYZG1IDmHt5VvHpTHACZ+XzT5r3Abyy8aotncqp26ia31rG52//k6x1Xgrvo/FG+suPartdudyNeAl/4+vf4/GO1OSvV7Xz4MIDjgiVJkhZBmR7hA8C6iFgbEecBW4E9zQdExOubNm8AnuhfFQerMXVabXqG5NVAOjlVY8vGcX7gtZ3/r1Bm5ESnG/GmZ2a7zlQhSZKkweoZhDPzZeAWYB/1gPtgZh6JiDsj4obisF+OiCMR8XXgl4EPDarC/dZr6rRuK8p9f6b3anPznQfYBTQkSZIWR6kxwpm5NzPflJlvzMxfK8puz8w9xeOdmXlFZv5YZr4jM781yEr3U6fg2SjvFmTLhNxON+JddP7oGV9TkiRJC1f5leU6Bc9G+fbN6xk95/Q15UZHotSsD51uxPvEe69oG5CdSUKSJGlxlFpZ7my25nXt5xB+x+X1WS0aN67dsefIqSWYLzp/dM7yy71s2Tje8dhON+lJkiRpsCodhCenavzFt/+h7b5HvvXqPMfdguxCDOq6kiRJ6q3SQyN27ztKp4kfvGlNkiTp7FbpINxuSESDN61JkiSd3SobhCenapx+C1xdgDetSZIkneUqG4S7DYv4wDWrHbsrSZJ0lqtsEO42BvhTW65cxJpIkiRpGCobhDuNAR53bLAkSVIlVDYIv+PylaeNEXZBC0mSpOqoZBCenKrx+cdqc8YIB/C+tzqvryRJUlVUckGN3fuOMjN7ck5ZMncRjX6anKq5gpwkSdISU8kg3OlGuUEsojE5VWPnw4dPBe/a9Aw7Hz4MYBiWJEkaokoOjeh0o9wgFtFo1/s8M3uS3fuO9v25JEmSVF4lg/D2zesZGx2ZUzaoG+UWs/dZkiRJ5VUyCG/ZOM5dN13J+IoxgvqUaXfddOVAhiosZu+zJEmSyis1RjgirgM+C4wA92bmrg7HvQ94CPjxzDzYt1oOwJaNizNDxPbN6+eMEQanaZMkSVoKegbhiBgB7gbeBRwHDkTEnsx8vOW4HwQ+Cnx1EBVdrhph21kjJEmSlpYyPcJXA8cy80mAiLgfuBF4vOW4/wz8OrC9rzUckMWc0myxep8lSZJUXpkxwuPAM03bx4uyUyLiLcBlmfnFPtZtYBpTmtWmZ0hendJscqo27KpJkiRpkSz4ZrmIOAf4NPArJY7dFhEHI+LgiRODWbyiDKc0kyRJUpkgXAMua9peVZQ1/CDwo8D/iYingGuAPREx0XqhzLwnMycyc2LlypVnXusFckozSZIklQnCB4B1EbE2Is4DtgJ7Gjsz8/uZeUlmrsnMNcCjwA1LedYIpzSTJElSzyCcmS8DtwD7gCeABzPzSETcGRE3DLqCg7CYC2pIkiRpaSo1j3Bm7gX2tpTd3uHYn1p4tQbLKc0kSZJUKgifjZzSTJIkqdoqGYQXcw5hSZIkLU2VC8KNOYQb06c15hAGDMOSJEkVsuB5hJebT/7ZEecQliRJUrWC8ORUjRdenG27zzmEJUmSqqVSQbhbr69zCEuSJFVLpYJwrUuvr3MIS5IkVUtlgvDkVI3osG/F2Kg3ykmSJFVMZYLw7n1HyTblAdxxwxWLXR1JkiQNWWWCcKeb4RKnTZMkSaqiygThTjfDjXuTnCRJUiVVJghv37yesdGROWVjoyPeJCdJklRRlVlZrjH8waWVJUmSBBUKwlAPwwZfSZIkQYWGRkiSJEnNDMKSJEmqJIOwJEmSKqlUEI6I6yLiaEQci4gdbfb/h4g4HBGHIuL/RsSG/ldVkiRJ6p+eQTgiRoC7geuBDcDNbYLuH2XmlZl5FfAbwKf7XlNJkiSpj8r0CF8NHMvMJzPzJeB+4MbmAzLzH5s2L4C2qxlLkiRJS0aZ6dPGgWeato8Db2s9KCI+AnwcOA+4tt2FImIbsA1g9erV862rJEmS1Dd9u1kuM+/OzDcC/wm4rcMx92TmRGZOrFy5sl9PLUmSJM1bmSBcAy5r2l5VlHVyP7BlIZWSJEmSBq1MED4ArIuItRFxHrAV2NN8QESsa9p8D/A3/auiJEmS1H89xwhn5ssRcQuwDxgBPpeZRyLiTuBgZu4BbomIdwKzwAvABwdZaUmSJGmhytwsR2buBfa2lN3e9Pijfa6XJEmSNFCuLCdJkqRKMghLkiSpkgzCkiRJqiSDsCRJkirJICxJkqRKMghLkiSpkgzCkiRJqiSDsCRJkirJICxJkqRKMghLkiSpkgzCkiRJqiSDsCRJkirJICxJkqRKMghLkiSpkgzCkiRJqiSDsCRJkiqpVBCOiOsi4mhEHIuIHW32fzwiHo+Ib0TElyPiDf2vqiRJktQ/PYNwRIwAdwPXAxuAmyNiQ8thU8BEZr4ZeAj4jX5XVJIkSeqnMj3CVwPHMvPJzHwJuB+4sfmAzHwkM18sNh8FVvW3mpIkSVJ/lQnC48AzTdvHi7JOPgz8z4VUSpIkSRq0c/t5sYj4BWAC+Fcd9m8DtgGsXr26n08tSZIkzUuZHuEacFnT9qqibI6IeCfwq8ANmfnP7S6Umfdk5kRmTqxcufJM6itJkiT1RZkgfABYFxFrI+I8YCuwp/mAiNgI/Db1EPxc/6spSZIk9VfPIJyZLwO3APuAJ4AHM/NIRNwZETcUh+0GfgD4k4g4FBF7OlxOkiRJWhJKjRHOzL3A3pay25sev7PP9ZIkSZIGypXlJEmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEmlgnBEXBcRRyPiWETsaLP/JyPiaxHxckS8v//VlCRJkvqrZxCOiBHgbuB6YANwc0RsaDnsaeBDwB/1u4KSJEnSIJxb4pirgWOZ+SRARNwP3Ag83jggM58q9r0ygDpKkiRJfVdmaMQ48EzT9vGibN4iYltEHIyIgydOnDiTS0iSJEl9sag3y2XmPZk5kZkTK1euXMynliRJkuYoE4RrwGVN26uKMkmSJGnZKhOEDwDrImJtRJwHbAX2DLZakiRJ0mD1DMKZ+TJwC7APeAJ4MDOPRMSdEXEDQET8eEQcB34W+O2IODLISkuSJEkLVWbWCDJzL7C3pez2pscHqA+ZkCRJkpYFV5aTJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJRmEJUmSVEkGYUmSJFWSQViSJEmVZBCWJElSJZUKwhFxXUQcjYhjEbGjzf7XRMQDxf6vRsSafle0HyanamzatZ+1O77Ipl37mZyqDbtKkiRJGpKeQTgiRoC7geuBDcDNEbGh5bAPAy9k5o8AnwF+vd8VXajJqRo7Hz5MbXqGBGrTM+x8+LBhWJIkqaLK9AhfDRzLzCcz8yXgfuDGlmNuBH6/ePwQ8NMREf2r5sLt3neUmdmTc8pmZk+ye9/RIdVIkiRJw1QmCI8DzzRtHy/K2h6TmS8D3wde13qhiNgWEQcj4uCJEyfOrMZn6NnpmXmVS5Ik6ey2qDfLZeY9mTmRmRMrV65czKfm0hVj8yqXJEnS2a1MEK4BlzVtryrK2h4TEecCFwLP96OC/bJ983rGRkfmlI2NjrB98/oh1UiSJEnDVCYIHwDWRcTaiDgP2ArsaTlmD/DB4vH7gf2Zmf2r5sJt2TjOXTddyfiKMQIYXzHGXTddyZaNraM8JEmSVAXn9jogM1+OiFuAfcAI8LnMPBIRdwIHM3MP8LvAH0TEMeAfqIflJWfLxnGDryRJkoASQRggM/cCe1vKbm96/P+An+1v1SRJkqTBcWU5SZIkVZJBWJIkSZVkEJYkSVIlGYQlSZJUSTGsWc4i4gTw3aE8OVwC/P2Qnnu5sa3Ks63Ks63Ks63Ks63Ks63mx/Yqb6m21Rsy87TV3IYWhIcpIg5m5sSw67Ec2Fbl2Vbl2Vbl2Vbl2Vbl2VbzY3uVt9zayqERkiRJqiSDsCRJkiqpqkH4nmFXYBmxrcqzrcqzrcqzrcqzrcqzrebH9ipvWbVVJccIS5IkSVXtEZYkSVLFVSoIR8R1EXE0Io5FxI5h12fYIuJzEfFcRHyzqeziiPhSRPxN8e9FRXlExH8t2u4bEfGW4dV88UXEZRHxSEQ8HhFHIuKjRbnt1SIiXhsRfxURXy/a6pNF+dqI+GrRJg9ExHlF+WuK7WPF/jXDrP8wRMRIRExFxBeKbduqg4h4KiIOR8ShiDhYlPl32EZErIiIhyLiWxHxRES83bY6XUSsL36fGl//GBG32lbtRcTHitf2b0bEHxev+cv2NasyQTgiRoC7geuBDcDNEbFhuLUaut8Drmsp2wF8OTPXAV8utqHebuuKr23Aby1SHZeKl4FfycwNwDXAR4rfH9vrdP8MXJuZPwZcBVwXEdcAvw58JjN/BHgB+HBx/IeBF4ryzxTHVc1HgSeatm2r7t6RmVc1TdHk32F7nwX+V2ZeDvwY9d8x26pFZh4tfp+uAt4KvAj8KbbVaSJiHPhlYCIzfxQYAbaynF+zMrMSX8DbgX1N2zuBncOu17C/gDXAN5u2jwKvLx6/HjhaPP5t4OZ2x1XxC/gfwLtsr57tdD7wNeBt1CdYP7coP/X3COwD3l48Prc4LoZd90Vso1XU32SvBb4AhG3Vtb2eAi5pKfPv8PR2uhD4Tuvvh23Vs91+BviKbdWxfcaBZ4CLi9egLwCbl/NrVmV6hHn1h9dwvCjTXD+Umd8rHv8t8EPFY9uvUHy0sxH4KrZXW8VH/YeA54AvAd8GpjPz5eKQ5vY41VbF/u8Dr1vcGg/VbwL/EXil2H4dtlU3Cfx5RDwWEduKMv8OT7cWOAH892LYzb0RcQG2VS9bgT8uHttWLTKzBvwX4Gnge9Rfgx5jGb9mVSkIa56y/l84pxVpEhE/AHweuDUz/7F5n+31qsw8mfWPGVcBVwOXD7lKS1JE/Gvgucx8bNh1WUZ+IjPfQv3j6Y9ExE827/Tv8JRzgbcAv5WZG4F/4tWP9gHbqlUxrvUG4E9a99lWdcU46Rup/0frUuACTh9iuaxUKQjXgMuatlcVZZrr7yLi9QDFv88V5ZVvv4gYpR6C78vMh4ti26uLzJwGHqH+UdmKiDi32NXcHqfaqth/IfD8Ild1WDYBN0TEU8D91IdHfBbbqqOiR4rMfI76OM6r8e+wnePA8cz8arH9EPVgbFt1dj3wtcz8u2LbtjrdO4HvZOaJzJwFHqb+OrZsX7OqFIQPAOuKOxvPo/7xx54h12kp2gN8sHj8QepjYRvl/664W/Ya4PtNHxmd9SIigN8FnsjMTzftsr1aRMTKiFhRPB6jPpb6CeqB+P3FYa1t1WjD9wP7i96Xs15m7szMVZm5hvpr0v7M/AC2VVsRcUFE/GDjMfXxnN/Ev8PTZObfAhgpHckAAAEXSURBVM9ExPqi6KeBx7GturmZV4dFgG3VztPANRFxfvG+2Pi9Wr6vWcMepLyYX8C7gb+mPl7xV4ddn2F/Uf+D/x4wS7334MPUx+58Gfgb4H8DFxfHBvVZN74NHKZ+x+jQv4dFbKufoP6x2DeAQ8XXu22vtm31ZmCqaKtvArcX5T8M/BVwjPpHj68pyl9bbB8r9v/wsL+HIbXbTwFfsK26ttEPA18vvo40Xsf9O+zYXlcBB4u/xUngItuqY1tdQL2n8sKmMtuqfVt9EvhW8fr+B8BrlvNrlivLSZIkqZKqNDRCkiRJOsUgLEmSpEoyCEuSJKmSDMKSJEmqJIOwJEmSKskgLEmSpEoyCEuSJKmSDMKSJEmqpP8P7lWEoRefcYIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}