demo01-basics.ipynb

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        "\n",
        "\n",
        "\n",
        "# PyTorch Basics\n",
        "\n",
        "I'll assume that everyone is familiar with Python. Training neural nets in bare Python is somewhat painful, but fortunately there are several well-established libraries which can help. I like PyTorch, which is built upon an earlier library called Torch. (There are many others, including TensorFlow and Jax, both of which I would encourage you to explore at your leisure.)\n"
      ]
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        "id": "VVRwR8OvAHWh",
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      "source": [
        "import numpy as np\n",
        "import torch\n",
        "import torchvision"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XC_zFy7KAL-h"
      },
      "source": [
        "Torch believes that everything is a *tensor*."
      ]
    },
    {
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      "execution_count": null,
      "metadata": {
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          "base_uri": "https://localhost:8080/"
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        "outputId": "3346cdbc-9386-4939-9e8d-f77f30fc870f",
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      "outputs": [
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          "name": "stdout",
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          "text": [
            "[[0.36886509 0.71902655 0.21237602]\n",
            " [0.08664056 0.92586243 0.75731764]]\n",
            "tensor([[0.3689, 0.7190, 0.2124],\n",
            "        [0.0866, 0.9259, 0.7573]], dtype=torch.float64)\n"
          ]
        }
      ],
      "source": [
        "a = np.random.rand(2,3)\n",
        "b = torch.from_numpy(a)\n",
        "\n",
        "print(a)\n",
        "print(b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lQ7Wv9RKAbe_"
      },
      "source": [
        "The main intuition is that tensors allow for intuitive and efficient matrix multiplication across different indexing dimensions. Soon we will see that training neural nets basically involves *forward* and *backward* passes, both of which are essentially matrix multiplies.\n",
        "\n",
        "The other thing about Torch variables is that they (natively) can be differentiated. (Again, we will see why this is important when we learn about backpropagation in deep learning.) "
      ]
    },
    {
      "cell_type": "code",
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      "metadata": {
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        "outputId": "b208c70b-c814-4913-de8f-77338bcfb980",
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      "outputs": [
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          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tensor([[1.6215],\n",
            "        [1.5528]], grad_fn=<AddBackward0>)\n"
          ]
        }
      ],
      "source": [
        "A = torch.rand(2,2)\n",
        "b = torch.rand(2,1)\n",
        "x = torch.rand(2,1,requires_grad=True)\n",
        "\n",
        "y = torch.matmul(A,x) + b\n",
        "\n",
        "print(y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "pJ3ClpQABNoM",
        "outputId": "2ddd1df0-b4e5-4681-c654-d54781c932bb",
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      "outputs": [
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          "output_type": "stream",
          "text": [
            "tensor(3.1743, grad_fn=<SumBackward0>)\n"
          ]
        }
      ],
      "source": [
        "z = y.sum()\n",
        "print(z)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3mzxp91VBY-A"
      },
      "source": [
        "Here, *z* is a function of the input *x*. Let us now compute the derivative of *z* with respect to *x* using backpropagation."
      ]
    },
    {
      "cell_type": "code",
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          "text": [
            "tensor([[1.4711],\n",
            "        [1.1740]])\n",
            "tensor([[0.8120],\n",
            "        [0.8263]], requires_grad=True)\n"
          ]
        }
      ],
      "source": [
        "z.backward()\n",
        "print(x.grad)\n",
        "print(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aaPN1ZSrBog5"
      },
      "source": [
        "# Training simple models\n",
        "\n",
        "OK, enough background. Let us now train a simple model. We will train a logistic classifier (equivalent to a single-layer neural network) on a popular image dataset called *Fashion-MNIST*. (TorchVision has several other image datasets which we can directly load as variables, feel free to train your own models on them). "
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      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz to ./FashionMNIST/FashionMNIST/raw/train-images-idx3-ubyte.gz\n"
          ]
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          "text": [
            "Extracting ./FashionMNIST/FashionMNIST/raw/train-images-idx3-ubyte.gz to ./FashionMNIST/FashionMNIST/raw\n",
            "\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz to ./FashionMNIST/FashionMNIST/raw/train-labels-idx1-ubyte.gz\n"
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        {
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          "output_type": "stream",
          "text": [
            "Extracting ./FashionMNIST/FashionMNIST/raw/train-labels-idx1-ubyte.gz to ./FashionMNIST/FashionMNIST/raw\n",
            "\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz to ./FashionMNIST/FashionMNIST/raw/t10k-images-idx3-ubyte.gz\n"
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          "metadata": {},
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        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Extracting ./FashionMNIST/FashionMNIST/raw/t10k-images-idx3-ubyte.gz to ./FashionMNIST/FashionMNIST/raw\n",
            "\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz to ./FashionMNIST/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
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        {
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          "metadata": {},
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        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Extracting ./FashionMNIST/FashionMNIST/raw/t10k-labels-idx1-ubyte.gz to ./FashionMNIST/FashionMNIST/raw\n",
            "\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/torchvision/datasets/mnist.py:498: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  /pytorch/torch/csrc/utils/tensor_numpy.cpp:180.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ]
        }
      ],
      "source": [
        "trainingdata = torchvision.datasets.FashionMNIST('./FashionMNIST/',train=True,download=True,transform=torchvision.transforms.ToTensor())\n",
        "testdata = torchvision.datasets.FashionMNIST('./FashionMNIST/',train=False,download=True,transform=torchvision.transforms.ToTensor())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E8jilneICxoQ"
      },
      "source": [
        "Let's quickly check that everything has been downloaded."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HGpkNdXDC0MW",
        "outputId": "9bafbab8-5fd3-433d-e940-843e391f4c7e",
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      "outputs": [
        {
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          "output_type": "stream",
          "text": [
            "60000\n",
            "10000\n"
          ]
        }
      ],
      "source": [
        "print(len(trainingdata))\n",
        "print(len(testdata))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nq_r5NZ6C4qp"
      },
      "source": [
        "Some of you might know that this is the same size as the (very commonly used) MNIST dataset. Let's plot some images."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ESuk-dMuDI50",
        "outputId": "ab842f9f-cf14-4c18-90cc-31d1ebe4a20d",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "torch.Size([1, 28, 28]) 9\n"
          ]
        }
      ],
      "source": [
        "image, label = trainingdata[0]\n",
        "print(image.shape, label)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aNUYBPGvDRGR"
      },
      "source": [
        "We cannot directly plot the 'image' object since it is a Torch tensor, so let's convert it back into a numpy array before displaying it. We will use matplotlib to show images."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "VFwxybfdDdJm",
        "outputId": "63972b4d-25a5-484d-b43a-ad9d21eb1a59",
        "vscode": {
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      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.imshow(image.squeeze().numpy())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ypDJepyWDviB"
      },
      "source": [
        "OK, that kinda sorta looks like a shoe? FashionMNIST is basically a bunch of black-white thumbnail images of different pieces of clothing. Let's try and plot a few of them. To step through the dataset, it will be helpful to construct a *data loader* object; we will use this while training our model below as well."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hnES23k0EN4_",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "trainDataLoader = torch.utils.data.DataLoader(trainingdata,batch_size=64,shuffle=True)\n",
        "testDataLoader = torch.utils.data.DataLoader(testdata,batch_size=64,shuffle=False)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7wj4aUENEiTf"
      },
      "source": [
        "Let's now use the DataLoader object to spit out a few images from the dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 146
        },
        "id": "aQkgEdydEoHH",
        "outputId": "7681829a-87f5-456e-8ab2-5d9755008dfa",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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ul+c6Q4cODY65zNAzzzwT6DgO7r777kMaRbDl9ddf7+Ubbrgh0PF7ziUaAGDjxo1eXrZsWaCbN2+elzmlAxA+b465sPEvHPP4zjvvBDp+9gMHDgx0nEKB49SAsDwFx0MBwM9//nMvP/jgg6iGItizGnjc7d69e6Bje9mYFluWKw2On7NlePbs2eNlG0+TtdRPZ9CstmwP7hOxtD4c92vPGzFihJeffPLJQMdlgfr169exxtYBZSIXQgghhMiJJlBCCCGEEDnpcBqDesBuO7tEzDp2GQDhkqJd4s+6jZ1danY7ZixrOLvt7NZPztJq0yvwMrRd+rTbgEX7dPZWZrazfQeGDBni5enTw5x57JrbsWNHoOP3mLf1AkfTeBRlizZn/7fpOjityOuvv56qsxmNud+uXbs20LE7n69ht7dzFmP7DC+55JI2r2GxLnTum7wVGwA+85nPeLlaF16zYkMnGLat7R/sxo3BduCUNkD4PlgXYZZUHyIfZ599tpf5dwwIf+f4nbChJ/w5+9u4d+9eL9vQlyKiFSghhBBCiJxoAiWEEEIIkZOmcOHxcrldlh08eLCXbdFQu6zPsHvMuhDYPRIrGMxL+ta1yO4M627hpWy7c4R399glb+vuE/UhbScfcKyNGC6iuXDhwkDHWZhtgezvfve7Xp45c2ag69u3L4BwqbuRnH766V62bvKYi5t3JQ4bNizQvfbaa162RcA5G3/s2XNf4Z1aAHDuued62Rbofuqpp7xs+zTv+LVVAVjX1eB32YZG8Jhpx9mY649hl/aR9/8IPH5a99769eszXV+kY39D2U1qQw/Y5ca2sLtZuX/3798/0LFLz44nPNbYiiSNQitQQgghhBA50QRKCCGEECInmkAJIYQQQuSkKWKgOH2AjRniOAvrA+dzbfxQLH6C/fh8jTxZqGPbd/lzBw4cCHQcN2O35XIaA5sJ+eDBg6ltEcdSbUbxGDZLPleYt9m2f/KTn3j5S1/6UqD78Y9/7GXOcA0cjQex8QGNgt9Rm0aEn6ntfxz3ZeOJuO/YOCTuS/w5G1/DsTc2HQinLti0aVOg40zkdvv1tddem6qLVakvOxwDZVO98Htq+1jWTOFsP7t1nmN07LZ3a1uRHxu/xClBOGs4AFx88cVefvHFF71s+wbHP9ps9PY3j+E+pxgoIYQQQogmRRMoIYQQQoicFNKFZ10hvJXZZgDmjMPWFRDL6s3LzjFi1+AlaOum43Otu4WvaZcs+fvY+zH2OciF1z6xdAQxYufyEveECRMC3T333ONlu5We7Xf77WFR9rvuusvL1i1ts303GnbNWfcKu9Ws6z2WAoQ/Z589n8vbmu157KaL9T8u3AyE7tQ//vGPgY7HDHu/ruzC42LN1oXHtrTj2bZt2zJdn7e9cyZsez/rQl69enWm64t0Bg0aFBzz75zt73w8atQoL9uUK/xO2DQlXEDY2pNTFr300kvtNb0uaAVKCCGEECInmkAJIYQQQuREEyghhBBCiJwUMgaqZ8+ewTH7QjnuAQj977t27Uq9pk1Jn3ULLcdPxKpD26ru7Oe192adLWfAPuCBAwcGOo7xsmkMRH340Y9+FByPHj3ay7Nnzw50V155pZdXrFgR6GJxVRyH88QTT1TVzs7CxitxXIt9z7nv2PgXPtc+C45Rsn2Oz+U+Z2MQOY2BjYHiuBmr49iNyZMnBzr+7i0tLYGuK8dA8TO04yo/M5vKIuu7vWTJEi/HbGJLIsVS1Yij2H7L/c/G2rKtOeUOEMZn8jVt/OPmzZu9bPs328zqOIVCUdAKlBBCCCFETjSBEkIIIYTISSFdeHYrLLu5hgwZEug426xdwmW3QSyDuV3CZNcAf85eg5ePOf0AEKYVsEvX7MKz29JjbglePrVuTtE+WVMXWDcVv3PsYgWA733ve15evnx5B1p3lEmTJnn56aefrsk1a4V1HXPfse6wWNoI7i+xrPC2b6bBLjuLdR/y9Tm7PxCOIRs3bgx0nDX5ggsuCHSxdCfWvV82+LvbMYvHPqtrbW3NdH3esn7GGWcEOk4tEQuxEOnY3zXG/s7wu8zhM0Do7uMqDFOmTAnOYxee7Rv2mkysjzcKrUAJIYQQQuREEyghhBBCiJxoAiWEEEIIkZNCxkDZGBROBX/eeecFOva7rlq1KtDxuVlLt1g4nsHGOXHshi25wSkVbBwHx2DYKvLsc7bfh9Pq29gN0THYzjbOjtNJcIoB4NhSBGnXzBMHw3EAHC9QBGwMVCzOKRaTwufaz2VNMRI7L6bjGEsuEwIAjz76qJdtPAb3VRuLM3HiRC/buBFbyqLM2PGM7WBjbWypjjR47LblX3hstSluRMex7zLH7A4dOjTQsS1YZ8cMHheszTgdiP3dtCkVioBWoIQQQgghctLuBMo5N8A5t9Q5t845t9Y597XK309zzi12zrVU/l+86aE4BtmyPKhvlgvZsjyob3YNsrjwPgDwjSRJVjrnTgbwonNuMYCbACxJkuR259xsALMB3FqLRln3FG9/tcu+7G555ZVXAh1nFbafi7nAeDs2n2eXFA8cOJB6Dc6aaqtWcwV460LgJVKbpZxdSSeffHLqvduhrrZsFvr37+/lvn37BjpOlRFz2VnYZRHL9muxLsQIde+b1r0ec+HFsK4eJvZs0u4d08Wy9v/yl78MjqdPn+7lRx55JNDdeeedXp4zZ06gGzt2rJdtBYEcLrym7Jv8btsUNDEdj61cZcHCbiQ77vEYnNX1Wyfq3jc7A9sXY31px44dXuY+YH97e/Xq5eUNGzYEOg5TsS70DvzmdRrtrkAlSdKaJMnKinwAwHoA/QB8FsC9ldPuBTC97SuIIiFblgf1zXIhW5YH9c2uQa4gcufcIABjACwH0DtJkiOZ0HYC6J3ymVkAZlXfRNEZyJblQvYsD7JluZA9y0vmIHLn3EkAfg/g60mSBD6p5PDafZvr90mSzEuSZFySJOM61FJRM2TLciF7lgfZslzInuUm0wqUc64bDr8E9ydJ8ofKn3c55/okSdLqnOsDYHf6FfLRo0eP4JjjJWw80f79+71s/eicWuCNN95IvZ/18/L9OH283YrOWzBtu/hztoQB+/T//Oc/B7prrrnGyzZOi33M1fr7O8OWsVIceeCt4bby9pYtW7xs7RB7FmltsVti+d62vI7102el2ucwbtzRMTNWrRyof9+025qzll2xzyL2bGKxY2nY8/g52Zikxx57zMuf+tSnAh3b3m6x5pIitjxFS0uLl22cWFbqbctaEbMXp/KwqWTsmJkGj6X2+hxXlSc+sR40qz0ZO/7w2Gvtyb/bPF4PHjw49fq2PAunbRkzZkyge+6559pvcJ3JsgvPAbgbwPokSeaS6mEAN1bkGwE8VPvmiU5AtiwJ6pulQ7YsCeqbXYMsK1D/BeAGAK845478E+x/AdwO4AHn3M0AtgC4tnOaKGqMbFke1DfLhWxZHtQ3uwDtTqCSJHkGQJqP5NLaNucwdlmPXTScqRQIt0jysqG9jq0UzzpbPZ2XJnl52rp2eJul3d7J7bJLnXyuzTTNrg2uZA6ErsWsrg1LkiQ1s2UWN2LMvTdt2rRAx9u9t2/fHuh4eyunFbDXjMHvTu/eYewmu2uefvrpTNdrD25XHpdr1gzmjeibtq9U62Jj7LPhc62Oj2NZrtmdYLdRz54928t33HFHoNu6dauXr7766kD3wgsveHnmzJmBju9RbZWAWvbNRmFTu7A706ZlyZqdf9++fV62duZxPBamUW8a0Tc7g1j6FZvuhfsOh0ScddZZwXnsCrc67jtvvvlmFS2uL8pELoQQQgiRE02ghBBCCCFyogmUEEIIIUROciXSrBextAI21ohLoVj/O29x5fIpQOg7t5/j7bB8b1t+guMebGwIp523cVvsV7bxPBwvZbdDcyxArNJ9vcgSexQ7Z9myZcFxv379vGyrrnNZnjzwO8B+ebu1/eWXX/ZyvbdDW1suWrTIy9WmQugsbD+KxXllLbViyRovFSsjw890165dqdd79913g2Pu04sXLw50v/rVr7y8bt26QPenP/3Jy7EyNWXHxnQOHz7cyzZ1SFY4Vsrai9OdcHoKURvs7y3/Jtn3/OMf/7iXOT6YS7cAYSoUGwfH4/LOnTsDXSwdQqPQCpQQQgghRE40gRJCCCGEyEkhXXh2+z5jtzbaJWNm2LBhqTpeOrTbjjldAbt9rNuBUyPYrMXsIrTfx7pBGP4+nEkdCJevG115vFu3bv572OfHWaCtvXgZ9gc/+EGgu+WWW7wcy+ZsnwsvM9slZ7Zz//79vczuUABobW1Fo7DZxUeOHNmglrSPzRBv04MwvMRv3fJZ39+s59k+xhUKLrrookB33333efmhh8I8hvxuLV26NPV+9nOvvvqql+3W7K6EDYdgd2y129LZ5WNT3PD1rcuHqVW1hK6GDU1h2E0HhPadNGmSlznMBgjDVKxLlsdl6yIsos20AiWEEEIIkRNNoIQQQgghcqIJlBBCCCFETgoZA2XjU3j7q/WDxspu/OY3v/Gy9c3HYjc4JoVjcey9Dx065GXrY+dt1HZbto3TYfj7TJ06NfVz69evT71GPXDO+RQBdpsq+7jtFv2xY8d62W5hvfTSoxUOPv/5zwc6jjnhki8AsHz58tRrcswO67gsRz2w/nxuiy2JcM4559SlTdVgY1Bi5ThsbBeTNY2B7XNpn7Pt4M/Zvs+pCuzW+liKkZtvvtnLI0aMCHQcuxiL4Sw7tmwVH2ct3WLh+DkbM8PP2sbnMUWMn2kGbBmkt99+28uxtD4cHxU7L5aOx97bHhcBrUAJIYQQQuREEyghhBBCiJwU0oVnUxMMGjTIyzZL9KpVq1Kv8/3vf7+WzaoLnNHYurE4pQJnzm4E7733nreTtRe7PTkjOwAsXLiwTRkArrrqKi/PnTs30HEFb97WfKQtR7BZ39lV++yzzx7zPY6QluEaOHYLfjXEXFY2LcODDz7Y4ft1FpxtGAifN6f/AMIs8DGsiztrJvLYZ/g8m2aD3Qvjx48PdOwmnzJlSqCbPHmylzltgeXCCy9M1ZWdCRMmBMf8flhXdVY47YtNAcPjC2c9t9j3oxZ9uiswevTo4JjT9QwYMCDQ2VCOIwwdOjQ4Xr16tZete4+vb0MAJk6cmKHF9UUrUEIIIYQQOdEESgghhBAiJ5pACSGEEELkpJAxULasxuOPP+5l6+fesWNH6nXY791In7eN2+B22XQKHONlSx+sXLmyE1pXe/g72Ji1GFljf2IlG2LvQwze5twZW55jW/rXrFkTHH/lK1+p+f1rxZNPPhkcc2megwcPBrrYdv5Y3+Rj23dqUcJow4YNXrbxGRyzY2P75s2b5+U9e/akXt/G9nUlZs2aFRxff/31XubnngeON1u0aFGg4zi7u+++O/UainmqjhUrVgTHnMaEY3KBMF0Ix6naMmctLS1eHjJkSKDbuHGjl3fv3h3obPqaIqAVKCGEEEKInGgCJYQQQgiRE1fPDK3OuT0AtgA4A0AR1uO6WjsGJklyZvuntY9sGaUebamZLQFvz4PoWs8wC+qbHaco7QDUN2tBUezZ8L5Z1wmUv6lzLyRJMq7uN1Y7ak5R2l6UdgDFakseitTuorSlKO2ohqK0vSjtAIrVljwUqd1FaUsR2iEXnhBCCCFETjSBEkIIIYTISaMmUPPaP6UuqB0dpyhtL0o7gGK1JQ9FandR2lKUdlRDUdpelHYAxWpLHorU7qK0peHtaEgMlBBCCCFEMyMXnhBCCCFETjSBEkIIIYTISV0nUM65K5xzG5xzm5xzs+t873ucc7udc2vob6c55xY751oq/z+1Du0Y4Jxb6pxb55xb65z7WqPa0hFky/LYEpA9K/cshT1ly/LYEpA9i2zLuk2gnHPHAbgLwJUARgK4zjk3sl73BzAfwBXmb7MBLEmSZBiAJZXjzuYDAN9IkmQkgPEA/rvyHBrRlqqQLT1Nb0tA9iSa3p6ypafpbQnInhWKa8skSeryH4BLADxOx3MAzKnX/Sv3HARgDR1vANCnIvcBsKGe7anc9yEAlxehLbJl17Ol7Fkue8qW5bGl7Fl8W9bThdcPwFY63lb5WyPpnSRJa0XeCYMxmycAAAFsSURBVKB3PW/unBsEYAyA5Y1uS05kS0MT2xKQPY+hie0pWxqa2JaA7BlQNFsqiLxCcngaW7ecDs65kwD8HsDXkyR5u5FtKRuyZbmQPcuDbFku6vkMi2jLek6gtgMYQMf9K39rJLucc30AoPL/3fW4qXOuGw6/CPcnSfKHRralSmTLCiWwJSB7ekpgT9myQglsCcieqNynkLas5wTqeQDDnHODnXPHA5gB4OE63r8tHgZwY0W+EYd9q52Kc84BuBvA+iRJ5jayLR1AtkRpbAnIngBKY0/ZEqWxJSB7FtuWdQ7+mgpgI4BXAfxfne+9AEArgPdx2I98M4DTcTh6vwXAEwBOq0M7JuLwUuPLAF6q/De1EW2RLWVL2bN89pQty2NL2bPYtlQpFyGEEEKInCiIXAghhBAiJ5pACSGEEELkRBMoIYQQQoicaAIlhBBCCJETTaCEEEIIIXKiCZQQQgghRE40gRJCCCGEyMn/A8IvJQycuNDLAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 720x288 with 5 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "images, labels = iter(trainDataLoader).next()\n",
        "\n",
        "plt.figure(figsize=(10,4))\n",
        "for index in np.arange(0,5):\n",
        "  plt.subplot(1,5,index+1)\n",
        "  plt.imshow(images[index].squeeze().numpy(),cmap=plt.cm.gray)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5xm_XdCDE9bY"
      },
      "source": [
        "OK! Time to set up our model. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fJy4Ow0WJ6Te",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "class LinearReg(torch.nn.Module):\n",
        "  def __init__(self):\n",
        "    super(LinearReg, self).__init__()\n",
        "    self.linear = torch.nn.Linear(28*28,10)\n",
        "\n",
        "  def forward(self, x):\n",
        "    x = x.view(-1,28*28)\n",
        "    transformed_x = self.linear(x)\n",
        "    return transformed_x\n",
        "\n",
        "net = LinearReg().cuda()\n",
        "Loss = torch.nn.CrossEntropyLoss()\n",
        "optimizer = torch.optim.SGD(net.parameters(), lr=0.01)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xs9-dDLsKFrc"
      },
      "source": [
        "Cool! Everything is set up. Let's now train our network."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M7uJydfJKNf1",
        "outputId": "b64686dd-004c-4e37-8a38-d5729573ca51",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 0, Train loss 0.9628831866199273, Test loss 0.7384625394253215\n",
            "Epoch 1, Train loss 0.669227090471589, Test loss 0.6481344644810744\n",
            "Epoch 2, Train loss 0.6048530459658169, Test loss 0.6072135472753245\n",
            "Epoch 3, Train loss 0.569712356558995, Test loss 0.5793859970038104\n",
            "Epoch 4, Train loss 0.5466805504583346, Test loss 0.5610787272453308\n",
            "Epoch 5, Train loss 0.5301150181717964, Test loss 0.5491215814450744\n",
            "Epoch 6, Train loss 0.517360219346689, Test loss 0.5395579376038472\n",
            "Epoch 7, Train loss 0.5070971899640078, Test loss 0.53012230726564\n",
            "Epoch 8, Train loss 0.4986808753248725, Test loss 0.5227101813456055\n",
            "Epoch 9, Train loss 0.4913868474871365, Test loss 0.5153622133716657\n",
            "Epoch 10, Train loss 0.48511413920090907, Test loss 0.51091866508411\n",
            "Epoch 11, Train loss 0.4795060167942983, Test loss 0.5053211141164136\n",
            "Epoch 12, Train loss 0.4750948576911934, Test loss 0.5025345730553766\n",
            "Epoch 13, Train loss 0.47048642020871134, Test loss 0.5005893255494962\n",
            "Epoch 14, Train loss 0.46683460000608523, Test loss 0.49515608503560354\n",
            "Epoch 15, Train loss 0.4634541854866024, Test loss 0.4925980729282282\n",
            "Epoch 16, Train loss 0.46015855986108656, Test loss 0.49006823046951536\n",
            "Epoch 17, Train loss 0.45749055062021526, Test loss 0.48770458986804743\n",
            "Epoch 18, Train loss 0.4546464907049116, Test loss 0.48619903880319776\n",
            "Epoch 19, Train loss 0.45197508274428627, Test loss 0.4853660855323646\n"
          ]
        }
      ],
      "source": [
        "train_loss_history = []\n",
        "test_loss_history = []\n",
        "\n",
        "for epoch in range(20):\n",
        "  train_loss = 0.0\n",
        "  test_loss = 0.0\n",
        "  for i, data in enumerate(trainDataLoader):\n",
        "    images, labels = data\n",
        "    images = images.cuda()\n",
        "    labels = labels.cuda()\n",
        "    optimizer.zero_grad()\n",
        "    predicted_output = net(images)\n",
        "    fit = Loss(predicted_output,labels)\n",
        "    fit.backward()\n",
        "    optimizer.step()\n",
        "    train_loss += fit.item()\n",
        "  for i, data in enumerate(testDataLoader):\n",
        "    with torch.no_grad():\n",
        "      images, labels = data\n",
        "      images = images.cuda()\n",
        "      labels = labels.cuda()\n",
        "      predicted_output = net(images)\n",
        "      fit = Loss(predicted_output,labels)\n",
        "      test_loss += fit.item()\n",
        "  train_loss = train_loss/len(trainDataLoader)\n",
        "  test_loss = test_loss/len(testDataLoader)\n",
        "  train_loss_history.append(train_loss)\n",
        "  test_loss_history.append(test_loss)\n",
        "  print('Epoch %s, Train loss %s, Test loss %s'%(epoch, train_loss, test_loss))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ioCw2SGkLMa-"
      },
      "source": [
        "Let's see how we did! We have tracked the losses so let's plot it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "xJL3FKJOLRWB",
        "outputId": "f3450716-2537-4dba-c1e2-ee31136dfc34",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3a6a163e50>"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(range(20),train_loss_history,'-',linewidth=3,label='Train error')\n",
        "plt.plot(range(20),test_loss_history,'-',linewidth=3,label='Test error')\n",
        "plt.xlabel('epoch')\n",
        "plt.ylabel('loss')\n",
        "plt.grid(True)\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-DsItFbLUdx"
      },
      "source": [
        "Not too bad (although more epochs would have helped, I suppose). Let's evaluate our final model on a few more images to wrap things up."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fk636QriLdGH",
        "outputId": "46196175-8e02-4a1f-f5f4-d3cefd886117",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "torch.return_types.max(\n",
            "values=tensor([ 6.0992,  2.8152,  8.9309,  7.8008,  6.4660,  5.8649, 10.1909,  4.3178,\n",
            "         6.8928, 11.3527, 10.3758, 10.0492,  6.7620,  4.6565,  9.3138,  4.4809],\n",
            "       device='cuda:0', grad_fn=<MaxBackward0>),\n",
            "indices=tensor([3, 1, 7, 5, 8, 2, 5, 6, 8, 9, 1, 9, 1, 8, 1, 5], device='cuda:0'))\n",
            "tensor([3, 2, 7, 5, 8, 4, 5, 6, 8, 9, 1, 9, 1, 8, 1, 5], device='cuda:0')\n",
            "tensor(0.3159, device='cuda:0', grad_fn=<NllLossBackward>)\n"
          ]
        }
      ],
      "source": [
        "predicted_output = net(images)\n",
        "print(torch.max(predicted_output, 1))\n",
        "fit = Loss(predicted_output, labels)\n",
        "print(labels)\n",
        "print(fit)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UH_5Ra7HMQhz"
      },
      "source": [
        "Cool, looks like 2 images in this batch are being misclassified; can you (as a human) guess what those are?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 593
        },
        "id": "SBFBElVML1vw",
        "outputId": "8c236e81-3a13-4d0c-f27a-0f89c670a26d",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 720x720 with 16 Axes>"
            ]
          },
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      ],
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      ]
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