mnistDuke.ipynb

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            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/RickLeite/mnist-DukeUniversity/blob/main/mnistDuke.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CvvH3q1OLzc7"
      },
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "from tqdm.notebook import tqdm"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573,
          "referenced_widgets": [
            "248ef4f8d09c45fca790e683f3d3ff9b",
            "eda5854612f44dc8bdfe8d220544b793",
            "8c9a7d975026439eb5f90f4664d03db5",
            "eadc91679f8747428ba68b856e19392b",
            "078a01befdf8441cb6758ed16a17df12",
            "0f26c5b4c0774678a3e9a9e5b6c75e86",
            "ac56d8244daa47e2a88bf59770e68538",
            "a077c3ba22f24623a29c418f5411103d",
            "5a061ff3ee2f4038bd598f8669361bef",
            "7d0931602d6644b99b8496a8894fa62b",
            "f2603c52e4d349289210d4a8ab540ee8",
            "654db666d74947bc981d5e3a21dad27b",
            "c6c43d4153cb4f6d806de7c942d56f7b",
            "6926a71e48774db69309b18b6fad6b14",
            "7ebc10d7e4914b32a73e864903f3e402",
            "b1ee65227ed34f4a9a2c2a565e3e09a1",
            "945613062f7b4f81b0828839f18acc8d",
            "ea56095d357c4174a0248bb43709d391",
            "9bfb8fb38b364dddbdf349332ef034de",
            "982234605f594dc3ac2e4eb5481ff06b",
            "396dffd90e454fc2a9021feaf1e0444e",
            "4ca044272f024d0ab8ab66941094806b",
            "91c23f5f3ba54962972d584a8410e67a",
            "b368eac77b8e42fc989779715c0ff891",
            "b76862ffa6d54760aae19ae98bdbe10b",
            "b8c753c3218043f98f794b3154901927",
            "b997eb8862e04c309603868037466828",
            "d9110d208a324e24a1e551ccacf0b348",
            "bc3e0cedcd9442af8854603e54d522fc",
            "d0b8f86adc6c410586a72e9ac143932b",
            "607b69e66265470fbe22716e998877a2",
            "b85adb78459847f287694f380f98ef98"
          ]
        },
        "id": "I2ZTiBgbMdUU",
        "outputId": "71b1daf9-8091-4245-b751-1e240ee6f4c9"
      },
      "source": [
        "from torchvision import datasets, transforms\n",
        "\n",
        "mnist_train = datasets.MNIST(root=\"./datasets\", train=True, transform=transforms.ToTensor(), download=True)\n",
        "mnist_test = datasets.MNIST(root=\"./datasets\", train=False, transform=transforms.ToTensor(), download=True)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./datasets/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "248ef4f8d09c45fca790e683f3d3ff9b",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=9912422.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ./datasets/MNIST/raw/train-images-idx3-ubyte.gz to ./datasets/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./datasets/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "5a061ff3ee2f4038bd598f8669361bef",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=28881.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ./datasets/MNIST/raw/train-labels-idx1-ubyte.gz to ./datasets/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./datasets/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "945613062f7b4f81b0828839f18acc8d",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=1648877.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ./datasets/MNIST/raw/t10k-images-idx3-ubyte.gz to ./datasets/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./datasets/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "b76862ffa6d54760aae19ae98bdbe10b",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=4542.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ./datasets/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./datasets/MNIST/raw\n",
            "\n",
            "Processing...\n",
            "Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/torchvision/datasets/mnist.py:502: 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:143.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1RShppYtNZEE",
        "outputId": "8bca7c5c-5d36-4e09-ed1c-2c0c81cc6ab1"
      },
      "source": [
        "print(\"Number of MNIST training examples: {}\".format(len(mnist_train)))\n",
        "print(\"Number of MNIST test examples: {}\".format(len(mnist_test)))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of MNIST training examples: 60000\n",
            "Number of MNIST test examples: 10000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "id": "glgG1cA2NwAS",
        "outputId": "358dddd2-aac9-412b-fad4-a0641a53368a"
      },
      "source": [
        "image, label = mnist_train[3]\n",
        "# Plot the image\n",
        "print(\"Default image shape: {}\".format(image.shape))\n",
        "image = image.reshape([28,28])\n",
        "print(\"Reshaped image shape: {}\".format(image.shape))\n",
        "plt.imshow(image, cmap=\"gray\")\n",
        "# Print the label\n",
        "print(\"The label for this image: {}\".format(label))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Default image shape: torch.Size([1, 28, 28])\n",
            "Reshaped image shape: torch.Size([28, 28])\n",
            "The label for this image: 1\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6csGLmYoOhiD"
      },
      "source": [
        "train_loader = torch.utils.data.DataLoader(mnist_train, batch_size=100, shuffle=True)\n",
        "test_loader = torch.utils.data.DataLoader(mnist_test, batch_size=100, shuffle=False)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QCWBAQY8OoIp",
        "outputId": "fe7051b9-4934-4646-d8fc-aedece68e3c6"
      },
      "source": [
        "data_train_iter = iter(train_loader)\n",
        "images, labels = data_train_iter.next()\n",
        "\n",
        "print(\"Shape of the minibatch of images: {}\".format(images.shape))\n",
        "print(\"Shape of the minibatch of labels: {}\".format(labels.shape))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape of the minibatch of images: torch.Size([100, 1, 28, 28])\n",
            "Shape of the minibatch of labels: torch.Size([100])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2lxbNSQ0PjpX",
        "outputId": "8b93aeec-6359-4f3d-983b-04c29507bb11"
      },
      "source": [
        "x = images.view(-1, 28*28)\n",
        "print(\"The shape of input x: {}\".format(x.shape))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The shape of input x: torch.Size([100, 784])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hngz6nCQRzr_"
      },
      "source": [
        "# Randomly initialize weights W\n",
        "W = torch.randn(784, 10)/np.sqrt(784)\n",
        "W.requires_grad_()\n",
        "\n",
        "# Initialize bias b as 0s\n",
        "b = torch.zeros(10, requires_grad=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XOsdfr-sSF4q"
      },
      "source": [
        "# Linear transformation with W and b\n",
        "y = torch.matmul(x, W) + b"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pKWT2iXISZMX",
        "outputId": "59d09eaa-f92f-4460-e8e8-13369592f7dd"
      },
      "source": [
        "print(y[0,:])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([-0.4972, -0.2483,  0.4735,  0.2043, -0.1219, -0.1566, -0.0216, -0.4513,\n",
            "        -0.0068, -0.4628], grad_fn=<SliceBackward>)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S32BlcNJS-e_",
        "outputId": "736c8e32-5c90-4c77-a116-92f4c90e9a45"
      },
      "source": [
        "# Option 1: Softmax to probabilities from equation\n",
        "py_eq = torch.exp(y) / torch.sum(torch.exp(y), dim=1, keepdim=True)\n",
        "print(\"py[0] from equation: {}\".format(py_eq[0]))\n",
        "\n",
        "# Option 2: Softmax to probabilities with torch.nn.functional\n",
        "import torch.nn.functional as F\n",
        "py = F.softmax(y, dim=1)\n",
        "print(\"py[0] with torch.nn.functional.softmax: {}\".format(py[0]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "py[0] from equation: tensor([0.0661, 0.0848, 0.1745, 0.1333, 0.0962, 0.0929, 0.1064, 0.0692, 0.1080,\n",
            "        0.0684], grad_fn=<SelectBackward>)\n",
            "py[0] with torch.nn.functional.softmax: tensor([0.0661, 0.0848, 0.1745, 0.1333, 0.0962, 0.0929, 0.1064, 0.0692, 0.1080,\n",
            "        0.0684], grad_fn=<SelectBackward>)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "29_gns1cUUmW",
        "outputId": "c4f1e016-45c9-4fcf-e376-a163db2d2dbd"
      },
      "source": [
        "print(labels.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([100])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gTgEpZdTUawD",
        "outputId": "c804f312-bc01-487a-ec21-2456a0fc3914"
      },
      "source": [
        "# Cross-entropy loss from equation\n",
        "cross_entropy_eq = torch.mean(-torch.log(py_eq)[range(labels.shape[0]),labels])\n",
        "print(\"cross entropy from equation: {}\".format(cross_entropy_eq))\n",
        "\n",
        "# Option 2: cross-entropy loss with torch.nn.functional\n",
        "cross_entropy = F.cross_entropy(y, labels)\n",
        "print(\"cross entropy with torch.nn.functional.cross_entropy: {}\".format(cross_entropy))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "cross entropy from equation: 2.5148797035217285\n",
            "cross entropy with torch.nn.functional.cross_entropy: 2.5148797035217285\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1-EQLRDxU-ce"
      },
      "source": [
        "# Optimizer\n",
        "optimizer = torch.optim.SGD([W,b], lr=0.1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dqPn6262VD5a"
      },
      "source": [
        "cross_entropy.backward()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VtAD_Y8gVJFc",
        "outputId": "0543cdaf-bd27-4507-c33f-91633fe77fd4"
      },
      "source": [
        "b.grad"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-0.0715, -0.0726,  0.0904, -0.0075,  0.0603,  0.0248, -0.0299,  0.0381,\n",
              "         0.0309, -0.0631])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t7avgEC7VO5D"
      },
      "source": [
        "optimizer.step()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mWUk4I5yVSj2",
        "outputId": "d4eb1240-47f1-4232-e82b-c53e53e67e24"
      },
      "source": [
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.0072,  0.0073, -0.0090,  0.0008, -0.0060, -0.0025,  0.0030, -0.0038,\n",
              "        -0.0031,  0.0063], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8REO0ndtVh6V",
        "outputId": "984bcac1-23b7-4c6c-9201-e51b9fb4f0cc"
      },
      "source": [
        "print(\"b.grad before zero_grad(): {}\".format(b.grad))\n",
        "optimizer.zero_grad()\n",
        "print(\"b.grad after zero_grad(): {}\".format(b.grad))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "b.grad before zero_grad(): tensor([-0.0715, -0.0726,  0.0904, -0.0075,  0.0603,  0.0248, -0.0299,  0.0381,\n",
            "         0.0309, -0.0631])\n",
            "b.grad after zero_grad(): tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 66,
          "referenced_widgets": [
            "3352aee9dce744b28020eae6be58fcd8",
            "33eb6fe699d3457eb361fb6fbf5e2d7c",
            "be34c8f1cf524a50960dbc049f77a537",
            "36447cf21167484795da298a5feb21f7",
            "4641c39d59344150aebf76d7e7ee37c9",
            "f7945df9fc154a56807e8beb1bbc279e",
            "2e1c8ddc736a4c7abd4316fb2f9057f1",
            "76761aeebf1e4a7ab9e670eb60c43917"
          ]
        },
        "id": "3tcYJSY5VuzA",
        "outputId": "523af4ff-f4a3-4143-deb1-792869de001d"
      },
      "source": [
        "# Iterate through train set minibatchs \n",
        "for images, labels in tqdm(train_loader):\n",
        "    # Zero out the gradients\n",
        "    optimizer.zero_grad()\n",
        "    \n",
        "    # Forward pass\n",
        "    x = images.view(-1, 28*28)\n",
        "    y = torch.matmul(x, W) + b\n",
        "    cross_entropy = F.cross_entropy(y, labels)\n",
        "    # Backward pass\n",
        "    cross_entropy.backward()\n",
        "    optimizer.step()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "3352aee9dce744b28020eae6be58fcd8",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=600.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 83,
          "referenced_widgets": [
            "572c92b68718456bb945efba9f36b1f6",
            "d824a4811efd4d2aa1961e175270e661",
            "5064a82ae12b4ca487a44846d13f16b4",
            "2ce393cb3be4408a8672fea8176ffa40",
            "6d5a687159344114a0e86ac928280e6f",
            "094bf50797f24eaeaa733f4c2c2741d5",
            "24b4f9d32b854e71893aff1b806010a2",
            "b53e00ac20de4541ad617985845c3003"
          ]
        },
        "id": "tFA3UiL0V9CV",
        "outputId": "c3577fe7-99c8-4445-b5a4-e31f21cf9d90"
      },
      "source": [
        "correct = 0\n",
        "total = len(mnist_test)\n",
        "\n",
        "with torch.no_grad():\n",
        "    # Iterate through test set minibatchs \n",
        "    for images, labels in tqdm(test_loader):\n",
        "        # Forward pass\n",
        "        x = images.view(-1, 28*28)\n",
        "        y = torch.matmul(x, W) + b\n",
        "        \n",
        "        predictions = torch.argmax(y, dim=1)\n",
        "        correct += torch.sum((predictions == labels).float())\n",
        "    \n",
        "print('Test accuracy: {}'.format(correct/total))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "572c92b68718456bb945efba9f36b1f6",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Test accuracy: 0.9023000001907349\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 145
        },
        "id": "P-ZZIFmEWMeM",
        "outputId": "14fd3930-f619-4cc2-89cf-558bdd3f215b"
      },
      "source": [
        "# Get weights\n",
        "fig, ax = plt.subplots(1, 10, figsize=(20, 2))\n",
        "\n",
        "for digit in range(10):\n",
        "    ax[digit].imshow(W[:,digit].detach().view(28,28), cmap='gray')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x144 with 10 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 132,
          "referenced_widgets": [
            "629285727a204ceca1ac441dc9bc9203",
            "af083d48fcbb483c99e32dfabd145ac3",
            "c6a897bcd47046baa8c0eb09615f66b5",
            "7785db48eb454563b6096c9eb4178a14",
            "24a6ba241ea547139016e2dfce873c13",
            "8b0c780b182b485c91f67d1be662a1af",
            "6d976d4070114ff887092e695647f5ff",
            "0b7669b4c88e49fb9c6f4fd8720b17e5",
            "ae07c05b329944bdb796eb4aa8af660a",
            "4c688ca58f5f4b8399108b1a05b01b88",
            "6d6801f02b024ee4a1dde7481cf16faf",
            "e3d77d568acc4530b1bf406d952cf427",
            "feca45d42aec47818e7960e3e0f05676",
            "6cf74098db654253a2ef93edc5b08f98",
            "e4d94cde94074c34a4a1f5b10a105896",
            "97c0a0aa25e2449591d3ec1edb9027ff"
          ]
        },
        "id": "vf-fUZL-YLEA",
        "outputId": "b5417db8-f2d0-4620-e27c-7a92327d4c2b"
      },
      "source": [
        "import numpy as np\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torchvision import datasets, transforms\n",
        "from tqdm.notebook import tqdm\n",
        "\n",
        "class MNIST_Logistic_Regression(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.lin = nn.Linear(784, 10)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.lin(x)\n",
        "\n",
        "# Load the data\n",
        "mnist_train = datasets.MNIST(root=\"./datasets\", train=True, transform=transforms.ToTensor(), download=True)\n",
        "mnist_test = datasets.MNIST(root=\"./datasets\", train=False, transform=transforms.ToTensor(), download=True)\n",
        "train_loader = torch.utils.data.DataLoader(mnist_train, batch_size=100, shuffle=True)\n",
        "test_loader = torch.utils.data.DataLoader(mnist_test, batch_size=100, shuffle=False)\n",
        "\n",
        "## Training\n",
        "# Instantiate model\n",
        "model = MNIST_Logistic_Regression()\n",
        "\n",
        "# Loss and Optimizer\n",
        "criterion = nn.CrossEntropyLoss()\n",
        "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n",
        "\n",
        "# Iterate through train set minibatchs \n",
        "for images, labels in tqdm(train_loader):\n",
        "    # Zero out the gradients\n",
        "    optimizer.zero_grad()\n",
        "    \n",
        "    # Forward pass\n",
        "    x = images.view(-1, 28*28)\n",
        "    y = model(x)\n",
        "    loss = criterion(y, labels)\n",
        "    # Backward pass\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "## Testing\n",
        "correct = 0\n",
        "total = len(mnist_test)\n",
        "\n",
        "with torch.no_grad():\n",
        "    # Iterate through test set minibatchs \n",
        "    for images, labels in tqdm(test_loader):\n",
        "        # Forward pass\n",
        "        x = images.view(-1, 28*28)\n",
        "        y = model(x)\n",
        "        \n",
        "        predictions = torch.argmax(y, dim=1)\n",
        "        correct += torch.sum((predictions == labels).float())\n",
        "    \n",
        "print('Test accuracy: {}'.format(correct/total))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "629285727a204ceca1ac441dc9bc9203",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=600.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "ae07c05b329944bdb796eb4aa8af660a",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Test accuracy: 0.9018999934196472\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}