dl_demo04.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YzXeTwhwlU_x"
      },
      "source": [
        "# Fun with Convolution \n",
        "\n",
        "The concept of *convolution* is fundamental to understanding modern deep network architectures (indeed, the success of deep convnets in object recognition was arguably the major driver in kickstarting the current wave of AI starting from the early 2010s). \n",
        "\n",
        "But convolution can be quite tricky to internalize, particularly when taught from a mathematical viewpoint. This short tutorial is non-mathematical in its treatment, and instead presents a visualization of 2D convolution of an input image with various filters. We will explore both filtering and pooling, both of which are commonly used operations in convnets."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "FNCfBOgwlSGw"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim\n",
        "import torch.utils.data as data\n",
        "\n",
        "import torchvision.transforms as transforms\n",
        "import torchvision.datasets as datasets\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xmFwYlRcnOl-"
      },
      "source": [
        "As visualization examples we will use the MNIST dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mgegj-pQnNjS",
        "outputId": "815bb510-9f2a-492d-f241-4b82b53ea1c9"
      },
      "outputs": [
        {
          "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": [
        "ROOT = '.data'\n",
        "mean = 0.13066 # we use this for normalization\n",
        "std = 0.30810 # we use this for normalization\n",
        "test_transforms = transforms.Compose([\n",
        "                           transforms.ToTensor(),\n",
        "                           transforms.Normalize(mean = [mean], std = [std])\n",
        "                                     ])\n",
        "\n",
        "test_data = datasets.MNIST(root = ROOT, \n",
        "                           train = False, \n",
        "                           download = True, \n",
        "                           transform = test_transforms)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2znIj7NOoILd"
      },
      "source": [
        "Let us also add some boilerplate code for plotting images."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "bbNMxDiUoLs8"
      },
      "outputs": [],
      "source": [
        "def plot_filter(images, filtered_images):\n",
        "    \n",
        "    n_images = images.shape[0]\n",
        "\n",
        "    fig = plt.figure(figsize = (20, 5))\n",
        "    \n",
        "    for i in range(n_images):\n",
        "\n",
        "        ax = fig.add_subplot(2, n_images, i+1)\n",
        "        ax.imshow(images[i].squeeze(0), cmap = 'bone')\n",
        "        ax.set_title('Original')\n",
        "        ax.axis('off')\n",
        "\n",
        "        image = filtered_images[i].squeeze(0)\n",
        "\n",
        "        ax = fig.add_subplot(2, n_images, n_images+i+1)\n",
        "        ax.imshow(image, cmap='bone')\n",
        "        ax.set_title(f'Output')\n",
        "        ax.axis('off');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wthw3ABiouEq"
      },
      "source": [
        "We can now try some basic filtering operations. Let us first grab some images from the test dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "TO6PJDropSXg"
      },
      "outputs": [],
      "source": [
        "num_images = 5\n",
        "images = []\n",
        "\n",
        "for i in range(num_images):\n",
        "  image, label = test_data[i]\n",
        "  images.append(image)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lRJAOZfmrqJp"
      },
      "source": [
        "Let's convert to a Torch tensor by adding a singleton dimension."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "GMj6yr7Grpel"
      },
      "outputs": [],
      "source": [
        "images = torch.cat([img.unsqueeze(0) for img in images], dim = 0)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jhnNcAkxr59n"
      },
      "source": [
        "We can now start using these images for illustrating 2D convolution. The `conv2d` function in Torch is perfect for this. \n",
        "\n",
        "Convolution, at a high level, takes every small window of input pixels, computes their weighted linear combination (where the weights are the filter values), and produces an output pixel. \n",
        "\n",
        "Two key points to note here:\n",
        "* Each output pixel only depends on a small *local* neighborhood of input pixels.\n",
        "* The weights of the filter remain the same no matter whether one is computing the first output pixel, or the second, or anywhere in the output (i.e., the filter is *shift-invariant*).\n",
        "\n",
        "To illustrate: let's start with a small 2x2 filter with all ones. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "7T2mwlTsoXKK",
        "outputId": "28f3429c-dcaf-4575-dd92-f7c19eaee60f"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1440x360 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "filter = [[1,1],\n",
        "          [1,1]]\n",
        "filter = torch.FloatTensor(filter).unsqueeze(0).unsqueeze(0)\n",
        "\n",
        "filtered_images = F.conv2d(images,filter)\n",
        "plot_filter(images, filtered_images)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BhLbQFLgsuh4"
      },
      "source": [
        "Hmm, can't really see much here (although the outputs look slightly grayer than the inputs). \n",
        "\n",
        "Also, if you examine the size of the output, you can see that the size has decreased by 1. (Reason why this is the case by counting the number of possible windows in the input image.)\n",
        "\n",
        "What if we increase the size of the filter?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "R69QYvoOs6N0",
        "outputId": "c56cde54-d345-4a85-8149-c630c5c6ecec"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1440x360 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "filter = [[1,1,1,1,1],\n",
        "          [1,1,1,1,1],\n",
        "          [1,1,1,1,1],\n",
        "          [1,1,1,1,1],\n",
        "          [1,1,1,1,1]\n",
        "          ]\n",
        "filter = torch.FloatTensor(filter).unsqueeze(0).unsqueeze(0)\n",
        "\n",
        "filtered_images = F.conv2d(images,filter)\n",
        "plot_filter(images, filtered_images)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OhNo7-SKtFAk"
      },
      "source": [
        "The effect is now much more visible. \n",
        "\n",
        "The all-ones filter averages (or smears) out values of the input, therefore producing blurry image outputs. Play around with different filter sizes to see what happens. At what point does the output become completely unrecognizable?\n",
        "\n",
        "\n",
        "Let us now try an different filter. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "ZZ7gUFgHuWDo",
        "outputId": "53cf7e8a-288e-4a6e-bfdf-1af33ffcfa71"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1440x360 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "filter = [[1,1],\n",
        "          [-1,-1]]\n",
        "filter = torch.FloatTensor(filter).unsqueeze(0).unsqueeze(0)\n",
        "\n",
        "filtered_images = F.conv2d(images,filter)\n",
        "plot_filter(images, filtered_images)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XYsTCFucuo4T"
      },
      "source": [
        "Interesting. If you stare carefully, features that are *vertical* (such as most of the 1, or the left side of the 0, or the stalk of the 4) have been grayed out, while features that are *horizontal* (such as the bar of the 7, or the bar of the 4) are bright. This particular filter is a type of *horizontal edge detector*. The effect is slightly more pronounced if we use 3x3 filters."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "H2xHbbsewKtu",
        "outputId": "6f309915-a89b-49a8-8b45-1a8b7c335af9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1440x360 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "filter = [[1,2,1],\n",
        "          [0,0,0],\n",
        "          [-1,-2,-1]]\n",
        "filter = torch.FloatTensor(filter).unsqueeze(0).unsqueeze(0)\n",
        "\n",
        "filtered_images = F.conv2d(images,filter)\n",
        "plot_filter(images, filtered_images)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TnNyFrW3w7N3"
      },
      "source": [
        "See if you can get better edge detection using other filters. Play around also with the direction; how would you detect vertical edges?\n",
        "\n",
        "\n",
        "Let us now also examine pooling. This is related to filtering, and is used to reduce resolution (size) of the input image. Like convolution, this also happens by operating on windows of the input; the difference, however, is that we now use a *stride*, i.e., we skip over certain windows. For example, with stride = 2, we skip computing output of every 2nd window; this means that the output is (approximately, barring fence effects) half the size of the input.\n",
        "\n",
        "The two most common types of pooling are *average* pooling and *max* pooling."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "4_BWEqMSzDN4",
        "outputId": "3f0a4e49-ce87-419a-e8d8-d5f2e066ea1b"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1440x360 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pooled_images = F.avg_pool2d(images,kernel_size=3)\n",
        "plot_filter(images, pooled_images)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5wbs8TZHzs0N"
      },
      "source": [
        "As visually evident, the output looks blocky and very low-res. Also, since we used average pooling here, the output is grayed out. Max-pool retains brightness (since the output is the max of the values in the given window)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 373
        },
        "id": "YmfVPjnmz_XT",
        "outputId": "73ad5c2c-00e7-4adf-e268-22691edeb18b"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/torch/nn/functional.py:718: UserWarning: Named tensors and all their associated APIs are an experimental feature and subject to change. Please do not use them for anything important until they are released as stable. (Triggered internally at  /pytorch/c10/core/TensorImpl.h:1156.)\n",
            "  return torch.max_pool2d(input, kernel_size, stride, padding, dilation, ceil_mode)\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1440x360 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pooled_images = F.max_pool2d(images,kernel_size=2)\n",
        "plot_filter(images, pooled_images)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UNbDS0ED0WKp"
      },
      "source": [
        "This is basically it! We now know what these elementary operations (filtering and pooling) mean in the context of convnets. \n",
        "\n",
        "In essence, the forward pass of any convolutional network (however deep) involves some combination of filtering and pooling operations as discussed above, interspersed with nonlinear (pixel-wise) activations, Sometimes possibly other types of pointwise operations such as batch-norm or drop-out are used, but the conv operations are the key.\n",
        "\n",
        "The crucial difference, of course, is that in convnets, the filter weights are not *a priori* set by hand (as we did in the above examples) but rather incrementally learned from data using back-propagation.\n",
        "\n",
        "A fun resource for playing around with convolutions: https://generic-github-user.github.io/Image-Convolution-Playground/src/"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "name": "demo4.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3.10.0 64-bit ('3.10.0')",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.10.0"
    },
    "vscode": {
      "interpreter": {
        "hash": "6aea8d84a86a1280a34780710c5e478b9c6b3c016841b907182e7484363820b1"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}