self_attention_analysis.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "921e17cb",
      "metadata": {
        "id": "921e17cb"
      },
      "source": [
        "# Self-Attention Analysis"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "6e66eb9f",
      "metadata": {
        "id": "6e66eb9f",
        "outputId": "289f72c3-4b6c-49b2-8223-910e36751c77",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Running in Colab.\n",
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting timm==0.5.4\n",
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            "Installing collected packages: timm\n",
            "Successfully installed timm-0.5.4\n",
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            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting einops==0.6.0\n",
            "  Downloading einops-0.6.0-py3-none-any.whl (41 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m41.6/41.6 kB\u001b[0m \u001b[31m4.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hInstalling collected packages: einops\n",
            "Successfully installed einops-0.6.0\n",
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting gdown==4.7.1\n",
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            "Installing collected packages: gdown\n",
            "  Attempting uninstall: gdown\n",
            "    Found existing installation: gdown 4.6.6\n",
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            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
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            "Installing collected packages: yacs\n",
            "Successfully installed yacs-0.1.8\n",
            "Cloning into 'cl-vs-mim'...\n",
            "remote: Enumerating objects: 58, done.\u001b[K\n",
            "remote: Counting objects: 100% (58/58), done.\u001b[K\n",
            "remote: Compressing objects: 100% (43/43), done.\u001b[K\n",
            "remote: Total 58 (delta 14), reused 51 (delta 12), pack-reused 0\u001b[K\n",
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            "/content/cl-vs-mim\n"
          ]
        }
      ],
      "source": [
        "import sys\n",
        "\n",
        "#@markdown Execute this cell to import third-party software into the Colab environment.\n",
        "\n",
        "# check whether it runs in Colab\n",
        "root = \".\"\n",
        "if \"google.colab\" in sys.modules:\n",
        "    print(\"Running in Colab.\")\n",
        "    !pip3 install timm==0.5.4\n",
        "    !pip3 install matplotlib==3.7.1\n",
        "    !pip3 install scikit-learn==1.2.2\n",
        "    !pip3 install fastai==2.7.12\n",
        "    !pip3 install einops==0.6.0\n",
        "    !pip3 install gdown==4.7.1\n",
        "    !pip3 install yacs==0.1.8    \n",
        "    !git clone https://github.com/naver-ai/cl-vs-mim.git\n",
        "    root = \"./cl-vs-mim\"\n",
        "    %cd $root"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "203dfb55",
      "metadata": {
        "id": "203dfb55",
        "outputId": "05af1fa7-424e-4f96-a3d4-49e8fe49fc6d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Torch: 2.0.1+cu118 \n",
            "Availability: True\n",
            "Number: 1 \n",
            "Current device: 0 \n",
            "First device: <torch.cuda.device object at 0x7fe1600f0c10> \n",
            "Device name: Tesla T4\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "\n",
        "#@markdown Execute this cell to check the Colab environment, including GPU availability.\n",
        "\n",
        "# check gpu env\n",
        "print(f\"Torch: {torch.__version__} \\n\" + \n",
        "      f\"Availability: {torch.cuda.is_available()}\")\n",
        "assert torch.cuda.is_available() == True, \"The GPU is turned off. To turn it on, navigate to: Runtime > Change Runtime Type.\"\n",
        "print(f\"Number: {torch.cuda.device_count()} \\n\" +\n",
        "      f\"Current device: {torch.cuda.current_device()} \\n\" +\n",
        "      f\"First device: {torch.cuda.device(0)} \\n\" +\n",
        "      f\"Device name: {torch.cuda.get_device_name(0)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "fff99e10",
      "metadata": {
        "id": "fff99e10",
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "5b985121-aea7-4509-c5c1-f3d09235d659"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<style>\n",
              "    /* Turns off some styling */\n",
              "    progress {\n",
              "        /* gets rid of default border in Firefox and Opera. */\n",
              "        border: none;\n",
              "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "        background-size: auto;\n",
              "    }\n",
              "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
              "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
              "    }\n",
              "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "        background: #F44336;\n",
              "    }\n",
              "</style>\n"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "    <div>\n",
              "      <progress value='99008512' class='' max='99003388' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
              "      100.01% [99008512/99003388 00:20&lt;00:00]\n",
              "    </div>\n",
              "    "
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "import os\n",
        "import math\n",
        "import numpy as np\n",
        "from torch.utils.data import DataLoader\n",
        "\n",
        "import torchvision.datasets as datasets\n",
        "import timm.data.transforms_factory as tff\n",
        "from fastai.data.external import untar_data, URLs\n",
        "from utils import subsample\n",
        "\n",
        "#@markdown Execute this cell to download and import the *Imagenette* dataset, which is a small subset of ImageNet, for simplicity.\n",
        "\n",
        "# use imagenette (a small subset of imagenet) as an example for simplicity\n",
        "imagenet_path = untar_data(URLs.IMAGENETTE_160)\n",
        "\n",
        "imagenet_mean = np.array([0.485, 0.456, 0.406])\n",
        "imagenet_std = np.array([0.229, 0.224, 0.225])\n",
        "\n",
        "transform_test = tff.transforms_imagenet_eval(\n",
        "    img_size=224, mean=imagenet_mean, std=imagenet_std,\n",
        ")\n",
        "\n",
        "test_dir = os.path.join(imagenet_path, 'val')\n",
        "dataset_test = datasets.ImageFolder(test_dir, transform_test)\n",
        "dataset_test = torch.utils.data.Subset(\n",
        "    dataset_test, \n",
        "    subsample(dataset_test, ratio=math.pow(2,-6))  # use a subsampled batch\n",
        ")\n",
        "\n",
        "dataset_test = DataLoader(\n",
        "    dataset_test, \n",
        "    num_workers=1, \n",
        "    batch_size=64,\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4532bc85",
      "metadata": {
        "id": "4532bc85"
      },
      "source": [
        "## Load the Models"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "dba96775",
      "metadata": {
        "id": "dba96775",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "05661634-cc0e-45d9-8c26-50258f61f243",
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 863M/863M [00:08<00:00, 98.1MiB/s]\n",
            "/usr/local/lib/python3.10/dist-packages/torch/functional.py:504: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at ../aten/src/ATen/native/TensorShape.cpp:3483.)\n",
            "  return _VF.meshgrid(tensors, **kwargs)  # type: ignore[attr-defined]\n"
          ]
        }
      ],
      "source": [
        "# MoCo\n",
        "import torch\n",
        "import models.moco as moco\n",
        "from models.moco import load_state_dict\n",
        "from utils import download\n",
        "\n",
        "#@markdown Execute this cell to download and import MoCo-v3 pre-trained model.\n",
        "\n",
        "name = \"moco_vit_b\"  #@param {type:\"string\"}\n",
        "path = \"checkpoints/moco_vit_b.pt\"  #@param {type:\"string\"}\n",
        "url = \"https://dl.fbaipublicfiles.com/moco-v3/vit-b-300ep/vit-b-300ep.pth.tar\"  #@param {type:\"string\"}\n",
        "\n",
        "download(url, path, force=False)  # download checkpoints\n",
        "\n",
        "model = moco.vit_base()\n",
        "model = model.cuda()\n",
        "model = model.eval()\n",
        "\n",
        "state_dict = load_state_dict(path)\n",
        "_ = model.load_state_dict(state_dict, strict=False)\n",
        "model_moco = model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "f959e0ff",
      "metadata": {
        "id": "f959e0ff",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "cellView": "form",
        "outputId": "b804d3eb-e7d5-4e3c-e4b9-0a6d3755b57d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Cached Downloading: checkpoints/simmim_vit_b.pt\n",
            "Downloading...\n",
            "From (uriginal): https://drive.google.com/u/1/uc?id=1dJn6GYkwMIcoP3zqOEyW1_iQfpBi8UOw\n",
            "From (redirected): https://drive.google.com/uc?id=1dJn6GYkwMIcoP3zqOEyW1_iQfpBi8UOw&confirm=t&uuid=f5dc2be8-d385-472b-99c8-27d3ba5daa79\n",
            "To: /root/.cache/gdown/tmpstkqmhqk/dl\n",
            "100%|██████████| 345M/345M [00:05<00:00, 65.4MB/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "=> merge config from configs/simmim_pretrain__vit_base__img224__800ep.yaml\n"
          ]
        }
      ],
      "source": [
        "# SimMIM \n",
        "import gdown\n",
        "import torch\n",
        "import models.simmim as simmim\n",
        "from models.simmim import load_state_dict\n",
        "\n",
        "#@markdown Execute this cell to download and import SimMIM pre-trained model.\n",
        "\n",
        "name = \"simmim_vit_b\"  #@param {type:\"string\"}\n",
        "path = \"checkpoints/simmim_vit_b.pt\"  #@param {type:\"string\"}\n",
        "url = \"https://drive.google.com/u/1/uc?id=1dJn6GYkwMIcoP3zqOEyW1_iQfpBi8UOw\"  #@param {type:\"string\"}\n",
        "\n",
        "gdown.cached_download(url, path, quiet=False)  # download checkpoints\n",
        "\n",
        "model = simmim.vit_base()\n",
        "model = model.cuda()\n",
        "model = model.eval()\n",
        "\n",
        "state_dict = load_state_dict(path)\n",
        "_ = model.load_state_dict(state_dict, strict=False)\n",
        "model_simmim = model"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7e1b1d97",
      "metadata": {
        "id": "7e1b1d97"
      },
      "source": [
        "## Attention Map Visualization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "17b41b3c",
      "metadata": {
        "scrolled": false,
        "id": "17b41b3c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "cellView": "form",
        "outputId": "a1bdfb4a-f8d4-490a-c618-51c878518e07"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 200x200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 150x150 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJEAAACRCAYAAADD2FojAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAABcSAAAXEgFnn9JSAAAFx0lEQVR4nO3dS2hcZRjG8fecmUnTmN6S1FoaU1MhQltBqSBWqejChdCFUhFEqxtbxcuu7typUNDuKhRXdaMi1I0tKNSNogspiJdaWo1NbUgbkia9pM1t5rhwG5+3zCOI8P9t35kzX84880Fevu87RVVVVQCG8r8eAP7/CBFshAg2QgQbIYKNEMFGiGAjRLARItgIEWyECDZCBBshgo0QwVZ33vx+z4ey/uK7h9Jr7Nj7vKwvREvW+1qdsn62djUdw5pqmayvqBqy3tPqSD+jCr3iZqKcl/WdXfozvpxZTMdwd7Vc1ve3nk6vsRRmItgIEWyECDZCBBshgo0QwWb9i39+Wv9r/MDe59JrbGx2yfrF8oYeQ21G1juq/Hfyzn3jsv7m9+tk/WTjUvoZdzXXyHozaQFMXddf1WSp70NExPGYTV/TDmYi2AgRbIQINkIEGyGCjRDBRohgI0SwWc3GX4o5ewBnapet98+GXkfTG3q9UUTEayd0I7Av+a11VLX0M64UC7K+Y3G1rH/S0A3RgVZ3OobulvV1/yNmItgIEWyECDZCBBshgo0QwUaIYLMaBzeKpqxPFHpBWUTE9UL3eVYne8Iyp2tT6WtWtfRnbEsWlG1s6v1cERHTpf47P+0YlfWVyX2YKPIFZ8N1vbetXcxEsBEi2AgRbIQINkIEGyGCjRDBZvWJhssrsr620hsTIyJOlXrjXy0Kq/7I/IZ0DNk1Jkq9FmgoOSMpIuJ4fUzWty2ulfV9Dw3L+rmR29IxfH6uL31NO5iJYCNEsBEi2AgRbIQINkIEGyGCzeoTzSZrgcaKa+k1tjZ7Zb0/OQRrZbLna6zM98YtFPqAqUfrug/0QUv3gCIiNjd7ZP3gnuOyfmlM36ddz+r3R0Rs+vjh9DXtYCaCjRDBRohgI0SwESLYCBFshAg2QgSb1WysJ6fVzyWbGyMiLhd6Q93maoWsn6znD8XLdFX6Nvwxpxet9dfyA6Z+qE3I+uhv/bK+bJm+T8cO7ErHMDCoN0i2i5kINkIEGyGCjRDBRohgI0SwESLYrD5Rd3TI+mShNzdGRLxe6M2F40nOLxbXZb2nyjcWzib9rHOlPkAqO+zr79foBXynT90h652duk80NX1LOoa16/InRLaDmQg2QgQbIYKNEMFGiGAjRLARItisPtF0cgD3vcnBTRER79X+lPWnYkDWryUPoxtqrk7HcKHUvabNLb2m6WZ+iSOlvtWfjep+1hPJWV2NRt6rOnPmdll/ML3C0piJYCNEsBEi2AgRbIQINkIEGyGCjRDBZjUbdy/oDXdH6uPpNW5NTt3/onFBj2FeNyN/TRaURUS8sUH/lo6OtGT9hUHdrIyI+O68bgaerelT5fp6Z2T925/0dxERsWXjdPqadjATwUaIYCNEsBEi2AgRbIQINkIEW1FVlT5OXmieGJL1/u170mtkJ83/Xl6W9Wxz4ttbdH8lIuLwj+tlfbbQfaLTNT3GiIjxZJNlmTz9cX+vvk/NVj4fzM7ppw+8OrU7vcZSmIlgI0SwESLYCBFshAg2QgQbIYLNWk90das+uOnJ+XyNy9f1SVmvJzkfTzYevnxS90YiIgbKG7K+qtKHec2Gvg8REZ2hxzGTbML8amy5HkPSy4qIeKxPf0a7mIlgI0SwESLYCBFshAg2QgQbIYLN6hONPrNT1g8cPJReY98rL8n6kY7zst5VNWQ9W6cTkT/c756kTzSSjCEiYtG71XGioQ8yH2quSq8xMqn3+LWLmQg2QgQbIYKNEMFGiGAjRLARItgIEWxWB+zosftl/fEqb/RtH5yS9eVn9cK2jxqjsr7pJppwP9f0wrjDpd4Aub6VP/XwzsVuWf+mcVHWW6H3mA6X+VMuh5P6W+kVlsZMBBshgo0QwUaIYCNEsBEi2AgRbNYhV0AEMxH+BYQINkIEGyGCjRDBRohgI0SwESLYCBFshAg2QgQbIYKNEMFGiGD7C0UzIYFMcHiMAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# visualize attns with samples\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def mark_token(ax, xs, batch, i, j, color='tab:red'):\n",
        "    import matplotlib.patches as patches\n",
        "    from einops import rearrange, reduce, repeat\n",
        "    from utils import restore\n",
        "    \n",
        "    ax.imshow(rearrange(restore(xs.cpu())[batch], 'c h w -> h w c'))\n",
        "    ax.set_axis_off()\n",
        "\n",
        "    # create a rectangle patch to visualize the query token\n",
        "    rect = patches.Rectangle((14 * i, 14 * j), 14, 14, linewidth=3, edgecolor=color, facecolor='none')\n",
        "    ax.add_patch(rect)\n",
        "\n",
        "def visualize_attn(ax, attns, batch, i, j, depth, head):\n",
        "    \"\"\"\n",
        "    ax: matplotlib axes\n",
        "    xs: batch\n",
        "    batch, i, j: batch coords \n",
        "    attns, depth, head: \n",
        "    \"\"\"\n",
        "    \n",
        "    attn_list = [list(attn[batch].cpu()) if attn is not None else None for attn in attns]\n",
        "    attn = torch.stack(attn_list[depth])\n",
        "    attn = attn[head]  # take head-th head\n",
        "    attn = attn[1:,1:]  # drop cls token\n",
        "    attn = attn / attn.sum(dim=-1, keepdim=True)  # normalize\n",
        "\n",
        "    attn = attn[j * 14 + i]\n",
        "    attn = attn.reshape([14, 14])\n",
        "\n",
        "    ax.imshow(attn, cmap=\"plasma\", )\n",
        "    ax.set_xticks([])\n",
        "    ax.set_yticks([])\n",
        "    ax.set_axis_off()\n",
        "    \n",
        "    \n",
        "#@markdown Execute this cell to visualize the attention maps. The red square in the visualization indicates the location of the query.\n",
        "#@markdown \n",
        "#@markdown This visualization demonstrates that the self-attentions of CL (MoCo) generally captures global relationships and objects. However, they tend to produce homogeneous attention maps for all query tokens and heads, particularly when compared to MIM. In contrast, the self-attentions of MIM (SimMIM) primarily focus on localized areas.\n",
        "\n",
        "model_option = \"moco\"  #@param [\"moco\", \"simmim\"]\n",
        "depth = 10  #@param {type:\"slider\", min:0, max:11, step:1}\n",
        "batch = 30  #@param {type:\"integer\"}\n",
        "coord_x = 3  #@param {type:\"integer\"}\n",
        "coord_y = 8  #@param {type:\"integer\"}\n",
        "head = 0  #@param {type:\"integer\"}\n",
        "\n",
        "if model_option == \"moco\":\n",
        "    model = model_moco\n",
        "elif model_option == \"simmim\":\n",
        "    model = model_simmim\n",
        "else:\n",
        "    raise Exception(\"Invalid option: \", model_option)\n",
        "\n",
        "xs, ys = next(iter(dataset_test))\n",
        "with torch.no_grad():\n",
        "    xs = xs.cuda()\n",
        "    _, _, attns, _ = model(xs)\n",
        "\n",
        "\n",
        "fig, ax = plt.subplots(1, 1, figsize=(2, 2), dpi=100)\n",
        "mark_token(ax, xs, batch=batch, i=coord_x, j=coord_y, color='tab:red')\n",
        "\n",
        "fig, ax = plt.subplots(1, 1, figsize=(1, 1), dpi=150)\n",
        "visualize_attn(ax, attns, batch=batch, i=coord_x, j=coord_y, depth=depth, head=head)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b7f8f456",
      "metadata": {
        "id": "b7f8f456"
      },
      "source": [
        "## Attention Distance"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "7dad3f9d",
      "metadata": {
        "id": "7dad3f9d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "outputId": "32c49d26-0d97-4ea6-f1b7-39a6dcf20c80",
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 645x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# build off the implementation of https://github.com/sayakpaul/probing-vits\n",
        "import numpy as np\n",
        "\n",
        "def compute_distance_matrix(patch_size, num_patches, length):\n",
        "    \"\"\"Helper function to compute distance matrix.\"\"\"\n",
        "    distance_matrix = np.zeros((num_patches, num_patches))\n",
        "    for i in range(num_patches):\n",
        "        for j in range(num_patches):\n",
        "            if i == j: # zero distance\n",
        "                continue\n",
        "\n",
        "            xi, yi = (int(i/length)), (i % length)\n",
        "            xj, yj = (int(j/length)), (j % length)\n",
        "            distance_matrix[i, j] = patch_size * np.linalg.norm([xi - xj, yi - yj])\n",
        "\n",
        "    return distance_matrix\n",
        "\n",
        "def calculate_mean_attention_dist(patch_size, attention_weights):\n",
        "    \"\"\" The attention_weights shape = (batch, num_heads, num_patches, num_patches)\"\"\"\n",
        "    \n",
        "    num_patches = attention_weights.shape[-1]\n",
        "    length = int(np.sqrt(num_patches))\n",
        "    assert (length**2 == num_patches), (\"Num patches is not perfect square\")\n",
        "\n",
        "    distance_matrix = compute_distance_matrix(patch_size, num_patches, length)\n",
        "    h, w = distance_matrix.shape\n",
        "\n",
        "    distance_matrix = distance_matrix.reshape((1, 1, h, w))\n",
        "    # The attention_weights along the last axis adds to 1\n",
        "    # this is due to the fact that they are softmax of the raw logits\n",
        "    # summation of the (attention_weights * distance_matrix)\n",
        "    # should result in an average distance per token\n",
        "    mean_distances = attention_weights * distance_matrix\n",
        "    mean_distances = np.sum(mean_distances, axis=-1) # sum along last axis to get average distance per token\n",
        "    mean_distances = np.mean(mean_distances, axis=-1) # now average across all the tokens\n",
        "\n",
        "    return torch.tensor(mean_distances)\n",
        "\n",
        "\n",
        "#@markdown Execute this cell to calculate attention distance. Attention distance is defined as the average distance between the query tokens and key tokens considering their self-attention weights. Therefore, it conceptually corresponds to the size of the receptive fields in CNNs.\n",
        "#@markdown \n",
        "#@markdown These results shows that the attention distance of CL (MoCo) is significantly higher than that of MIM (SimMIM), especially in the later layers. As seen above, the qualitative visualization, this implies that the representations of CL contain global patterns and shape information, so CL can help ViTs distinguish between objects of images. Conversely, the self-attentions of MIM mainly capture local relationships; i.e., MIM may have difficulty recognizing whole objects and their shapes.\n",
        "\n",
        "from timm.utils import AverageMeter\n",
        "\n",
        "model_option = \"moco\"  #@param [\"moco\", \"simmim\"]\n",
        "if model_option == \"moco\":\n",
        "    model = model_moco\n",
        "elif model_option == \"simmim\":\n",
        "    model = model_simmim\n",
        "else:\n",
        "    raise Exception(\"Invalid option: \", model_option)\n",
        "    \n",
        "encoder_length = len(model.blocks)  # for example 12 for ViT-B\n",
        "distances = [AverageMeter() for _ in range(encoder_length)]\n",
        "\n",
        "for idx, (xs, _) in enumerate(dataset_test):\n",
        "    xs = xs.cuda()\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        _, _, attns, _ = model(xs)\n",
        "        \n",
        "    for i, attn in enumerate([attn for attn in attns if attn is not None]):    \n",
        "        attn = attn[:,:,1:,1:]\n",
        "        attn = attn + 1e-32\n",
        "        attn = attn / attn.sum(dim=-1, keepdim=True)  # normalize\n",
        "        attn = attn.cpu().float().detach().numpy()\n",
        "\n",
        "        distance = calculate_mean_attention_dist(patch_size=16, attention_weights=attn)\n",
        "        distances[i].update(torch.mean(distance, dim=0))  # average w.r.t. batch\n",
        "        \n",
        "    if idx > -1:\n",
        "        break\n",
        "    \n",
        "\n",
        "fig, ax = plt.subplots(1, 1, figsize=(4.3, 4), dpi=150)\n",
        "distances = [torch.mean(distance.avg) for distance in distances]\n",
        "ax.plot(range(1, 13), distances, marker=\"o\")\n",
        "ax.set_xlabel(\"Depth\")\n",
        "ax.set_ylabel(\"Attention distance (px)\")\n",
        "ax.set_ylim(top=120, bottom=0)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "34e8593d",
      "metadata": {
        "id": "34e8593d"
      },
      "source": [
        "## Normalized Mutual Information"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "7cfc022f",
      "metadata": {
        "id": "7cfc022f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "outputId": "50c84d60-6e1c-4b61-ff90-8546d8ca038a",
        "cellView": "form"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 645x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import torch.nn.functional as F \n",
        "from einops import rearrange, reduce, repeat\n",
        "\n",
        "def calculate_nmi(attn): \n",
        "    \"\"\" Normalized mutual information with a return type of (batch, head) \"\"\"\n",
        "    b, h, q, k = attn.shape\n",
        "    pq = torch.ones([b, h, q]).to(attn.device)\n",
        "    pq = F.softmax(pq, dim=-1)\n",
        "    pq_ext = repeat(pq, \"b h q -> b h q k\", k=k)\n",
        "    pk = reduce(attn * pq_ext, \"b h q k -> b h k\", \"sum\")\n",
        "    pk_ext = repeat(pk, \"b h k -> b h q k\", q=q)\n",
        "    \n",
        "    mi = reduce(attn * pq_ext * torch.log(attn / pk_ext), \"b h q k -> b h\", \"sum\")\n",
        "    eq = - reduce(pq * torch.log(pq), \"b h q -> b h\", \"sum\")\n",
        "    ek = - reduce(pk * torch.log(pk), \"b h k -> b h\", \"sum\")\n",
        "    \n",
        "    nmiv = mi / torch.sqrt(eq * ek)\n",
        "    \n",
        "    return nmiv\n",
        "\n",
        "#@markdown Execute this cell to calculate the Normalized Mutual Information (NMI). NMI measures the inhomogeneity of self-attentions with respect to queries. In other words, *attention collapse* occurs when the NMI approaches zero.\n",
        "#@markdown \n",
        "#@markdown The results indicate that the mutual information of CL is significantly lower than that of MIM, especially in the later layers. This suggests that the self-attentions of CL tend to collapse into homogeneous distributions.\n",
        "\n",
        "\n",
        "from timm.utils import AverageMeter\n",
        "\n",
        "model_option = \"moco\"  #@param [\"moco\", \"simmim\"]\n",
        "if model_option == \"moco\":\n",
        "    model = model_moco\n",
        "elif model_option == \"simmim\":\n",
        "    model = model_simmim\n",
        "else:\n",
        "    raise Exception(\"Invalid option: \", model_option)\n",
        "\n",
        "encoder_length = len(model.blocks)  # 12 for ViT-B\n",
        "nmis = [AverageMeter() for _ in range(encoder_length)]\n",
        "\n",
        "for idx, (xs, _) in enumerate(dataset_test):\n",
        "    xs = xs.cuda()\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        _, _, attns, _ = model(xs)\n",
        "        \n",
        "    for i, attn in enumerate([attn for attn in attns if attn is not None]):\n",
        "        attn = attn[:,:,1:,1:]  # drop cls token\n",
        "        attn = attn + 1e-8\n",
        "        attn = attn / attn.sum(dim=-1, keepdim=True)  # normalize\n",
        "        attn = attn.cpu().float()\n",
        "        \n",
        "        nmi = calculate_nmi(attn)\n",
        "        nmis[i].update(torch.mean(nmi, dim=0))  # average w.r.t. batch\n",
        "        \n",
        "    if idx > -1:\n",
        "        break\n",
        "    \n",
        "    \n",
        "fig, ax = plt.subplots(1, 1, figsize=(4.3, 4), dpi=150)\n",
        "nmis = [torch.mean(nmi.avg) for nmi in nmis]\n",
        "ax.plot(range(1, 13), nmis, marker=\"o\")\n",
        "ax.set_xlabel(\"Depth\")\n",
        "ax.set_ylabel(\"Normalized MI\")\n",
        "ax.set_ylim(top=0.6, bottom=0.0)\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "cl_vs_mim",
      "language": "python",
      "name": "cl_vs_mim"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.16"
    },
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "accelerator": "GPU",
    "gpuClass": "standard"
  },
  "nbformat": 4,
  "nbformat_minor": 5
}