concrete_mnist.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "Rd_Xi75QV8ce"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The autoreload extension is already loaded. To reload it, use:\n",
            "  %reload_ext autoreload\n"
          ]
        }
      ],
      "source": [
        "%load_ext autoreload\n",
        "%autoreload 2\n",
        "\n",
        "import torch\n",
        "import torch.nn.functional as F\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "from torchinfo import summary\n",
        "from torchvision.datasets import MNIST\n",
        "from torchvision.transforms import ToTensor, Compose, Resize, InterpolationMode, Lambda\n",
        "# InterpolationMode.NEAREST"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "ml4NnoH5MLSK"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "data:\n",
              "  dataset: MNIST\n",
              "  image_size: 32\n",
              "  num_categories: 3\n",
              "  random_flip: true\n",
              "device: !!python/object/apply:torch.device\n",
              "- mps\n",
              "eval:\n",
              "  batch_size: 1024\n",
              "model:\n",
              "  num_scales: 10\n",
              "  tau_max: 10\n",
              "  tau_min: 2.0\n",
              "optim:\n",
              "  grad_clip: 1.0\n",
              "  lr: 0.0002\n",
              "  optimizer: Adam\n",
              "  warmup: 5000\n",
              "  weight_decay: 0\n",
              "seed: 42\n",
              "training:\n",
              "  batch_size: 256\n",
              "  n_epochs: 100"
            ]
          },
          "execution_count": 28,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from  dataloader import get_dataset\n",
        "from configs.mnist_config import get_config\n",
        "config = get_config()\n",
        "N_CATEGORIES = config.data.num_categories\n",
        "config"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pWhfOoz4cWgX",
        "outputId": "d3df3de5-20ae-4e86-a20b-64d53c436131"
      },
      "outputs": [],
      "source": [
        "train_ds, val_ds = get_dataset(config)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tR933IXFOdVG",
        "outputId": "20a228e4-c047-43a5-9c23-a18b4a72028a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "torch.Size([1024, 3, 8, 8])"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "X, y = next(iter(val_ds))\n",
        "X.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "m7zb7zsHOhgo"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x177df2df0>"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.imshow(X[0,0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "51Auv6fZ2AFn"
      },
      "outputs": [],
      "source": [
        "from utils import prob_to_logit, log_concrete_sample"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aQmUPlj7aLdM",
        "outputId": "3cd288b8-9b68-4a81-e221-f734b94f4d15"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "torch.Size([1000, 3, 8, 8])"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = X[13].clone().unsqueeze(0).repeat(1000,1,1,1)\n",
        "x.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZPd9H74fOXk-",
        "outputId": "739771ab-714a-42ea-a498-615a76a02346"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor(8)"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y[13]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "vnnchie_bVyg",
        "outputId": "8bbf26ce-6d0b-4068-866d-c166837e0a25"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<AxesSubplot: >"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "img = prob_to_logit(x).argmax(dim=1)\n",
        "sns.heatmap(img[1], cmap=\"Accent\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "id": "wzLDEfryFAWU",
        "outputId": "82373581-15f6-475d-e05f-2be36036e0a5"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 2000x400 with 6 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, axs = plt.subplots(1, N_CATEGORIES, figsize=(20,4))\n",
        "x_logit = prob_to_logit(x)\n",
        "_x = x_logit.softmax(1)\n",
        "for i in range(N_CATEGORIES):\n",
        "  sns.heatmap(x_logit[1,i], ax=axs[i], cmap=\"Reds\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "8T_fl_2SaS18",
        "outputId": "1fddedce-99ed-4d23-fcda-aba486d8b50d"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1600x600 with 12 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "MAX_TAU=10.0\n",
        "x_logit = prob_to_logit(x)\n",
        "x_noisy = log_concrete_sample(x_logit, tau=MAX_TAU)\n",
        "fig, axs = plt.subplots(2,N_CATEGORIES, figsize=(16,6))\n",
        "for i in range(x_noisy.shape[1]):\n",
        "  sns.heatmap(x_logit[0,i], ax=axs[0,i], cmap=\"Reds\")\n",
        "  sns.heatmap(x_noisy[0,i].exp(), ax=axs[1,i], cmap=\"Reds\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        },
        "id": "AfhglQHbaIyi",
        "outputId": "186afdf0-a737-482b-81e5-bcce2988e14c"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 2000x400 with 6 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "x_grad = log_concrete_grad(x_noisy, x_logit, tau=MAX_TAU)\n",
        "fig, axs = plt.subplots(1,N_CATEGORIES, figsize=(20,4))\n",
        "for i in range(N_CATEGORIES):\n",
        "  sns.heatmap(x_grad[0][i], ax=axs[i])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9rh2zoM_LNuB"
      },
      "source": [
        "Note that each pixel is an independent \"feature\" with its own categories.\n",
        "It just happens to be that every one has 5 categories\n",
        "Think abouit how you would convert the image into a tabular form\n",
        "You would have 5*(28*28) features from which you would have to compute gradients on chunks of five."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RMEwq5s3F9bk",
        "outputId": "0ea5d044-41a0-4e40-9fa7-c40700f8d9a6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(torch.Size([3, 8, 8]), torch.Size([3, 8, 8]), torch.Size([1000, 3, 8, 8]))"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x_rec = x_noisy + (x_grad * 1e-2)\n",
        "# x_rec = torch.softmax(x_rec, dim=1)\n",
        "x_rec_mean = x_rec.mean(0)\n",
        "x_rec_probs = (x_rec - torch.logsumexp(x_rec, dim=1, keepdims=True)).mean(0).exp()\n",
        "x_noisy_mean = x_noisy.mean(0)\n",
        "x_rec_mean.shape, x_noisy_mean.shape, x_rec.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 775
        },
        "id": "ziZne_g7nr_f",
        "outputId": "df2bd24e-9fed-4497-f1c7-6492ac8ba9bc"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1280x960 with 18 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, axs = plt.subplots(3, N_CATEGORIES, figsize=(16,12), dpi=80)\n",
        "for i in range(N_CATEGORIES):\n",
        "  sns.heatmap(x_noisy[0].exp()[i], ax=axs[0,i], vmin=None, vmax=None, cmap=\"Reds\")\n",
        "  sns.heatmap(x_rec[0].exp()[i], ax=axs[1,i], vmax=None, cmap=\"Reds\")\n",
        "  sns.heatmap((x_rec[0][i]-x_noisy[0][i]), ax=axs[2,i], vmin=None, vmax=None, cmap=\"RdBu\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ezIWY10iVZhu"
      },
      "source": [
        "## Training code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "DBp9WI-BWVat"
      },
      "outputs": [],
      "source": [
        "from losses import categorical_dsm_loss, log_concrete_grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6ILePFBtRAar",
        "outputId": "c76ccb85-fa4b-4159-b5fe-4fe05a984a30"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Zero-prediction Loss: tensor(24.9137)\n",
            "Random-prediction Loss: tensor(75.4289)\n"
          ]
        }
      ],
      "source": [
        "print(\"Zero-prediction Loss:\", categorical_dsm_loss(x_logit, x_noisy, torch.zeros_like(x_grad), tau=MAX_TAU))\n",
        "print(\"Random-prediction Loss:\", categorical_dsm_loss(x_logit, x_noisy, MAX_TAU+torch.randn_like(x_grad), tau=MAX_TAU))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "id": "ApVGTNLF7K3s"
      },
      "outputs": [],
      "source": [
        "from torch import nn\n",
        "\n",
        "class GaussianFourierProjection(nn.Module):\n",
        "    \"\"\"Gaussian Fourier embeddings for noise levels.\"\"\"\n",
        "\n",
        "    def __init__(self, embedding_size=256, scale=1.0):\n",
        "        super().__init__()\n",
        "        self.W = nn.Parameter(torch.randn(embedding_size) * scale, requires_grad=False)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x_proj = x[:, None] * self.W[None, :] * 2 * np.pi\n",
        "        return torch.cat([torch.sin(x_proj), torch.cos(x_proj)], dim=-1)\n",
        "\n",
        "class FiLMBlock(nn.Module):\n",
        "  def __init__(self, time_dim_sz, num_channels):\n",
        "    super().__init__()\n",
        "    self.c = num_channels\n",
        "    self.dense = nn.Linear(time_dim_sz, num_channels*2)\n",
        "  \n",
        "  def forward(self, X, time_emb):\n",
        "    gamma, beta = torch.split(self.dense(time_emb), (self.c, self.c), dim=1)\n",
        "    # print(gamma[:,:,None, None].shape)\n",
        "    return X*gamma[:,:,None, None] + beta[:,:,None, None]\n",
        "\n",
        "class ResNeXtBlock(nn.Module):\n",
        "    \"\"\"The ResNeXt block taken from d2l.ai.\"\"\"\n",
        "    def __init__(self, num_channels, time_emb_size, groups=1, bot_mul=1, use_1x1conv=True,\n",
        "                 strides=1):\n",
        "        super().__init__()\n",
        "        \n",
        "        # !FIXME: Get this from config\n",
        "        self.act = F.gelu\n",
        "\n",
        "        bot_channels = int(round(num_channels * bot_mul))\n",
        "        self.conv1 = nn.Conv2d(num_channels, bot_channels, kernel_size=1,\n",
        "                               stride=1)\n",
        "        self.norm1 = nn.InstanceNorm2d(bot_channels)\n",
        "        \n",
        "        self.conv2 = nn.Conv2d(bot_channels, bot_channels, kernel_size=3,\n",
        "                               stride=strides, padding=1,\n",
        "                               groups=bot_channels//groups)\n",
        "        self.norm2 = nn.InstanceNorm2d(bot_channels)\n",
        "\n",
        "        self.conv3 = nn.Conv2d(bot_channels, num_channels, kernel_size=1,\n",
        "                               stride=1)\n",
        "        self.norm3 = nn.InstanceNorm2d(num_channels)\n",
        "        \n",
        "        if use_1x1conv:\n",
        "            self.conv4 = nn.Conv2d(num_channels,num_channels, kernel_size=1,\n",
        "                                       stride=strides)\n",
        "            self.norm4 = nn.InstanceNorm2d(num_channels)\n",
        "        else:\n",
        "            self.conv4 = None\n",
        "\n",
        "        self.film1 = FiLMBlock(time_emb_size, bot_channels)\n",
        "        self.film2 = FiLMBlock(time_emb_size, bot_channels)\n",
        "        self.film3 = FiLMBlock(time_emb_size, num_channels)\n",
        "\n",
        "    def forward(self, X, time_emb):\n",
        "        Y = self.act(self.norm1(self.conv1(X)))\n",
        "        Y = self.film1(Y, time_emb)\n",
        "\n",
        "        Y = self.act(self.norm2(self.conv2(Y)))\n",
        "        Y = self.film2(Y, time_emb)\n",
        "\n",
        "        Y = self.norm3(self.conv3(Y))\n",
        "        Y = self.film3(Y, time_emb)\n",
        "\n",
        "        if self.conv4:\n",
        "            X = self.norm4(self.conv4(X))\n",
        "        \n",
        "        return self.act(Y + X)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 102,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2hsTFTAyDzEC",
        "outputId": "6229bd11-2696-4769-e2c6-7fb040a18197"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "ResNeXtBlock(\n",
            "  (conv1): Conv2d(32, 32, kernel_size=(1, 1), stride=(1, 1))\n",
            "  (norm1): InstanceNorm2d(32, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
            "  (conv2): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), groups=32)\n",
            "  (norm2): InstanceNorm2d(32, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
            "  (conv3): Conv2d(32, 32, kernel_size=(1, 1), stride=(1, 1))\n",
            "  (norm3): InstanceNorm2d(32, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
            "  (conv4): Conv2d(32, 32, kernel_size=(1, 1), stride=(1, 1))\n",
            "  (norm4): InstanceNorm2d(32, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
            "  (film1): FiLMBlock(\n",
            "    (dense): Linear(in_features=4, out_features=64, bias=True)\n",
            "  )\n",
            "  (film2): FiLMBlock(\n",
            "    (dense): Linear(in_features=4, out_features=64, bias=True)\n",
            "  )\n",
            "  (film3): FiLMBlock(\n",
            "    (dense): Linear(in_features=4, out_features=64, bias=True)\n",
            "  )\n",
            ")\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "(=================================================================\n",
              " Layer (type:depth-idx)                   Param #\n",
              " =================================================================\n",
              " ResNeXtBlock                             --\n",
              " ├─Conv2d: 1-1                            1,056\n",
              " ├─InstanceNorm2d: 1-2                    --\n",
              " ├─Conv2d: 1-3                            320\n",
              " ├─InstanceNorm2d: 1-4                    --\n",
              " ├─Conv2d: 1-5                            1,056\n",
              " ├─InstanceNorm2d: 1-6                    --\n",
              " ├─Conv2d: 1-7                            1,056\n",
              " ├─InstanceNorm2d: 1-8                    --\n",
              " ├─FiLMBlock: 1-9                         --\n",
              " │    └─Linear: 2-1                       320\n",
              " ├─FiLMBlock: 1-10                        --\n",
              " │    └─Linear: 2-2                       320\n",
              " ├─FiLMBlock: 1-11                        --\n",
              " │    └─Linear: 2-3                       320\n",
              " =================================================================\n",
              " Total params: 4,448\n",
              " Trainable params: 4,448\n",
              " Non-trainable params: 0\n",
              " =================================================================,\n",
              " torch.Size([4, 32, 28, 28]))"
            ]
          },
          "execution_count": 102,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "net = ResNeXtBlock(32, 4)\n",
        "_x = torch.randn(4, 32, 28, 28)\n",
        "\n",
        "print(net)\n",
        "summary(net), net(_x, torch.zeros(4,4)).shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6y9hxa2HtjAK"
      },
      "source": [
        "> ### TODO: Train a proper conditional model and see if you can generate samples via Langevin Dynamics\n",
        "\n",
        "- [x] Overfit a single batch with only one scale\n",
        "- [ ] Overfit batch with multiple scales\n",
        "- [ ] Generate samples"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 103,
      "metadata": {
        "id": "Zw5u4OGmqHOk"
      },
      "outputs": [],
      "source": [
        "class ScoreNet(nn.Module):\n",
        "    \"\"\"The ResNeXt block taken from d2l.ai.\"\"\"\n",
        "    def __init__(self, num_channels, nf=32, embedding_size=16):\n",
        "      super().__init__()\n",
        "\n",
        "      self.proj = GaussianFourierProjection(embedding_size=embedding_size)\n",
        "      self.dense = nn.Linear(embedding_size*2, embedding_size*4)\n",
        "      self.film1 = FiLMBlock(embedding_size*4, nf)\n",
        "\n",
        "      self.c1 = nn.Conv2d(num_channels, nf, kernel_size=3, stride=1)\n",
        "      self.resblock1 = ResNeXtBlock(nf, embedding_size*4, groups=2, bot_mul=2)\n",
        "      self.resblock2 = ResNeXtBlock(nf, embedding_size*4, groups=4, bot_mul=4)\n",
        "      self.resblock3 = ResNeXtBlock(nf, embedding_size*4, groups=4, bot_mul=4)\n",
        "      self.resblock4 = ResNeXtBlock(nf, embedding_size*4, groups=2, bot_mul=2)\n",
        "\n",
        "      self.c2 = nn.ConvTranspose2d(nf, num_channels, kernel_size=3, stride=1)\n",
        "\n",
        "    def forward(self, x,t):\n",
        "      temb = self.dense(self.proj(t))\n",
        "      x = self.film1(self.c1(x), temb)\n",
        "      # print(x.shape)\n",
        "      x = self.resblock1(x,temb)\n",
        "      x = self.resblock2(x,temb)\n",
        "      x = self.resblock3(x,temb)\n",
        "      x = self.resblock4(x,temb)\n",
        "      \n",
        "      x = self.c2(x)\n",
        "\n",
        "      return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 106,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "--WmynFZqzSs",
        "outputId": "a9958b67-8297-4aa3-bd72-c15a9266bc08"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(ScoreNet(\n",
              "   (proj): GaussianFourierProjection()\n",
              "   (dense): Linear(in_features=2, out_features=4, bias=True)\n",
              "   (film1): FiLMBlock(\n",
              "     (dense): Linear(in_features=4, out_features=128, bias=True)\n",
              "   )\n",
              "   (c1): Conv2d(3, 64, kernel_size=(3, 3), stride=(1, 1))\n",
              "   (resblock1): ResNeXtBlock(\n",
              "     (conv1): Conv2d(64, 128, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm1): InstanceNorm2d(128, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), groups=64)\n",
              "     (norm2): InstanceNorm2d(128, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv3): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm3): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv4): Conv2d(64, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm4): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (film1): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=256, bias=True)\n",
              "     )\n",
              "     (film2): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=256, bias=True)\n",
              "     )\n",
              "     (film3): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=128, bias=True)\n",
              "     )\n",
              "   )\n",
              "   (resblock2): ResNeXtBlock(\n",
              "     (conv1): Conv2d(64, 256, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm1): InstanceNorm2d(256, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), groups=64)\n",
              "     (norm2): InstanceNorm2d(256, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv3): Conv2d(256, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm3): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv4): Conv2d(64, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm4): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (film1): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=512, bias=True)\n",
              "     )\n",
              "     (film2): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=512, bias=True)\n",
              "     )\n",
              "     (film3): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=128, bias=True)\n",
              "     )\n",
              "   )\n",
              "   (resblock3): ResNeXtBlock(\n",
              "     (conv1): Conv2d(64, 256, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm1): InstanceNorm2d(256, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), groups=64)\n",
              "     (norm2): InstanceNorm2d(256, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv3): Conv2d(256, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm3): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv4): Conv2d(64, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm4): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (film1): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=512, bias=True)\n",
              "     )\n",
              "     (film2): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=512, bias=True)\n",
              "     )\n",
              "     (film3): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=128, bias=True)\n",
              "     )\n",
              "   )\n",
              "   (resblock4): ResNeXtBlock(\n",
              "     (conv1): Conv2d(64, 128, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm1): InstanceNorm2d(128, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), groups=64)\n",
              "     (norm2): InstanceNorm2d(128, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv3): Conv2d(128, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm3): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (conv4): Conv2d(64, 64, kernel_size=(1, 1), stride=(1, 1))\n",
              "     (norm4): InstanceNorm2d(64, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)\n",
              "     (film1): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=256, bias=True)\n",
              "     )\n",
              "     (film2): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=256, bias=True)\n",
              "     )\n",
              "     (film3): FiLMBlock(\n",
              "       (dense): Linear(in_features=4, out_features=128, bias=True)\n",
              "     )\n",
              "   )\n",
              "   (c2): ConvTranspose2d(64, 3, kernel_size=(3, 3), stride=(1, 1))\n",
              " ),\n",
              " =================================================================\n",
              " Layer (type:depth-idx)                   Param #\n",
              " =================================================================\n",
              " ScoreNet                                 --\n",
              " ├─GaussianFourierProjection: 1-1         (1)\n",
              " ├─Linear: 1-2                            12\n",
              " ├─FiLMBlock: 1-3                         --\n",
              " │    └─Linear: 2-1                       640\n",
              " ├─Conv2d: 1-4                            1,792\n",
              " ├─ResNeXtBlock: 1-5                      --\n",
              " │    └─Conv2d: 2-2                       8,320\n",
              " │    └─InstanceNorm2d: 2-3               --\n",
              " │    └─Conv2d: 2-4                       2,432\n",
              " │    └─InstanceNorm2d: 2-5               --\n",
              " │    └─Conv2d: 2-6                       8,256\n",
              " │    └─InstanceNorm2d: 2-7               --\n",
              " │    └─Conv2d: 2-8                       4,160\n",
              " │    └─InstanceNorm2d: 2-9               --\n",
              " │    └─FiLMBlock: 2-10                   --\n",
              " │    │    └─Linear: 3-1                  1,280\n",
              " │    └─FiLMBlock: 2-11                   --\n",
              " │    │    └─Linear: 3-2                  1,280\n",
              " │    └─FiLMBlock: 2-12                   --\n",
              " │    │    └─Linear: 3-3                  640\n",
              " ├─ResNeXtBlock: 1-6                      --\n",
              " │    └─Conv2d: 2-13                      16,640\n",
              " │    └─InstanceNorm2d: 2-14              --\n",
              " │    └─Conv2d: 2-15                      9,472\n",
              " │    └─InstanceNorm2d: 2-16              --\n",
              " │    └─Conv2d: 2-17                      16,448\n",
              " │    └─InstanceNorm2d: 2-18              --\n",
              " │    └─Conv2d: 2-19                      4,160\n",
              " │    └─InstanceNorm2d: 2-20              --\n",
              " │    └─FiLMBlock: 2-21                   --\n",
              " │    │    └─Linear: 3-4                  2,560\n",
              " │    └─FiLMBlock: 2-22                   --\n",
              " │    │    └─Linear: 3-5                  2,560\n",
              " │    └─FiLMBlock: 2-23                   --\n",
              " │    │    └─Linear: 3-6                  640\n",
              " ├─ResNeXtBlock: 1-7                      --\n",
              " │    └─Conv2d: 2-24                      16,640\n",
              " │    └─InstanceNorm2d: 2-25              --\n",
              " │    └─Conv2d: 2-26                      9,472\n",
              " │    └─InstanceNorm2d: 2-27              --\n",
              " │    └─Conv2d: 2-28                      16,448\n",
              " │    └─InstanceNorm2d: 2-29              --\n",
              " │    └─Conv2d: 2-30                      4,160\n",
              " │    └─InstanceNorm2d: 2-31              --\n",
              " │    └─FiLMBlock: 2-32                   --\n",
              " │    │    └─Linear: 3-7                  2,560\n",
              " │    └─FiLMBlock: 2-33                   --\n",
              " │    │    └─Linear: 3-8                  2,560\n",
              " │    └─FiLMBlock: 2-34                   --\n",
              " │    │    └─Linear: 3-9                  640\n",
              " ├─ResNeXtBlock: 1-8                      --\n",
              " │    └─Conv2d: 2-35                      8,320\n",
              " │    └─InstanceNorm2d: 2-36              --\n",
              " │    └─Conv2d: 2-37                      2,432\n",
              " │    └─InstanceNorm2d: 2-38              --\n",
              " │    └─Conv2d: 2-39                      8,256\n",
              " │    └─InstanceNorm2d: 2-40              --\n",
              " │    └─Conv2d: 2-41                      4,160\n",
              " │    └─InstanceNorm2d: 2-42              --\n",
              " │    └─FiLMBlock: 2-43                   --\n",
              " │    │    └─Linear: 3-10                 1,280\n",
              " │    └─FiLMBlock: 2-44                   --\n",
              " │    │    └─Linear: 3-11                 1,280\n",
              " │    └─FiLMBlock: 2-45                   --\n",
              " │    │    └─Linear: 3-12                 640\n",
              " ├─ConvTranspose2d: 1-9                   1,731\n",
              " =================================================================\n",
              " Total params: 161,872\n",
              " Trainable params: 161,871\n",
              " Non-trainable params: 1\n",
              " =================================================================,\n",
              " torch.Size([4, 3, 8, 8]))"
            ]
          },
          "execution_count": 106,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "nf = 64\n",
        "model = ScoreNet(N_CATEGORIES, nf, embedding_size=1)\n",
        "_x = torch.randn(4, N_CATEGORIES, 8, 8)\n",
        "model, summary(model), model(_x, torch.zeros(4)).shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 107,
      "metadata": {
        "id": "7ALToc3PPUc1"
      },
      "outputs": [],
      "source": [
        "from tqdm.asyncio import tqdm\n",
        "def train(model, num_epochs = 10, learning_rate=1e-3,\n",
        "          name=\"vanilla\", sample_interval=1, dataset=None,\n",
        "          device=\"cuda\"):\n",
        "\n",
        "  model.to(device)\n",
        "  # print(model.is)\n",
        "  optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate,\n",
        "                              weight_decay=0.0)\n",
        "  train_losses = []\n",
        "  val_losses = []\n",
        "  \n",
        "  NUM_SCALES=1\n",
        "  taus = torch.Tensor(np.linspace(MAX_TAU, 2.0, NUM_SCALES), device=\"cpu\")\n",
        "  print(taus)\n",
        "  # train_batch =  [next(iter(train_ds))]\n",
        "  model.train()\n",
        "  niters = 0\n",
        "  pbar = tqdm(range(num_epochs), desc=\"?\")\n",
        "\n",
        "  for epoch in pbar:\n",
        "      epoch_loss = 0\n",
        "      eval_loss = 0\n",
        "      nbatches = 0\n",
        "\n",
        "      for img, lab in train_ds:\n",
        "        # ===================forward=====================\n",
        "        img_logit = prob_to_logit(img)\n",
        "        idx = torch.randint(NUM_SCALES, size=(img.shape[0],),\n",
        "                            dtype=torch.long, device=\"cpu\")\n",
        "        tau = taus[idx][:,None,None,None]\n",
        "        x_noisy = log_concrete_sample(img_logit, tau=tau).to(device)\n",
        "        t = torch.ones(img.shape[0], device=device) * idx.to(device)\n",
        "        \n",
        "        scores = model(x_noisy, t)\n",
        "        loss = categorical_dsm_loss(img_logit.to(device), x_noisy, scores, tau.to(device))\n",
        "        # ===================backward====================\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0) \n",
        "        optimizer.step()\n",
        "        epoch_loss += loss.detach().cpu().data\n",
        "        train_losses.append(loss.detach().cpu().data)\n",
        "        nbatches += 1\n",
        "        niters += 1\n",
        "\n",
        "        if niters % 10 == 0:\n",
        "          model.eval()\n",
        "          eval_batches = 0\n",
        "          eval_loss = 0\n",
        "          for img, lab in val_ds:\n",
        "            img_logit = prob_to_logit(img).to(device)\n",
        "            idx = torch.randint(NUM_SCALES, size=(img.shape[0],),\n",
        "                            dtype=torch.long, device=device)\n",
        "            tau = taus[idx].to(device)[:,None,None,None]\n",
        "            t = torch.ones(img.shape[0], device=device) * idx\n",
        "            x_noisy = log_concrete_sample(img_logit, tau=tau)\n",
        "            scores = model(x_noisy, t)\n",
        "            loss = categorical_dsm_loss(img_logit, x_noisy, scores, tau)\n",
        "            eval_loss += loss.data\n",
        "            eval_batches += 1\n",
        "\n",
        "          eval_loss /= eval_batches\n",
        "          pbar.set_description(\"iter:{} - loss:{:.4f} - val_loss:{:.4f}\".format(niters, epoch_loss/nbatches, eval_loss))\n",
        "          val_losses.append(eval_loss.cpu().numpy())\n",
        "          model.train()\n",
        "        \n",
        "      model.train()\n",
        "  \n",
        "  return np.array(train_losses), np.array(val_losses)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WDLFysHOVemk"
      },
      "source": [
        "## Train model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 108,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vydx0QMMUdRr",
        "outputId": "898a8115-09f6-4a43-a9c3-f6adc84d946b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tensor([10.])\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "iter:60 - loss:23.9082 - val_loss:21.9669:   0%|          | 0/10 [00:51<?, ?it/s]\n"
          ]
        },
        {
          "ename": "KeyboardInterrupt",
          "evalue": "",
          "output_type": "error",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "Cell \u001b[0;32mIn [108], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m train_losses, val_losses \u001b[39m=\u001b[39m train(model, num_epochs\u001b[39m=\u001b[39;49m\u001b[39m10\u001b[39;49m, learning_rate\u001b[39m=\u001b[39;49m\u001b[39m3e-4\u001b[39;49m, device\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mcpu\u001b[39;49m\u001b[39m\"\u001b[39;49m)\n",
            "Cell \u001b[0;32mIn [107], line 39\u001b[0m, in \u001b[0;36mtrain\u001b[0;34m(model, num_epochs, learning_rate, name, sample_interval, dataset, device)\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[39m# ===================backward====================\u001b[39;00m\n\u001b[1;32m     38\u001b[0m optimizer\u001b[39m.\u001b[39mzero_grad()\n\u001b[0;32m---> 39\u001b[0m loss\u001b[39m.\u001b[39;49mbackward()\n\u001b[1;32m     40\u001b[0m torch\u001b[39m.\u001b[39mnn\u001b[39m.\u001b[39mutils\u001b[39m.\u001b[39mclip_grad_norm_(model\u001b[39m.\u001b[39mparameters(), max_norm\u001b[39m=\u001b[39m\u001b[39m1.0\u001b[39m) \n\u001b[1;32m     41\u001b[0m optimizer\u001b[39m.\u001b[39mstep()\n",
            "File \u001b[0;32m~/miniforge3/envs/ml-env/lib/python3.9/site-packages/torch/_tensor.py:396\u001b[0m, in \u001b[0;36mTensor.backward\u001b[0;34m(self, gradient, retain_graph, create_graph, inputs)\u001b[0m\n\u001b[1;32m    387\u001b[0m \u001b[39mif\u001b[39;00m has_torch_function_unary(\u001b[39mself\u001b[39m):\n\u001b[1;32m    388\u001b[0m     \u001b[39mreturn\u001b[39;00m handle_torch_function(\n\u001b[1;32m    389\u001b[0m         Tensor\u001b[39m.\u001b[39mbackward,\n\u001b[1;32m    390\u001b[0m         (\u001b[39mself\u001b[39m,),\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    394\u001b[0m         create_graph\u001b[39m=\u001b[39mcreate_graph,\n\u001b[1;32m    395\u001b[0m         inputs\u001b[39m=\u001b[39minputs)\n\u001b[0;32m--> 396\u001b[0m torch\u001b[39m.\u001b[39;49mautograd\u001b[39m.\u001b[39;49mbackward(\u001b[39mself\u001b[39;49m, gradient, retain_graph, create_graph, inputs\u001b[39m=\u001b[39;49minputs)\n",
            "File \u001b[0;32m~/miniforge3/envs/ml-env/lib/python3.9/site-packages/torch/autograd/__init__.py:173\u001b[0m, in \u001b[0;36mbackward\u001b[0;34m(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)\u001b[0m\n\u001b[1;32m    168\u001b[0m     retain_graph \u001b[39m=\u001b[39m create_graph\n\u001b[1;32m    170\u001b[0m \u001b[39m# The reason we repeat same the comment below is that\u001b[39;00m\n\u001b[1;32m    171\u001b[0m \u001b[39m# some Python versions print out the first line of a multi-line function\u001b[39;00m\n\u001b[1;32m    172\u001b[0m \u001b[39m# calls in the traceback and some print out the last line\u001b[39;00m\n\u001b[0;32m--> 173\u001b[0m Variable\u001b[39m.\u001b[39;49m_execution_engine\u001b[39m.\u001b[39;49mrun_backward(  \u001b[39m# Calls into the C++ engine to run the backward pass\u001b[39;49;00m\n\u001b[1;32m    174\u001b[0m     tensors, grad_tensors_, retain_graph, create_graph, inputs,\n\u001b[1;32m    175\u001b[0m     allow_unreachable\u001b[39m=\u001b[39;49m\u001b[39mTrue\u001b[39;49;00m, accumulate_grad\u001b[39m=\u001b[39;49m\u001b[39mTrue\u001b[39;49;00m)\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ],
      "source": [
        "train_losses, val_losses = train(model, num_epochs=10, learning_rate=3e-4, device=\"cpu\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "fBAazDkVUa8u",
        "outputId": "258283e4-a014-48a4-83de-76922637df2b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fd37ae67110>"
            ]
          },
          "execution_count": 83,
          "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": [
        "df = pd.DataFrame(train_losses[1000:])\n",
        "ema_loss= df.ewm(alpha=0.1).mean()\n",
        "ema_loss.plot()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "WbawhzmHnUnx",
        "outputId": "e50c084b-8396-4f8a-c7aa-93057cac7304"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fd37792e750>"
            ]
          },
          "execution_count": 86,
          "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": [
        "df = pd.DataFrame(train_losses[500:])\n",
        "ema_loss= df.ewm(alpha=0.1).mean()\n",
        "ema_loss.plot()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_fxiqsk0tDWm"
      },
      "outputs": [],
      "source": [
        "x_batch = x_noisy.cuda()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O2o-n948lJw_",
        "outputId": "5705f813-0258-48c5-86a6-190fd1743468"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "CPU times: user 79.3 ms, sys: 4.87 ms, total: 84.2 ms\n",
            "Wall time: 84 ms\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "torch.Size([1000, 3, 8, 8])"
            ]
          },
          "execution_count": 88,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "%%time\n",
        "# model.cpu()\n",
        "model.eval()\n",
        "with torch.no_grad():\n",
        "  scores = model(x_batch, torch.zeros(x_batch.shape[0], device=x_batch.device)).cpu()\n",
        "scores.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "5M9O4liQPD0s",
        "outputId": "ae728ded-2794-46d6-c6a8-0447480d3d2d"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1440x288 with 6 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "score_mean = scores.mean(0)\n",
        "fig, axs = plt.subplots(1,N_CATEGORIES, figsize=(20,4))\n",
        "for i in range(N_CATEGORIES):\n",
        "  sns.heatmap(score_mean[i], ax=axs[i], cmap=\"RdBu\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eSINkT1Smz7a",
        "outputId": "24af77d4-decf-4028-db17-a37cb46f3e7f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(torch.Size([3, 8, 8]), torch.Size([3, 8, 8]), torch.Size([3, 8, 8]))"
            ]
          },
          "execution_count": 112,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x_rec = x_noisy + (scores * 2e-2)\n",
        "x_rec_mean = x_rec.mean(0)\n",
        "x_rec_probs = x_rec_mean.softmax(0)\n",
        "\n",
        "anal_x_rec = x_noisy + (x_grad * 2e-2)\n",
        "anal_x_rec_probs = anal_x_rec.mean(0).softmax(0)\n",
        "x_rec_mean.shape, x_noisy_mean.shape, x_rec_probs.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 776
        },
        "id": "5CmWM1LAthT7",
        "outputId": "cc9f5036-de15-4452-ebc8-baddd539a048"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1280x960 with 18 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "idx=3\n",
        "fig, axs = plt.subplots(3, N_CATEGORIES, figsize=(16,12), dpi=80)\n",
        "for i in range(N_CATEGORIES):\n",
        "  sns.heatmap(x_noisy[idx].exp()[i], ax=axs[0,i], vmin=0.0, vmax=None, cmap=\"Reds\")\n",
        "  sns.heatmap(x_rec[idx].exp()[i], ax=axs[1,i], vmin=0.0, cmap=\"Reds\")\n",
        "  sns.heatmap(anal_x_rec[idx].exp()[i], ax=axs[2,i], vmin=0.0, vmax=None, cmap=\"Reds\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CHctNf0a98Mr",
        "outputId": "526ea924-cb8b-455a-acc8-9a9b76cf9896"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor(0.1443)"
            ]
          },
          "execution_count": 114,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "torch.sum((x_rec[idx] - anal_x_rec[idx])**2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lLnkZu2RA_JM",
        "outputId": "98d7e543-90b5-45c1-d702-d5a44ddf19a5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tensor(2.0027e-05)\n"
          ]
        }
      ],
      "source": [
        "print(torch.logsumexp(x_logit, dim=1).mean())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6-Pvk0X2EqpD"
      },
      "source": [
        "> ### If I subtract LSE everytime, then I am \"removing\" more than I am updating via score\n",
        "> ### so it will prolly nullify all my score climbing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TwszHBda_Z1E",
        "outputId": "e903f05a-205f-4332-9e05-6b95a269884f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "torch.Size([1, 3, 8, 8])"
            ]
          },
          "execution_count": 191,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "model.eval()\n",
        "with torch.no_grad():\n",
        "  x_denoised = x_noisy[:1].clone().cuda()\n",
        "  for i in range(20):\n",
        "    # print(torch.logsumexp(x_denoised, dim=1).mean())\n",
        "    s = model(x_denoised, torch.zeros(1,device=\"cuda\"))\n",
        "    x_denoised = x_denoised + s * 1e-2\n",
        "\n",
        "    # Small hack to normalize logits back to conform with\n",
        "    # concrete distribution as it expects LSE to be zero ideally\n",
        "    if torch.logsumexp(x_denoised, dim=1).mean().abs() > 1e-5:\n",
        "      x_denoised -= torch.logsumexp(x_denoised, dim=1)\n",
        "\n",
        "x_denoised.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r9o88CMUFCTa",
        "outputId": "3dba26c7-b730-405e-c32f-b5b482e06e33"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(tensor(0.0129, device='cuda:0'), tensor(2.5810e-07))"
            ]
          },
          "execution_count": 196,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "torch.linalg.norm(s * 1e-2), torch.logsumexp(x_noisy[:1], dim=1).norm()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2EK3nG3MApC_",
        "outputId": "3ce6a0c1-5588-4bf6-ad49-6dc6d14ad4f7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor(1.3970e-09, device='cuda:0')"
            ]
          },
          "execution_count": 192,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "torch.logsumexp(x_denoised, dim=1).mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "yww6xw8h_ykW",
        "outputId": "8b27be55-26f8-4f37-a6d8-3ce43c5f2d25"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1152x576 with 12 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, axs = plt.subplots(2, N_CATEGORIES, figsize=(16,8))\n",
        "for i in range(N_CATEGORIES):\n",
        "  sns.heatmap(x_noisy[0].exp()[i], ax=axs[0,i], vmin=0.0, vmax=None, cmap=\"Reds\")\n",
        "  sns.heatmap(x_denoised[0,i].exp().cpu(), ax=axs[1,i], cmap=\"Reds\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "d1gHpfYAABwL"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "collapsed_sections": [],
      "provenance": []
    },
    "gpuClass": "standard",
    "kernelspec": {
      "display_name": "Python 3.9.13 ('ml-env')",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.13"
    },
    "vscode": {
      "interpreter": {
        "hash": "b8e3016ad78f72f4f7374acabde5ab0274e8ff7d7511d6f467ddd3d698452913"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}