07_VAE.ipynb

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  "metadata": {
    "colab": {
      "name": "07_VAE.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNCd4tJHR+LW9LSNDarRCA1",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OUCTheoryGroup/colab_demo/blob/master/07_VAE.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RfEpWhQdVTxI",
        "colab_type": "text"
      },
      "source": [
        "## 变分自编码器 （Variational Auto-Encoder， VAE）\n",
        "\n",
        "VAE的示意图如下所示：\n",
        "\n",
        "![VAE示意图](https://raw.githubusercontent.com/summitgao/ImageGallery/master/20200227190742.jpg)\n",
        "\n",
        "通常会拿 VAE 跟 GAN 比较，的确，它们两个的目标基本是一致的：希望构建一个从隐变量 Z 生成目标数据 X 的模型，但是实现上有所不同。\n",
        "\n",
        "下面结合代码来分析。首先是引入基本的库文件，以及定义一个用于显示图像的函数。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NL_aqocWFpq6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import torchvision\n",
        "from torch import nn\n",
        "from torch.utils.data import DataLoader\n",
        "from torchvision import transforms\n",
        "from torchvision.datasets import MNIST\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "# Displaying routine\n",
        "def display_images(in_, out, n=1, label=None, count=False):\n",
        "    for N in range(n):\n",
        "        if in_ is not None:\n",
        "            in_pic = in_.data.cpu().view(-1, 28, 28)\n",
        "            plt.figure(figsize=(6, 2))\n",
        "            plt.suptitle(label + ' – real test data / reconstructions', color='w', fontsize=16)\n",
        "            for i in range(4):\n",
        "                plt.subplot(1,4,i+1)\n",
        "                plt.imshow(in_pic[i+4*N], 'gray')\n",
        "                plt.axis('off')\n",
        "        out_pic = out.data.cpu().view(-1, 28, 28)\n",
        "        plt.figure(figsize=(6, 2))\n",
        "        for i in range(4):\n",
        "            plt.subplot(1,4,i+1)\n",
        "            plt.imshow(out_pic[i+4*N], 'gray')\n",
        "            plt.axis('off')\n",
        "            if count: plt.title(str(4 * N + i), color='w')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PNPVjkC7W8Lk",
        "colab_type": "text"
      },
      "source": [
        "接下来是定义 train_loader 和 test_loader"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x9_Pn8KuF30l",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Set random seeds\n",
        "torch.manual_seed(1)\n",
        "torch.cuda.manual_seed(1)\n",
        "\n",
        "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
        "\n",
        "batch_size = 256\n",
        "\n",
        "train_loader = torch.utils.data.DataLoader(\n",
        "    MNIST('./data', train=True, download=True,\n",
        "                   transform=transforms.ToTensor()),\n",
        "    batch_size=batch_size, shuffle=True)\n",
        "test_loader = torch.utils.data.DataLoader(\n",
        "    MNIST('./data', train=False, transform=transforms.ToTensor()),\n",
        "    batch_size=batch_size, shuffle=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XnLPRPOkXE1y",
        "colab_type": "text"
      },
      "source": [
        "接下来就是定义VAE模型。\n",
        "包括 编码器 和 解码器，维度变化细节为：\n",
        "- 编码器： 784 ==> 40 ==> 40\n",
        "- 解码器： 20 ==> 40 ==> 784\n",
        "\n",
        "这里可以看，编码器输出数据维度是 40 ，但解码器输入的数据维度是 20。 中间连接有一个 reparameterise 函数，即重参数，图示如下：\n",
        "\n",
        "![重参数](https://raw.githubusercontent.com/summitgao/ImageGallery/master/20200227191909.jpg)\n",
        "\n",
        "其中原理的话，大家可以看看知乎文章《[变分自编码器VAE：原来是这么一回事](https://zhuanlan.zhihu.com/p/34998569)》\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ExbCGXpRGJdj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "d = 20\n",
        "\n",
        "class VAE(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.encoder = nn.Sequential(\n",
        "            nn.Linear(784, d ** 2),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(d ** 2, d * 2))\n",
        "        self.decoder = nn.Sequential(\n",
        "            nn.Linear(d, d ** 2),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(d ** 2, 784),\n",
        "            nn.Sigmoid())\n",
        "\n",
        "    def reparameterise(self, mu, logvar):\n",
        "        if self.training:\n",
        "            std = logvar.mul(0.5).exp_()\n",
        "            eps = std.data.new(std.size()).normal_()\n",
        "            return eps.mul(std).add_(mu)\n",
        "        else:\n",
        "            return mu\n",
        "\n",
        "    def forward(self, x):\n",
        "        mu_logvar = self.encoder(x.view(-1, 784)).view(-1, 2, d)\n",
        "        mu = mu_logvar[:, 0, :]\n",
        "        logvar = mu_logvar[:, 1, :]\n",
        "        z = self.reparameterise(mu, logvar)\n",
        "        return self.decoder(z), mu, logvar\n",
        "\n",
        "model = VAE().to(device)\n",
        "learning_rate = 1e-3\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_H-C_rC8Gae0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Reconstruction + KL divergence losses summed over all elements and batch\n",
        "def loss_function(x_hat, x, mu, logvar):\n",
        "    BCE = nn.functional.binary_cross_entropy(\n",
        "        x_hat, x.view(-1, 784), reduction='sum')\n",
        "    KLD = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())\n",
        "    return BCE + KLD"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iZZQrVBYGhBJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "7b3d7f6e-d1bd-43f9-ed2d-a619f4fe88bd"
      },
      "source": [
        "# Training and testing the VAE\n",
        "epochs = 10\n",
        "for epoch in range(1, epochs + 1):\n",
        "    # Training\n",
        "    model.train()\n",
        "    train_loss = 0\n",
        "    for x, _ in train_loader:\n",
        "        x = x.to(device)\n",
        "        # ===================forward=====================\n",
        "        x_hat, mu, logvar = model(x)\n",
        "        loss = loss_function(x_hat, x, mu, logvar)\n",
        "        train_loss += loss.item()\n",
        "        # ===================backward====================\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "    # ===================log========================\n",
        "    print(f'====> Epoch: {epoch} Average loss: {train_loss / len(train_loader.dataset):.4f}')\n",
        "    \n",
        "    # Testing\n",
        "    with torch.no_grad():\n",
        "        model.eval()\n",
        "        test_loss = 0\n",
        "        for x, _ in test_loader:\n",
        "            x = x.to(device)\n",
        "            # ===================forward=====================\n",
        "            x_hat, mu, logvar = model(x)\n",
        "            test_loss += loss_function(x_hat, x, mu, logvar).item()\n",
        "    # ===================log========================\n",
        "    test_loss /= len(test_loader.dataset)\n",
        "    print(f'====> Test set loss: {test_loss:.4f}')\n",
        "    display_images(x, x_hat, 1, f'Epoch {epoch}')"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "====> Epoch: 1 Average loss: 188.2892\n",
            "====> Test set loss: 135.9683\n",
            "====> Epoch: 2 Average loss: 132.5792\n",
            "====> Test set loss: 116.0247\n",
            "====> Epoch: 3 Average loss: 121.1741\n",
            "====> Test set loss: 109.1417\n",
            "====> Epoch: 4 Average loss: 116.2666\n",
            "====> Test set loss: 105.1034\n",
            "====> Epoch: 5 Average loss: 113.3771\n",
            "====> Test set loss: 104.1403\n",
            "====> Epoch: 6 Average loss: 111.5197\n",
            "====> Test set loss: 101.6781\n",
            "====> Epoch: 7 Average loss: 110.1940\n",
            "====> Test set loss: 100.5811\n",
            "====> Epoch: 8 Average loss: 109.2270\n",
            "====> Test set loss: 100.0496\n",
            "====> Epoch: 9 Average loss: 108.4431\n",
            "====> Test set loss: 98.6812\n",
            "====> Epoch: 10 Average loss: 107.7578\n",
            "====> Test set loss: 98.2803\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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jOLz99tsD8Mwzz8SyYcOGATB9+vQi5TgVe5KGYRiBMAVsGIYRCHNBrGO8+eabcbhPnz4A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\nEQhTwIZhGIEwBWwYhhEIU8CGYRiB+Dc1i+g7sZv9dwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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arjqy2dhj5syZIWMgTSvGtLqMmljqwD/VKlJal7YWfPrpp2PMSrYqtHVrNayKuueee0Km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\nGmNMRrzpGmNMRrzpGmNMRv4F9Lb8ale1LKMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ccksf/vDDDwFo3bp1KbLOyq233urDF198cdnKMROEYRhGhbHeaMAbb7yxD7u3qtPmADbc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\ngg==\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jzW1MV9Ql0h6i3MqqoYAZM2Ys8+drcm733XcHkB5tM2XKFADA4sWLQ9ekgxTpIqsbyTHV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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KwEGlkAUshBApIQUshBApUZUuiIsuuihJ53I9PPTQQwBccsklSd5XX31VfsEE66yzDgBt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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dwIEDC/8CxYIjo7XUwbVAZYjQE088ETpGHNpemtpV2Bns6RpjTEa86BpjTEaa2gu5m5qa\nHI9Xobm5ucNHS/SEfVmMnDhxYujuuOMOAMWdgU8++WTI7K3moBIgXwGyo/bNZVtNeXHOrg60IWov\n7SVlONwThclat62muzgTm/O2AWDMmDGFf1vCtIPaW+cSL1q0CEAxvck0UGe/j/Zsa0/XGGMy4kXX\nGGMy4vRCJylbeoHooBYel6RzjbV3kcct6XFJuaj1ELjM1IttNQ2RGkak17qmDdj11B2pHacXjDGm\nRrCn20nK6umWhXrxxmoR27b7sKdrjDE1ghddY4zJiBddY4zJiBddY4zJiBddY4zJiBddY4zJiBdd\nY4zJSLt9usYYY7oWe7rGGJMRL7rGGJMRL7rGGJMRL7rGGJMRL7rGGJMRL7rGGJOR/wGXg8l2Mn5Z\nOAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mPm7LLbf04S+//LJ0hc1gbZuMp1u3bgCMHTs2rjw+XIx8y8Vrr73mw+E9De9fLmwyHsMw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\nkhk1mo8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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V7vijRaQ7Ajl+mpzU5AMP/tRdarRgtfZZvQpasqkabP1MtahffvllAMX7oONbFktX0Z61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\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dEM8880wc9kfjJLF3714AZs6cGcf5z/OKFSuATPfaaaedFoeXLl0KwJo1ayoucB7MBWEY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\npAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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u70hZ2yhz1G7JGG8K1XAb7YzURNpQJn5G+9qOZPpaW1u6xhhTEB+6xhhTkD7DC8YYY1qL\nLV1jjCmID11jjCmID11jjCmID11jjCmID11jjCmID11jjCnIvyumP4/L7uQQAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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m14aHHnrIy717966TfSZRTlZabTjwwAO97GJaAU4++WQAtttuu8TtHn30UQDOPvvsOq9T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\ntdT+AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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yaOuwDqqJGvJFixalTutOo063Efu5GddW52wPHDgw5biGR2ug586dC8DYsWNTp8OZOjJE\ntqK1taVrjDE10mEXU1ZdPLmsbFYeTUKMHj065Zisr+uvVpZZecIj0yRvyHoFu/k34ZnFrRgAI0eO\nTDk8BbWEI7HZ2W6EsaVrjDE14kPXGGNqpMPCC6YxhPulNw2oSxa3dOgFfTGvuOpSUGPqoOrCWg3T\nRKuvhh8vv/xyAObNm5e6zlBfbkvXGGNqpMNKxlqFZi0ZU3SgUHT6aSItysOa0UpoxrKmVqEZ11a9\nLZVjaJMOb4p924xXzrtkzBhjmgQfusYYUyMrDC8YY4xZvdjSNcaYGvGha4wxNeJD1xhjasSHrjHG\n1IgPXWOMqREfusYYUyN/A0mGVDpKTDaXAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xxwbZ/PnzC1i6MmqrBXzccceF8NSpU0PY661x48YF2dChQwH46KOPgmz79u0hvPfeewPw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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HhhemT58eMl1jnbuer4dG2WrTbekaY0xCWtp7qra0tHTaI1d3mbDFm3aA1x1nPNdIrQlt\nclGLkytIa2trhw9968zxLQsdHV+PbWU8trWjvbG1pWuMMQnxomuMMQlpN7xgjDGmutjSNcaYhHjR\nNcaYhHjRNcaYhHjRNcaYhHjRNcaYhHjRNcaYhPwHVf1hNDuvzbEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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98ssvR+G33347Cv/2t78FYOzYsZFs7dq1AJxwwgmR7MMPPyy4nPXpvli3bh0AzZs3L/iY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\nIEwpG4ZhJIj/B6vNEBZ3NdQVAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TYnjSNcaYjGSv0+WqMt10ThM4s2bNAgAsXbo0dFVsmlIL6Epp8597770XQLme8eyzzw6Z\nNZIacmDiRl3cFOpaaXKCG/xxtZueWxVRV//5558PmSvJdNeOiRMnAignx/R41ulqIxatVeVuHFqT\ny9Cb3mO9d7VYNVUlNFSgY8ZQQqoeuJ4rXm3pGmNMRjzpGmNMRtq6Mp3b2tpqYlentjRR91ZdVWZu\nWyWk0N7e3rVP3gW1Gl+FNdG67HTcuHEhsw/u5MmTQ8fqBD1GXS66ZFySCgALFiwIec6cOQDKWfda\n0dvxrcfYrsdnd5A1xKahBtbpas2q1rUz9KZLXpmB7+uy+FYc276SCqHVIwzT1dja0jXGmIxksXSr\nTLNZun1BrTGlkTsR9EdrLBce2/phS9cYY5oET7rGGJOR7DtHmOalyrW1xjQLtnSNMSYjnnSNMSYj\nnnSNMSYjnnSNMSYjXdbpGmOMqS22dI0xJiOedI0xJiOedI0xJiOedI0xJiOedI0xJiOedI0xJiP/\nA5juu82gy4VYAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tXiJ4Mf6aSsh",
        "colab_type": "text"
      },
      "source": [
        "在 VAE 训练完成以后，我们输入一组噪声，试试样本生成的效果。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vPZ0egTLHe2Q",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 429
        },
        "outputId": "cdf720bf-2529-4bd3-8f6d-b4699ee2e13e"
      },
      "source": [
        "N = 16\n",
        "z = torch.randn((N, d)).to(device)\n",
        "sample = model.decoder(z)\n",
        "display_images(None, sample, N // 4, count=True)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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fD8CYMWOSTsMwEU4r6+S2pqNhlgg1aHgg9gg9vq59muM56VrVdR8dyfQYcXymr2e8OtjS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\nZMSbrjHGZMSbrjHGZOT/AbYRgt1Qui2bAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x144 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K3GAEbcQbKqp",
        "colab_type": "text"
      },
      "source": [
        "可以看到，上面的代码基本完成了输入一组随机噪声，生成数字的任务，但是效果差强人意。"
      ]
    }
  ]
}