1447 lines
54 KiB
Plaintext
1447 lines
54 KiB
Plaintext
{
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"cells": [
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{
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||
"cell_type": "markdown",
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||
"id": "ded8d82e",
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||
"metadata": {
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"origin_pos": 0
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||
},
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"source": [
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"# 残差网络（ResNet）\n",
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":label:`sec_resnet`\n",
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"\n",
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"随着我们设计越来越深的网络，深刻理解“新添加的层如何提升神经网络的性能”变得至关重要。更重要的是设计网络的能力，在这种网络中，添加层会使网络更具表现力，\n",
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"为了取得质的突破，我们需要一些数学基础知识。\n",
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"\n",
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"## 函数类\n",
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"\n",
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"首先，假设有一类特定的神经网络架构$\\mathcal{F}$，它包括学习速率和其他超参数设置。\n",
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"对于所有$f \\in \\mathcal{F}$，存在一些参数集（例如权重和偏置），这些参数可以通过在合适的数据集上进行训练而获得。\n",
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"现在假设$f^*$是我们真正想要找到的函数，如果是$f^* \\in \\mathcal{F}$，那我们可以轻而易举的训练得到它，但通常我们不会那么幸运。\n",
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"相反，我们将尝试找到一个函数$f^*_\\mathcal{F}$，这是我们在$\\mathcal{F}$中的最佳选择。\n",
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"例如，给定一个具有$\\mathbf{X}$特性和$\\mathbf{y}$标签的数据集，我们可以尝试通过解决以下优化问题来找到它：\n",
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"\n",
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"$$f^*_\\mathcal{F} := \\mathop{\\mathrm{argmin}}_f L(\\mathbf{X}, \\mathbf{y}, f) \\text{ subject to } f \\in \\mathcal{F}.$$\n",
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"\n",
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"那么，怎样得到更近似真正$f^*$的函数呢？\n",
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"唯一合理的可能性是，我们需要设计一个更强大的架构$\\mathcal{F}'$。\n",
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"换句话说，我们预计$f^*_{\\mathcal{F}'}$比$f^*_{\\mathcal{F}}$“更近似”。\n",
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"然而，如果$\\mathcal{F} \\not\\subseteq \\mathcal{F}'$，则无法保证新的体系“更近似”。\n",
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"事实上，$f^*_{\\mathcal{F}'}$可能更糟：\n",
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"如 :numref:`fig_functionclasses`所示，对于非嵌套函数（non-nested function）类，较复杂的函数类并不总是向“真”函数$f^*$靠拢（复杂度由$\\mathcal{F}_1$向$\\mathcal{F}_6$递增）。\n",
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"在 :numref:`fig_functionclasses`的左边，虽然$\\mathcal{F}_3$比$\\mathcal{F}_1$更接近$f^*$，但$\\mathcal{F}_6$却离的更远了。\n",
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"相反对于 :numref:`fig_functionclasses`右侧的嵌套函数（nested function）类$\\mathcal{F}_1 \\subseteq \\ldots \\subseteq \\mathcal{F}_6$，我们可以避免上述问题。\n",
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"\n",
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"\n",
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":label:`fig_functionclasses`\n",
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"\n",
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"因此，只有当较复杂的函数类包含较小的函数类时，我们才能确保提高它们的性能。\n",
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"对于深度神经网络，如果我们能将新添加的层训练成*恒等映射*（identity function）$f(\\mathbf{x}) = \\mathbf{x}$，新模型和原模型将同样有效。\n",
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"同时，由于新模型可能得出更优的解来拟合训练数据集，因此添加层似乎更容易降低训练误差。\n",
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"\n",
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"针对这一问题，何恺明等人提出了*残差网络*（ResNet） :cite:`He.Zhang.Ren.ea.2016`。\n",
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"它在2015年的ImageNet图像识别挑战赛夺魁，并深刻影响了后来的深度神经网络的设计。\n",
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"残差网络的核心思想是：每个附加层都应该更容易地包含原始函数作为其元素之一。\n",
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"于是，*残差块*（residual blocks）便诞生了，这个设计对如何建立深层神经网络产生了深远的影响。\n",
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"凭借它，ResNet赢得了2015年ImageNet大规模视觉识别挑战赛。\n",
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"\n",
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"## (**残差块**)\n",
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"\n",
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"让我们聚焦于神经网络局部：如图 :numref:`fig_residual_block`所示，假设我们的原始输入为$x$，而希望学出的理想映射为$f(\\mathbf{x})$（作为 :numref:`fig_residual_block`上方激活函数的输入）。\n",
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" :numref:`fig_residual_block`左图虚线框中的部分需要直接拟合出该映射$f(\\mathbf{x})$，而右图虚线框中的部分则需要拟合出残差映射$f(\\mathbf{x}) - \\mathbf{x}$。\n",
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"残差映射在现实中往往更容易优化。\n",
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"以本节开头提到的恒等映射作为我们希望学出的理想映射$f(\\mathbf{x})$，我们只需将 :numref:`fig_residual_block`中右图虚线框内上方的加权运算（如仿射）的权重和偏置参数设成0，那么$f(\\mathbf{x})$即为恒等映射。\n",
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"实际中，当理想映射$f(\\mathbf{x})$极接近于恒等映射时，残差映射也易于捕捉恒等映射的细微波动。\n",
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" :numref:`fig_residual_block`右图是ResNet的基础架构--*残差块*（residual block）。\n",
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"在残差块中，输入可通过跨层数据线路更快地向前传播。\n",
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"\n",
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"\n",
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":label:`fig_residual_block`\n",
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"\n",
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"ResNet沿用了VGG完整的$3\\times 3$卷积层设计。\n",
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"残差块里首先有2个有相同输出通道数的$3\\times 3$卷积层。\n",
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"每个卷积层后接一个批量规范化层和ReLU激活函数。\n",
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"然后我们通过跨层数据通路，跳过这2个卷积运算，将输入直接加在最后的ReLU激活函数前。\n",
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"这样的设计要求2个卷积层的输出与输入形状一样，从而使它们可以相加。\n",
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"如果想改变通道数，就需要引入一个额外的$1\\times 1$卷积层来将输入变换成需要的形状后再做相加运算。\n",
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"残差块的实现如下：\n"
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]
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},
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{
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"cell_type": "code",
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||
"execution_count": 1,
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||
"id": "de076347",
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||
"metadata": {
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||
"execution": {
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||
"iopub.execute_input": "2023-08-18T07:23:09.985121Z",
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||
"iopub.status.busy": "2023-08-18T07:23:09.984259Z",
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||
"iopub.status.idle": "2023-08-18T07:23:13.061925Z",
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||
"shell.execute_reply": "2023-08-18T07:23:13.061035Z"
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},
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||
"origin_pos": 2,
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||
"tab": [
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||
"pytorch"
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||
]
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},
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"outputs": [],
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"source": [
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"import torch\n",
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"from torch import nn\n",
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"from torch.nn import functional as F\n",
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"from d2l import torch as d2l\n",
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"\n",
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"\n",
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"class Residual(nn.Module): #@save\n",
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" def __init__(self, input_channels, num_channels,\n",
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" use_1x1conv=False, strides=1):\n",
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" super().__init__()\n",
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" self.conv1 = nn.Conv2d(input_channels, num_channels,\n",
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" kernel_size=3, padding=1, stride=strides)\n",
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" self.conv2 = nn.Conv2d(num_channels, num_channels,\n",
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" kernel_size=3, padding=1)\n",
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" if use_1x1conv:\n",
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" self.conv3 = nn.Conv2d(input_channels, num_channels,\n",
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" kernel_size=1, stride=strides)\n",
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" else:\n",
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" self.conv3 = None\n",
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" self.bn1 = nn.BatchNorm2d(num_channels)\n",
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" self.bn2 = nn.BatchNorm2d(num_channels)\n",
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"\n",
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" def forward(self, X):\n",
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" Y = F.relu(self.bn1(self.conv1(X)))\n",
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" Y = self.bn2(self.conv2(Y))\n",
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" if self.conv3:\n",
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" X = self.conv3(X)\n",
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" Y += X\n",
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" return F.relu(Y)"
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]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"id": "800b1b46",
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||
"metadata": {
|
||
"origin_pos": 5
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||
},
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||
"source": [
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||
"如 :numref:`fig_resnet_block`所示，此代码生成两种类型的网络：\n",
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"一种是当`use_1x1conv=False`时，应用ReLU非线性函数之前，将输入添加到输出。\n",
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"另一种是当`use_1x1conv=True`时，添加通过$1 \\times 1$卷积调整通道和分辨率。\n",
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"\n",
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"\n",
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":label:`fig_resnet_block`\n",
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"\n",
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"下面我们来查看[**输入和输出形状一致**]的情况。\n"
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]
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||
},
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{
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||
"cell_type": "code",
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||
"execution_count": 2,
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||
"id": "af9ca1b9",
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||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:23:13.066634Z",
|
||
"iopub.status.busy": "2023-08-18T07:23:13.065953Z",
|
||
"iopub.status.idle": "2023-08-18T07:23:13.103556Z",
|
||
"shell.execute_reply": "2023-08-18T07:23:13.102121Z"
|
||
},
|
||
"origin_pos": 7,
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||
"tab": [
|
||
"pytorch"
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||
]
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||
},
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||
"outputs": [
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||
{
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||
"data": {
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||
"text/plain": [
|
||
"torch.Size([4, 3, 6, 6])"
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||
]
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||
},
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||
"execution_count": 2,
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||
"metadata": {},
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||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
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||
"blk = Residual(3,3)\n",
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||
"X = torch.rand(4, 3, 6, 6)\n",
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||
"Y = blk(X)\n",
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"Y.shape"
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||
]
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||
},
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||
{
|
||
"cell_type": "markdown",
|
||
"id": "419b9a4a",
|
||
"metadata": {
|
||
"origin_pos": 10
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||
},
|
||
"source": [
|
||
"我们也可以在[**增加输出通道数的同时，减半输出的高和宽**]。\n"
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||
]
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||
},
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||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "e9a01bd0",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:23:13.108447Z",
|
||
"iopub.status.busy": "2023-08-18T07:23:13.107641Z",
|
||
"iopub.status.idle": "2023-08-18T07:23:13.127450Z",
|
||
"shell.execute_reply": "2023-08-18T07:23:13.126006Z"
|
||
},
|
||
"origin_pos": 12,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"torch.Size([4, 6, 3, 3])"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"blk = Residual(3,6, use_1x1conv=True, strides=2)\n",
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||
"blk(X).shape"
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||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a77a7e4f",
|
||
"metadata": {
|
||
"origin_pos": 15
|
||
},
|
||
"source": [
|
||
"## [**ResNet模型**]\n",
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"\n",
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||
"ResNet的前两层跟之前介绍的GoogLeNet中的一样：\n",
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"在输出通道数为64、步幅为2的$7 \\times 7$卷积层后，接步幅为2的$3 \\times 3$的最大汇聚层。\n",
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||
"不同之处在于ResNet每个卷积层后增加了批量规范化层。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "e4fe2ed6",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:23:13.134088Z",
|
||
"iopub.status.busy": "2023-08-18T07:23:13.133092Z",
|
||
"iopub.status.idle": "2023-08-18T07:23:13.141355Z",
|
||
"shell.execute_reply": "2023-08-18T07:23:13.140086Z"
|
||
},
|
||
"origin_pos": 17,
|
||
"tab": [
|
||
"pytorch"
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||
]
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),\n",
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||
" nn.BatchNorm2d(64), nn.ReLU(),\n",
|
||
" nn.MaxPool2d(kernel_size=3, stride=2, padding=1))"
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||
]
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||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4c0dcc5c",
|
||
"metadata": {
|
||
"origin_pos": 20
|
||
},
|
||
"source": [
|
||
"GoogLeNet在后面接了4个由Inception块组成的模块。\n",
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||
"ResNet则使用4个由残差块组成的模块，每个模块使用若干个同样输出通道数的残差块。\n",
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||
"第一个模块的通道数同输入通道数一致。\n",
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||
"由于之前已经使用了步幅为2的最大汇聚层，所以无须减小高和宽。\n",
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||
"之后的每个模块在第一个残差块里将上一个模块的通道数翻倍，并将高和宽减半。\n",
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"\n",
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||
"下面我们来实现这个模块。注意，我们对第一个模块做了特别处理。\n"
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||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "748cfd51",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:23:13.146374Z",
|
||
"iopub.status.busy": "2023-08-18T07:23:13.145731Z",
|
||
"iopub.status.idle": "2023-08-18T07:23:13.152040Z",
|
||
"shell.execute_reply": "2023-08-18T07:23:13.150742Z"
|
||
},
|
||
"origin_pos": 22,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def resnet_block(input_channels, num_channels, num_residuals,\n",
|
||
" first_block=False):\n",
|
||
" blk = []\n",
|
||
" for i in range(num_residuals):\n",
|
||
" if i == 0 and not first_block:\n",
|
||
" blk.append(Residual(input_channels, num_channels,\n",
|
||
" use_1x1conv=True, strides=2))\n",
|
||
" else:\n",
|
||
" blk.append(Residual(num_channels, num_channels))\n",
|
||
" return blk"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3351bfea",
|
||
"metadata": {
|
||
"origin_pos": 25
|
||
},
|
||
"source": [
|
||
"接着在ResNet加入所有残差块，这里每个模块使用2个残差块。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "cbb6978f",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:23:13.157627Z",
|
||
"iopub.status.busy": "2023-08-18T07:23:13.156822Z",
|
||
"iopub.status.idle": "2023-08-18T07:23:13.350496Z",
|
||
"shell.execute_reply": "2023-08-18T07:23:13.349272Z"
|
||
},
|
||
"origin_pos": 27,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"b2 = nn.Sequential(*resnet_block(64, 64, 2, first_block=True))\n",
|
||
"b3 = nn.Sequential(*resnet_block(64, 128, 2))\n",
|
||
"b4 = nn.Sequential(*resnet_block(128, 256, 2))\n",
|
||
"b5 = nn.Sequential(*resnet_block(256, 512, 2))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "badd44e1",
|
||
"metadata": {
|
||
"origin_pos": 29
|
||
},
|
||
"source": [
|
||
"最后，与GoogLeNet一样，在ResNet中加入全局平均汇聚层，以及全连接层输出。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "2e587937",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:23:13.355546Z",
|
||
"iopub.status.busy": "2023-08-18T07:23:13.354729Z",
|
||
"iopub.status.idle": "2023-08-18T07:23:13.361543Z",
|
||
"shell.execute_reply": "2023-08-18T07:23:13.360406Z"
|
||
},
|
||
"origin_pos": 31,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"net = nn.Sequential(b1, b2, b3, b4, b5,\n",
|
||
" nn.AdaptiveAvgPool2d((1,1)),\n",
|
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" nn.Flatten(), nn.Linear(512, 10))"
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]
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},
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"cell_type": "markdown",
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},
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"source": [
|
||
"每个模块有4个卷积层（不包括恒等映射的$1\\times 1$卷积层）。\n",
|
||
"加上第一个$7\\times 7$卷积层和最后一个全连接层，共有18层。\n",
|
||
"因此，这种模型通常被称为ResNet-18。\n",
|
||
"通过配置不同的通道数和模块里的残差块数可以得到不同的ResNet模型，例如更深的含152层的ResNet-152。\n",
|
||
"虽然ResNet的主体架构跟GoogLeNet类似，但ResNet架构更简单，修改也更方便。这些因素都导致了ResNet迅速被广泛使用。\n",
|
||
" :numref:`fig_resnet18`描述了完整的ResNet-18。\n",
|
||
"\n",
|
||
"\n",
|
||
":label:`fig_resnet18`\n",
|
||
"\n",
|
||
"在训练ResNet之前，让我们[**观察一下ResNet中不同模块的输入形状是如何变化的**]。\n",
|
||
"在之前所有架构中，分辨率降低，通道数量增加，直到全局平均汇聚层聚集所有特征。\n"
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]
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},
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"cell_type": "code",
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"execution_count": 8,
|
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"id": "3ea90646",
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"metadata": {
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"execution": {
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"shell.execute_reply": "2023-08-18T07:23:13.414636Z"
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},
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"tab": [
|
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"pytorch"
|
||
]
|
||
},
|
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"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
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"text": [
|
||
"Sequential output shape:\t torch.Size([1, 64, 56, 56])\n",
|
||
"Sequential output shape:\t torch.Size([1, 64, 56, 56])\n",
|
||
"Sequential output shape:\t torch.Size([1, 128, 28, 28])\n",
|
||
"Sequential output shape:\t torch.Size([1, 256, 14, 14])\n",
|
||
"Sequential output shape:\t torch.Size([1, 512, 7, 7])\n",
|
||
"AdaptiveAvgPool2d output shape:\t torch.Size([1, 512, 1, 1])\n",
|
||
"Flatten output shape:\t torch.Size([1, 512])\n",
|
||
"Linear output shape:\t torch.Size([1, 10])\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"X = torch.rand(size=(1, 1, 224, 224))\n",
|
||
"for layer in net:\n",
|
||
" X = layer(X)\n",
|
||
" print(layer.__class__.__name__,'output shape:\\t', X.shape)"
|
||
]
|
||
},
|
||
{
|
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"cell_type": "markdown",
|
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"metadata": {
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},
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"source": [
|
||
"## [**训练模型**]\n",
|
||
"\n",
|
||
"同之前一样，我们在Fashion-MNIST数据集上训练ResNet。\n"
|
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]
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},
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"id": "e8e65fec",
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"metadata": {
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"pytorch"
|
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]
|
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},
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"outputs": [
|
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{
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"name": "stdout",
|
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"output_type": "stream",
|
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"text": [
|
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"loss 0.012, train acc 0.997, test acc 0.893\n",
|
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"5032.7 examples/sec on cuda:0\n"
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]
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},
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|
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"## 小结\n",
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"\n",
|
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"* 学习嵌套函数（nested function）是训练神经网络的理想情况。在深层神经网络中，学习另一层作为恒等映射（identity function）较容易（尽管这是一个极端情况）。\n",
|
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"* 残差映射可以更容易地学习同一函数，例如将权重层中的参数近似为零。\n",
|
||
"* 利用残差块（residual blocks）可以训练出一个有效的深层神经网络：输入可以通过层间的残余连接更快地向前传播。\n",
|
||
"* 残差网络（ResNet）对随后的深层神经网络设计产生了深远影响。\n",
|
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"\n",
|
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"## 练习\n",
|
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"\n",
|
||
"1. :numref:`fig_inception`中的Inception块与残差块之间的主要区别是什么？在删除了Inception块中的一些路径之后，它们是如何相互关联的？\n",
|
||
"1. 参考ResNet论文 :cite:`He.Zhang.Ren.ea.2016`中的表1，以实现不同的变体。\n",
|
||
"1. 对于更深层次的网络，ResNet引入了“bottleneck”架构来降低模型复杂性。请试着去实现它。\n",
|
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"1. 在ResNet的后续版本中，作者将“卷积层、批量规范化层和激活层”架构更改为“批量规范化层、激活层和卷积层”架构。请尝试做这个改进。详见 :cite:`He.Zhang.Ren.ea.2016*1`中的图1。\n",
|
||
"1. 为什么即使函数类是嵌套的，我们仍然要限制增加函数的复杂性呢？\n"
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