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                                                                —— 25.3.16

一、残差神经网络的核心思想

1. ​残差映射：传统神经网络直接学习输入到输出的复杂映射 H(x)，而残差网络改为学习残差函数 F(x)=H(x)−x，最终输出为 y=F(x)+x ，这种设计使得深层网络即使无法学习有效特征，也能通过恒等映射 x 保持性能不退化。

2. ​跳跃连接（Shortcut Connection）​：
   在残差块中，输入通过跨层连接直接传递到输出端，与经过卷积层、激活函数后的结果相加。这种设计为梯度提供了“直达路径”，缓解了反向传播中的梯度消失问题

二、残差块的设计

1.BasicBlock

• 含 ​两个 3×3 卷积层，每层后接批量归一化（BatchNorm）和 ReLU 激活函数
• 输入通过跳跃连接直接与第二个卷积层的输出相加，再经过一次 ReLU 激活

class BasicBlock(nn.Module):def __init__(self, in_channels, out_channels, stride=1):super().__init__()self.conv1 = nn.Conv2d(in_channels, out_channels, kernel_size=3, stride=stride, padding=1)self.bn1 = nn.BatchNorm2d(out_channels)self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=3, padding=1)self.bn2 = nn.BatchNorm2d(out_channels)self.shortcut = nn.Identity()  # 恒等映射（输入输出通道相同时）if stride != 1 or in_channels != out_channels:self.shortcut = nn.Sequential(nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=stride),nn.BatchNorm2d(out_channels))def forward(self, x):out = F.relu(self.bn1(self.conv1(x)))out = self.bn2(self.conv2(out))out += self.shortcut(x)  # 跳跃连接return F.relu(out)

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2.Bottleneck

• 使用 ​1×1→3×3→1×1 的卷积组合，通过降维和升维减少计算量
• 典型应用于 ResNet-50/101/152 等深层变体

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三、残差网络如何解决梯度消失

1.​梯度传播公式：

根据链式法则，残差块的梯度为：

即使趋近于零，梯度仍可通过恒等项 1 有效传播

2.实际效果：

跳跃连接使得反向传播时梯度可直接回传到浅层，避免指数级衰减实验表明，ResNet-152（152层）的训练误差低于普通 CNN 的 20 层网络

3.代码示例

import torch
import torch.nn as nn
import torch.nn.functional as Fclass ResNet18(nn.Module):def __init__(self, num_classes=10):super().__init__()self.conv1 = nn.Conv2d(3, 64, kernel_size=7, stride=2, padding=3)self.bn1 = nn.BatchNorm2d(64)self.maxpool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)# 残差块组self.layer1 = self._make_layer(64, 64, stride=1, num_blocks=2)self.layer2 = self._make_layer(64, 128, stride=2, num_blocks=2)self.layer3 = self._make_layer(128, 256, stride=2, num_blocks=2)self.layer4 = self._make_layer(256, 512, stride=2, num_blocks=2)self.avgpool = nn.AdaptiveAvgPool2d((1, 1))self.fc = nn.Linear(512, num_classes)def _make_layer(self, in_channels, out_channels, stride, num_blocks):layers = [BasicBlock(in_channels, out_channels, stride)]for _ in range(num_blocks-1):layers.append(BasicBlock(out_channels, out_channels, stride=1))return nn.Sequential(*layers)def forward(self, x):x = F.relu(self.bn1(self.conv1(x)))  # 初始卷积层x = self.maxpool(x)x = self.layer1(x)  # 4组残差块x = self.layer2(x)x = self.layer3(x)x = self.layer4(x)x = self.avgpool(x)  # 全局平均池化x = torch.flatten(x, 1)x = self.fc(x)return x# 使用示例
model = ResNet18(num_classes=1000)
input_tensor = torch.randn(1, 3, 224, 224)
output = model(input_tensor)
print(output.shape)  # torch.Size([1, 1000])