深度学习基础——残差神经网络（ResNet）

1. 定义

残差神经网络（ResNet）是一种深度神经网络结构，由微软研究院的Kaiming He等人于2015年提出。它通过引入残差块（Residual Block）来解决深度神经网络的退化问题，使得网络可以更深地进行训练。ResNet在ImageNet图像识别挑战赛上取得了第一名的成绩，并在许多领域取得了显著的成功应用。

2. 如何计算

ResNet的核心思想是引入残差连接（Residual Connection）。传统的神经网络是通过堆叠一系列的层来逐层提取特征，但随着网络层数的增加，网络往往会遭遇梯度消失（Gradient Vanishing）和梯度爆炸（Gradient Exploding）等问题，导致训练困难。ResNet通过在原始输入和输出之间添加一个跳跃连接，使得网络可以学习残差，从而解决了这些问题。

残差块的计算方式可以表示为：

$\text{Output} = \mathcal{F}(\text{Input}) + \text{Input}$

其中， $\mathcal{F}(\cdot)$ 表示残差学习的映射函数。通过残差块，网络学习到的是残差 $\mathcal{F}(\text{Input})$ ，而不是直接学习输出。这种设计使得网络可以更轻松地学习到恒等映射，从而避免了梯度消失和梯度爆炸的问题。

3. 用Python实现（结果可视化）

下面是使用PyTorch实现的一个简单的ResNet模型，并使用CIFAR-10数据集进行训练和测试的示例代码：

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision
import torchvision.transforms as transforms# 定义ResNet残差块
class ResidualBlock(nn.Module):def __init__(self, in_channels, out_channels, stride=1):super(ResidualBlock, self).__init__()self.conv1 = nn.Conv2d(in_channels, out_channels, kernel_size=3, stride=stride, padding=1, bias=False)self.bn1 = nn.BatchNorm2d(out_channels)self.relu = nn.ReLU(inplace=True)self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=3, stride=1, padding=1, bias=False)self.bn2 = nn.BatchNorm2d(out_channels)self.downsample = Noneif stride != 1 or in_channels != out_channels:self.downsample = nn.Sequential(nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=stride, bias=False),nn.BatchNorm2d(out_channels))def forward(self, x):residual = xout = self.conv1(x)out = self.bn1(out)out = self.relu(out)out = self.conv2(out)out = self.bn2(out)if self.downsample is not None:residual = self.downsample(residual)out += residualout = self.relu(out)return out# 定义ResNet网络
class ResNet(nn.Module):def __init__(self, block, num_blocks, num_classes=10):super(ResNet, self).__init__()self.in_channels = 64self.conv1 = nn.Conv2d(3, 64, kernel_size=3, stride=1, padding=1, bias=False)self.bn1 = nn.BatchNorm2d(64)self.relu = nn.ReLU(inplace=True)self.layer1 = self.make_layer(block, 64, num_blocks[0], stride=1)self.layer2 = self.make_layer(block, 128, num_blocks[1], stride=2)self.layer3 = self.make_layer(block, 256, num_blocks[2], stride=2)self.layer4 = self.make_layer(block, 512, num_blocks[3], stride=2)self.avg_pool = nn.AdaptiveAvgPool2d((1, 1))self.fc = nn.Linear(512, num_classes)def make_layer(self, block, out_channels, num_blocks, stride):layers = []layers.append(block(self.in_channels, out_channels, stride))self.in_channels = out_channelsfor _ in range(1, num_blocks):layers.append(block(out_channels, out_channels, stride=1))return nn.Sequential(*layers)def forward(self, x):out = self.conv1(x)out = self.bn1(out)out = self.relu(out)out = self.layer1(out)out = self.layer2(out)out = self.layer3(out)out = self.layer4(out)out = self.avg_pool(out)out = out.view(out.size(0), -1)out = self.fc(out)return out# 定义数据预处理
transform = transforms.Compose([transforms.ToTensor(),transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))
])# 加载CIFAR-10数据集
trainset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform)
trainloader = torch.utils.data.DataLoader(trainset, batch_size=128, shuffle=True, num_workers=2)testset = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform)
testloader = torch.utils.data.DataLoader(testset, batch_size=128, shuffle=False, num_workers=2)classes = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck')# 定义设备
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")# 定义ResNet模型
net = ResNet(ResidualBlock, [2, 2, 2, 2]).to(device)# 定义损失函数和优化器
criterion = nn.CrossEntropyLoss()
optimizer = optim.SGD(net.parameters(), lr=0.1, momentum=0.9, weight_decay=5e-4)# 训练网络
num_epochs = 50
for epoch in range(num_epochs):net.train()running_loss = 0.0for i, data in enumerate(trainloader, 0):inputs, labels = data[0].to(device), data[1].to(device)optimizer.zero_grad()outputs = net(inputs)loss = criterion(outputs, labels)loss.backward()optimizer.step()running_loss += loss.item()print('[%d, %5d] loss: %.3f' % (epoch + 1, i + 1, running_loss / len(trainloader)))print('Finished Training')# 测试网络
net.eval()
correct = 0
total = 0
with torch.no_grad():for data in testloader:images, labels = data[0].to(device), data[1].to(device)outputs = net(images)_, predicted = torch.max(outputs.data, 1)total += labels.size(0)correct += (predicted == labels).sum().item()print('Accuracy of the network on the 10000 test images: %d %%' % (100 * correct / total))# 保存模型
torch.save(net.state_dict(), 'resnet_model.pth')# 加载模型
net.load_state_dict(torch.load('resnet_model.pth'))# 输出结果可视化
import matplotlib.pyplot as plt
import numpy as np# 输出图像的函数
def imshow(img):img = img / 2 + 0.5     # unnormalizenpimg = img.numpy()plt.imshow(np.transpose(npimg, (1, 2, 0)))plt.show()# 获取随机数据
dataiter = iter(testloader)
images, labels = dataiter.next()# 输出图像
imshow(torchvision.utils.make_grid(images))
print('GroundTruth: ', ' '.join('%5s' % classes[labels[j]] for j in range(4)))# 预测图像
outputs = net(images.to(device))
_, predicted = torch.max(outputs, 1)print('Predicted: ', ' '.join('%5s' % classes[predicted[j]] for j in range(4)))