使用PyTh实现LeNet网络。 使用已下载好的本地Fashion MNIST 对LeNet进行训练和测试。优化算法采用SGD或Adam。 torch.optim.SGD 或 torch.optim.Adam。可复用多层感知器的相关代码 分别绘制训练和测试的损失函数曲线和分类正确率曲线 调节BatchSize、学习率，并依据测试损失曲线的拐点确定最佳模型，保存该模型。 使用测试集测试所保存模型的性能，以混淆矩阵展示。 扩展任务：以旋转的方式扩充测试集，在前述最佳模型上测试扩充

以下是实现LeNet网络的代码，使用了PyTorch框架和Fashion MNIST数据集进行训练和测试。其中优化算法采用了Adam。

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision.datasets as datasets
import torchvision.transforms as transforms
from torch.utils.data import DataLoader

# 定义LeNet网络
class LeNet(nn.Module):
    def __init__(self):
        super(LeNet, self).__init__()
        self.conv1 = nn.Conv2d(1, 6, kernel_size=5)
        self.pool1 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.conv2 = nn.Conv2d(6, 16, kernel_size=5)
        self.pool2 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.fc1 = nn.Linear(16*4*4, 120)
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):
        x = self.pool1(torch.relu(self.conv1(x)))
        x = self.pool2(torch.relu(self.conv2(x)))
        x = x.view(-1, 16*4*4)
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x

# 定义训练函数
def train(model, train_loader, optimizer, criterion):
    model.train()
    train_loss = 0
    correct = 0
    total = 0
    for inputs, targets in train_loader:
        optimizer.zero_grad()
        outputs = model(inputs)
        loss = criterion(outputs, targets)
        loss.backward()
        optimizer.step()
        train_loss += loss.item()
        _, predicted = outputs.max(1)
        total += targets.size(0)
        correct += predicted.eq(targets).sum().item()
    return train_loss / len(train_loader), correct / total

# 定义测试函数
def test(model, test_loader, criterion):
    model.eval()
    test_loss = 0
    correct = 0
    total = 0
    with torch.no_grad():
        for inputs, targets in test_loader:
            outputs = model(inputs)
            loss = criterion(outputs, targets)
            test_loss += loss.item()
            _, predicted = outputs.max(1)
            total += targets.size(0)
            correct += predicted.eq(targets).sum().item()
    return test_loss / len(test_loader), correct / total

# 数据集处理
train_transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
])

test_transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
])

train_set = datasets.FashionMNIST(root='./data', train=True, download=True, transform=train_transform)
test_set = datasets.FashionMNIST(root='./data', train=False, download=True, transform=test_transform)

# 参数设置
batch_size = 64
lr = 0.001
num_epochs = 30
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

# 数据加载
train_loader = DataLoader(train_set, batch_size=batch_size, shuffle=True)
test_loader = DataLoader(test_set, batch_size=batch_size, shuffle=False)

# 模型、损失函数、优化器定义
model = LeNet().to(device)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=lr)

# 训练和测试
train_losses = []
train_accs = []
test_losses = []
test_accs = []
best_test_loss = float('inf')

for epoch in range(num_epochs):
    train_loss, train_acc = train(model, train_loader, optimizer, criterion)
    test_loss, test_acc = test(model, test_loader, criterion)
    
    train_losses.append(train_loss)
    train_accs.append(train_acc)
    test_losses.append(test_loss)
    test_accs.append(test_acc)

    print('Epoch [{}/{}] - Train Loss: {:.4f}, Train Acc: {:.4f}, Test Loss: {:.4f}, Test Acc: {:.4f}'.format(
        epoch+1, num_epochs, train_loss, train_acc, test_loss, test_acc))

    if test_loss < best_test_loss:
        best_test_loss = test_loss
        torch.save(model.state_dict(), 'best_model.pth')

# 扩展任务：旋转测试集
test_set_rotate = datasets.FashionMNIST(root='./data', train=False, download=True, transform=transforms.Compose([
    transforms.RandomRotation(90),
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
]))

test_loader_rotate = DataLoader(test_set_rotate, batch_size=batch_size, shuffle=False)

# 加载最佳模型
model.load_state_dict(torch.load('best_model.pth'))

# 在旋转的测试集上测试模型性能
confusion_matrix = torch.zeros(10, 10)
with torch.no_grad():
    for inputs, targets in test_loader_rotate:
        inputs, targets = inputs.to(device), targets.to(device)
        outputs = model(inputs)
        _, predicted = outputs.max(1)
        for i in range(targets.size(0)):
            confusion_matrix[targets[i]][predicted[i]] += 1

print('Confusion Matrix:')
print(confusion_matrix)

可以通过调节BatchSize、学习率等参数，得到不同的训练和测试结果。在训练过程中，我们记录了训练和测试的损失函数曲线和分类正确率曲线，来观察模型的训练和测试过程。

import matplotlib.pyplot as plt

plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.plot(train_losses, label='train')
plt.plot(test_losses, label='test')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(train_accs, label='train')
plt.plot(test_accs, label='test')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.legend()

plt.show()

最后，我们保存了在测试集上表现最好的模型，并在扩展任务中使用旋转的测试集来测试该模型的性能，得到了混淆矩阵。