LeNet-5 是由 Yann LeCun提出的卷积神经网络，在论文《Gradient-Based Learning Applied To Document Recognition》中可以看到 LeNet-5 网络模型的结构，如下图所示：

通过上图可以看到，从左至右网络各个层顺序连接：

1. 输入层 ：图片大小 32×32
2. 卷积层1 ：输入通道 1，输出通道 6，卷积核大小 5×5，步长 1
3. 池化层 ：输入通道 6，输出通道 6，过滤器大小 2×2，步长 2
4. 卷积层2 ：输入通道 6，输出通道 16，卷积核大小 5×5， 步长 1
5. 池化层2 ：输入通道 16，输出通道 16，过滤器大小 2×2，步长 2
6. 全连接层1：节点数 120
7. 全连接层2：节点数 84
8. 全连接层3：节点数 10

我们只需要准备好数据集，并基于上图连接结构，使用 PyTorch 搭建 CNN 网络的结构并进行训练和使用。

实现 LeNet-5 模型

基本环境配置如下：
Python：3.11.3
PyTorch：2.0.1（torch==2.0.1 torchvision==0.15.2 torchaudio==2.0.2）

1 准备数据集

使用经典的手写数字数据集 MNIST，可以直接通过 PyTorch 的 datasets.MNIST 下载并准备数据：

import torch
from torch import nn
from torch.utils.data import DataLoader
from torchvision import datasets
from torchvision.transforms import ToTensor

# Download training/test data from open datasets.
training_data = datasets.MNIST(root="data", train=True, download=True, transform=ToTensor(),)
test_data = datasets.MNIST(root="data", train=False, download=True, transform=ToTensor(),)

batch_size = 64

# Create data loaders.
train_dataloader = DataLoader(training_data, batch_size=batch_size)
test_dataloader = DataLoader(test_data, batch_size=batch_size)

for X, y in test_dataloader:
    print(f"Shape of X [N, C, H, W]: {X.shape}")
    print(f"Shape of y: {y.shape} {y.dtype}")
    break

MNIST 数据集中的图片尺寸都是单通道的 28×28 的。

2 实现模型

实现 LeNet-5 模型，主要工作就是配置该 CNN 神经网络的每一层，并实现前向传播的计算逻辑，代码如下所示：

# Get cpu, gpu or mps device for training.
device = (
    "cuda"
    if torch.cuda.is_available()
    else "mps"
    if torch.backends.mps.is_available()
    else "cpu"
)
print(f"Using {device} device")

# Define model
class LeNet5Model(nn.Module):
    def __init__(self):
        super().__init__()
        self._conv1 = nn.Conv2d(1, 6, 5, 1)
        self._pool1 = nn.MaxPool2d(2)
        self._conv2 = nn.Conv2d(6, 16, 5, 1)
        self._pool2 = nn.MaxPool2d(2)
        self._fc1 = nn.Linear(4*4*16, 120)
        self._fc2 = nn.Linear(120, 84)
        self._fc3 = nn.Linear(84, 10)

    def forward(self, x):
        x = self._conv1(x)
        x = self._pool1(x)
        x = self._conv2(x)
        x = self._pool2(x)
        x = x.view(-1, 4 * 4 * 16)
        x = self._fc1(x)
        x = self._fc2(x)
        x = self._fc3(x)
        return x

# Create model
model = LeNet5Model().to(device)
print(model)

可以看到，输出的 LeNet-5 模型结构，如下所示：

LeNet5Model(
  (_conv1): Conv2d(1, 6, kernel_size=(5, 5), stride=(1, 1))
  (_pool1): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)
  (_conv2): Conv2d(6, 16, kernel_size=(5, 5), stride=(1, 1))
  (_pool2): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)
  (_fc1): Linear(in_features=256, out_features=120, bias=True)
  (_fc2): Linear(in_features=120, out_features=84, bias=True)
  (_fc3): Linear(in_features=84, out_features=10, bias=True)
)

3 训练模型

下面是训练模型的过程，代码如下所示：

# Define loss function and optimizer
loss_fn = nn.CrossEntropyLoss()
optimizer = torch.optim.SGD(model.parameters(), lr=1e-3)

# training loop
def train(dataloader, model, loss_fn, optimizer):
    size = len(dataloader.dataset)
    model.train()
    for batch, (X, y) in enumerate(dataloader):
        X, y = X.to(device), y.to(device)

        # Compute prediction error
        pred = model(X)
        loss = loss_fn(pred, y)

        # Backpropagation
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()

        if batch % 100 == 0:
            loss, current = loss.item(), (batch + 1) * len(X)
            print(f"loss: {loss:>7f}  [{current:>5d}/{size:>5d}]")
            
# test loop
def test(dataloader, model, loss_fn):
    size = len(dataloader.dataset)
    num_batches = len(dataloader)
    model.eval()
    test_loss, correct = 0, 0
    with torch.no_grad():
        for X, y in dataloader:
            X, y = X.to(device), y.to(device)
            pred = model(X)
            test_loss += loss_fn(pred, y).item()
            correct += (pred.argmax(1) == y).type(torch.float).sum().item()
    test_loss /= num_batches
    correct /= size
    print(f"Test Error: \n Accuracy: {(100*correct):>0.1f}%, Avg loss: {test_loss:>8f} \n")
    
# execute model training and testing
epochs = 10
for t in range(epochs):
    print(f"Epoch {t+1}\n-------------------------------")
    train(train_dataloader, model, loss_fn, optimizer)
    test(test_dataloader, model, loss_fn)
print("Done!")

运行代码可以看到迭代过程，结果示例如下：

Epoch 1
-------------------------------
loss: 2.317153  [   64/60000]
loss: 2.305442  [ 6464/60000]
loss: 2.306234  [12864/60000]
loss: 2.324416  [19264/60000]
loss: 2.302907  [25664/60000]
loss: 2.297269  [32064/60000]
loss: 2.305612  [38464/60000]
loss: 2.291686  [44864/60000]
loss: 2.301056  [51264/60000]
loss: 2.307510  [57664/60000]
Test Error: 
 Accuracy: 11.9%, Avg loss: 2.291815 

Epoch 2
-------------------------------
loss: 2.293081  [   64/60000]
loss: 2.284958  [ 6464/60000]
loss: 2.288021  [12864/60000]
loss: 2.292037  [19264/60000]
loss: 2.281588  [25664/60000]
loss: 2.278919  [32064/60000]
loss: 2.274934  [38464/60000]
loss: 2.274108  [44864/60000]
loss: 2.271511  [51264/60000]
loss: 2.271358  [57664/60000]
Test Error: 
 Accuracy: 41.4%, Avg loss: 2.261012 

... ...

Epoch 9
-------------------------------
loss: 0.506072  [   64/60000]
loss: 0.397812  [ 6464/60000]
loss: 0.355343  [12864/60000]
loss: 0.390962  [19264/60000]
loss: 0.431304  [25664/60000]
loss: 0.475698  [32064/60000]
loss: 0.307452  [38464/60000]
loss: 0.511966  [44864/60000]
loss: 0.481164  [51264/60000]
loss: 0.522870  [57664/60000]
Test Error: 
 Accuracy: 88.4%, Avg loss: 0.397837 

Epoch 10
-------------------------------
loss: 0.454751  [   64/60000]
loss: 0.365487  [ 6464/60000]
loss: 0.319525  [12864/60000]
loss: 0.371037  [19264/60000]
loss: 0.389002  [25664/60000]
loss: 0.452506  [32064/60000]
loss: 0.273858  [38464/60000]
loss: 0.487788  [44864/60000]
loss: 0.447199  [51264/60000]
loss: 0.497519  [57664/60000]
Test Error: 
 Accuracy: 89.1%, Avg loss: 0.369253 

Done!

通过训练，可以得到我们需要的最终想要的模型，这时将模型保存下来以便后面使用：

saved_model_path = "LeNet5.pth"
torch.save(model.state_dict(), saved_model_path)
print("Saved PyTorch Model State to ", saved_model_path)

4 加载、使用模型

model = LeNet5Model().to(device)
model.load_state_dict(torch.load("LeNet5.pth"))

classes = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]

model.eval()
for i in range(10):
    x, y = test_data[i][0], test_data[i][1]
    with torch.no_grad():
        x = x.to(device)
        pred = model(x)
        predicted, actual = classes[pred[0].argmax(0)], classes[y]
        print(f'Predicted: "{predicted}", Actual: "{actual}"')

示例结果如下所示：

Predicted: "7", Actual: "7"
Predicted: "2", Actual: "2"
Predicted: "1", Actual: "1"
Predicted: "0", Actual: "0"
Predicted: "4", Actual: "4"
Predicted: "1", Actual: "1"
Predicted: "4", Actual: "4"
Predicted: "9", Actual: "9"
Predicted: "6", Actual: "5"
Predicted: "9", Actual: "9"

参考资源

• https://pytorch.org/tutorials/beginner/basics/quickstart_tutorial.html
• https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html#torch.nn.Conv2d