### 使用 PyTorch 构建卷积神经网络（CNN）进行 MNIST 手写数字识别 #### 导入必要的库 为了构建和训练一个卷积神经网络来处理MNIST数据集，首先需要导入一系列Python包。这其中包括PyTorch本身及其子模块`torchvision`用于加载数据集，还有其他辅助工具如NumPy等。 ```python import torch from torchvision import datasets, transforms from torch.utils.data import DataLoader import numpy as np ``` #### 数据预处理与加载 对于任何机器学习任务来说，准备干净的数据都是非常重要的一步。这里通过定义转换规则来标准化输入图像，并创建DataLoader实例以便于后续迭代读取批次样本。 ```python transform = transforms.Compose([ transforms.ToTensor(), # 将PIL Image或numpy.ndarray转换成tensor transforms.Normalize((0.1307,), (0.3081,)) # 对张量进行归一化操作 ]) train_dataset = datasets.MNIST(root='./data', train=True, download=True, transform=transform) test_dataset = datasets.MNIST(root='./data', train=False, download=True, transform=transform) batch_size = 64 train_loader = DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True) test_loader = DataLoader(dataset=test_dataset, batch_size=batch_size*2, shuffle=False) ``` #### 定义模型结构 接下来就是设计具体的网络架构了。在这个例子中采用了一个简单的两层卷积加一层全连接的设计方案。每一层后面都接有ReLU激活函数以引入非线性因素；最后输出层则采用了LogSoftmax作为激活方式配合负对数似然损失(NLLLoss)来进行多类别分类的学习过程[^1]。 ```python class Net(torch.nn.Module): def __init__(self): super().__init__() self.conv1 = torch.nn.Conv2d(in_channels=1, out_channels=10, kernel_size=5) self.conv2 = torch.nn.Conv2d(in_channels=10, out_channels=20, kernel_size=5) self.fc1 = torch.nn.Linear(in_features=320, out_features=50) self.fc2 = torch.nn.Linear(in_features=50, out_features=10) def forward(self, x): x = torch.relu(torch.max_pool2d(self.conv1(x), 2)) x = torch.relu(torch.max_pool2d(self.conv2(x), 2)) x = x.view(-1, 320) # 展平多维的卷积图形式为二维张量 x = torch.relu(self.fc1(x)) x = self.fc2(x) return torch.log_softmax(x, dim=-1) ``` #### 设置超参数并初始化优化器 选择合适的优化方法同样至关重要，在此选择了Adam这一自适应矩估计法作为梯度下降策略之一，并设定了初始学习率为0.01。同时指定了交叉熵作为衡量预测值与真实标签之间差异程度的标准[^4]。 ```python model = Net() optimizer = torch.optim.Adam(model.parameters(), lr=0.01) criterion = torch.nn.NLLLoss() # 负对数似然损失 device = 'cuda' if torch.cuda.is_available() else 'cpu' model.to(device); ``` #### 开始训练循环 进入实际的训练阶段之前还需要做一些准备工作——比如把整个流程封装在一个for循环里重复执行若干轮次(epoch)，每次遍历所有训练集中每一批(batch)的数据点更新权重直至收敛为止。另外也别忘了定期保存最佳版本的模型文件哦！ ```python epochs = 10 best_accuracy = 0. for epoch in range(epochs): model.train() running_loss = 0. for images, labels in train_loader: optimizer.zero_grad(set_to_none=True) outputs = model(images.to(device)) loss = criterion(outputs, labels.to(device)) loss.backward() optimizer.step() running_loss += loss.item() avg_train_loss = running_loss / len(train_loader.dataset) correct_predictions = 0 with torch.no_grad(): model.eval() test_running_loss = 0 for t_images, t_labels in test_loader: output = model(t_images.to(device)) pred_label = output.argmax(dim=-1).to('cpu') correct_predictions += sum(pred_label == t_labels).item() accuracy = correct_predictions/len(test_loader.dataset)*100. print(f'\nEpoch {epoch+1}/{epochs}, Loss: {avg_train_loss:.4f}') print(f'Test Accuracy of the model on the 10000 test images: {accuracy:.2f} %') if best_accuracy < accuracy : best_accuracy = accuracy torch.save({ 'epoch': epoch, 'model_state_dict': model.state_dict(), 'optimizer_state_dict': optimizer.state_dict(), }, './checkpoint.pth.tar') print('\nTraining complete.') ```