### 构建并训练MNIST数据集上的手写数字识别模型 #### 准备工作环境 为了确保能够顺利运行代码，首先需要安装必要的库。如果尚未安装`torch`和`torchvision`，可以使用pip命令进行安装。 ```bash pip install torch torchvision ``` #### 加载MNIST数据集 通过`torchvision.datasets.MNIST`可以直接获取到MNIST数据集，并对其进行预处理操作，比如转换为张量形式以及标准化等[^2]。 ```python import torch from torchvision import datasets, transforms transform = transforms.Compose([ transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,)) ]) train_dataset = datasets.MNIST( root='./data', train=True, download=True, transform=transform ) test_dataset = datasets.MNIST( root='./data', train=False, download=True, transform=transform ) ``` #### 创建数据加载器 创建迭代器用于批量读取图像及其标签，在训练过程中会更加高效。 ```python batch_size = 64 train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True) test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=batch_size, shuffle=False) ``` #### 定义卷积神经网络架构 这里定义了一个简单的CNN结构来进行分类任务。 ```python class Net(torch.nn.Module): def __init__(self): super(Net, self).__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) x = torch.relu(self.fc1(x)) x = self.fc2(x) return torch.log_softmax(x, dim=1) model = Net() device = 'cuda' if torch.cuda.is_available() else 'cpu' model.to(device=device); ``` #### 设置优化器与损失函数 选择适合的优化算法对于提高收敛速度至关重要；交叉熵作为多类别分类问题的标准损失度量被广泛采用。 ```python optimizer = torch.optim.Adam(model.parameters(), lr=0.001) criterion = torch.nn.CrossEntropyLoss().to(device=device) ``` #### 训练过程 循环遍历整个训练集多次（epoch），每次更新权重参数以最小化预测误差。 ```python epochs = 5 for epoch in range(1, epochs + 1): model.train() running_loss = 0.0 for data, target in train_loader: data, target = data.to(device), target.to(device) optimizer.zero_grad() output = model(data) loss = criterion(output, target) loss.backward() optimizer.step() running_loss += loss.item() print(f'Train Epoch: {epoch}, Loss: {(running_loss / len(train_loader)):.4f}') ``` #### 测试评估性能 完成一轮或多轮次的学习之后，应该利用测试集合检验最终效果如何。 ```python def evaluate(): correct = 0 total = 0 with torch.no_grad(): # 不计算梯度 for images, labels in test_loader: images, labels = images.to(device), labels.to(device) outputs = model(images) _, predicted = torch.max(outputs.data, 1) total += labels.size(0) correct += (predicted == labels).sum().item() accuracy = 100 * correct / total print('Accuracy of the network on the 10000 test images: %.2f %%' % ( accuracy)) evaluate() ```