MNIST

50000 个训练数据

10000 个测试数据

图像大小 28x28

10 类（0~9）

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LeNet

LeNet（LeNet-5）由两个部分组成：

  • 卷积编码器：由两个卷积层组成
  • 全连接层密集块：由三个全连接层组成

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每个卷积块中的基本单元是一个卷积层、一个 sigmoid 激活函数和平均池化层。

每个卷积层使用 5×5 卷积核和一个 sigmoid 激活函数。

每个 2×2 池操作通过空间下采样将维数减少 4 倍。

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总结

  • LeNet 是早期成功的卷积神经网络
  • 先使用卷积层来学习图片空间信息
  • 为了构造高性能的卷积神经网络，通常对卷积层进行排列，逐渐降低其表示的空间分辨率，同时增加通道数
  • 使用全连接层来转换到类别的空间

代码实现

LeNet（LeNet-5）由两个部分组成：
卷积编码器和全连接层密集块

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import torch
from torch import nn
from d2l import torch as d2l


class Reshape(torch.nn.Module):
  def forward(self, x):
    return x.view(-1, 1, 28, 28)

net = torch.nn.Sequential(
  Reshape(),
  nn.Conv2d(1, 6, kernel_size=5, padding=2), nn.Sigmoid(),
  nn.AvgPool2d(kernel_size=2, stride=2),
  nn.Conv2d(6, 16, kernel_size=5), nn.Sigmoid(),
  nn.AvgPool2d(kernel_size=2, stride=2),
  nn.Flatten(),
  nn.Linear(16 * 5 * 5, 120), nn.Sigmoid(),
  nn.Linear(120, 84), nn.Sigmoid(),
  nn.Linear(84, 10))

检查模型

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X = torch.rand(size=(1, 1, 28, 28), dtype=torch.float32)
for layer in net:
  X = layer(X)
  print(layer.__class__.__name__,'output shape: \t',X.shape)
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Reshape output shape:    torch.Size([1, 1, 28, 28])
Conv2d output shape:     torch.Size([1, 6, 28, 28])
Sigmoid output shape:    torch.Size([1, 6, 28, 28])
AvgPool2d output shape:      torch.Size([1, 6, 14, 14])
Conv2d output shape:     torch.Size([1, 16, 10, 10])
Sigmoid output shape:    torch.Size([1, 16, 10, 10])
AvgPool2d output shape:      torch.Size([1, 16, 5, 5])
Flatten output shape:    torch.Size([1, 400])
Linear output shape:     torch.Size([1, 120])
Sigmoid output shape:    torch.Size([1, 120])
Linear output shape:     torch.Size([1, 84])
Sigmoid output shape:    torch.Size([1, 84])
Linear output shape:     torch.Size([1, 10])

LeNet在Fashion-MNIST数据集上的表现

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batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)

对evaluate_accuracy函数进行轻微的修改

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def evaluate_accuracy_gpu(net, data_iter, device=None):
  """使用GPU计算模型在数据集上的精度。"""
  if isinstance(net, torch.nn.Module):
    net.eval()
    if not device:
      device = next(iter(net.parameters())).device
  metric = d2l.Accumulator(2)
  for X, y in data_iter:
    if isinstance(X, list):
      X = [x.to(device) for x in X]
    else:
      X = X.to(device)
    y = y.to(device)
    metric.add(d2l.accuracy(net(X), y), y.numel())
  return metric[0] / metric[1]

为了使用 GPU，我们还需要一点小改动

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def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
  """用GPU训练模型。"""
  def init_weights(m):
    if type(m) == nn.Linear or type(m) == nn.Conv2d:
      nn.init.xavier_uniform_(m.weight)
  net.apply(init_weights)
  print('training on', device)
  net.to(device)
  optimizer = torch.optim.SGD(net.parameters(), lr=lr)
  loss = nn.CrossEntropyLoss()
  animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
              legend=['train loss', 'train acc', 'test acc'])
  timer, num_batches = d2l.Timer(), len(train_iter)
  for epoch in range(num_epochs):
    metric = d2l.Accumulator(3)
    net.train()
    for i, (X, y) in enumerate(train_iter):
      timer.start()
      optimizer.zero_grad()
      X, y = X.to(device), y.to(device)
      y_hat = net(X)
      l = loss(y_hat, y)
      l.backward()
      optimizer.step()
      with torch.no_grad():
        metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
      timer.stop()
      train_l = metric[0] / metric[2]
      train_acc = metric[1] / metric[2]
      if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
        animator.add(epoch + (i + 1) / num_batches,
               (train_l, train_acc, None))
    test_acc = evaluate_accuracy_gpu(net, test_iter)
    animator.add(epoch + 1, (None, None, test_acc))
  print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
     f'test acc {test_acc:.3f}')
  print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
     f'on {str(device)}')

训练和评估LeNet-5模型

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lr, num_epochs = 0.9, 10
train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
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loss 0.460, train acc 0.828, test acc 0.828
67659.4 examples/sec on cuda:0

output_11_1.svg