标准化后，生成的小批量的均值为0，单位方差为1，可以加快收敛速度

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


def batch_norm(X, gamma, beta, moving_mean, moving_var, eps, momentum):
    # momentum is designed to update moving_mean moving_var
    # 通过is_grad_enabled方法来判断当前模式是训练模式还是预测模式
    if not torch.is_grad_enabled():
        # 如果在预测模式下，直接用传入的移动平均所得的均值和方差
        X_hat = (X - moving_mean) / torch.sqrt(moving_var + eps)
    else:
        assert len(X.shape) in (2, 4)
        if len(X.shape) == 2:
            # 使用全连接层的情况，计算特征维上的均值和方差
            mean = X.mean(dim=0)
            var = ((X - mean) ** 2).mean(dim=0)
        else:
            # 使用二维卷积层的情况，计算通道维上(axis=1)的均值和方差
            # 这里我们需要保持X的形状以便后面可以做广播运算
            mean = X.mean(dim=(0, 2, 3), keepdim=True)
            var = ((X - mean) ** 2).mean(dim=(0, 2, 3), keepdim=True)
        X_hat = (X - mean) / torch.sqrt(var + eps)
        moving_mean = momentum * moving_mean + (1 - momentum) * mean
        moving_var = momentum * moving_var + (1 - momentum) * var
    Y = gamma * X_hat + beta
    return Y, moving_mean.data, moving_var.data


# 创建BatchNorm层
class BatchNorm(nn.Module):
    # num_features: 全连接层的输出数量或卷积层的输出通道数
    # num_dims: 2表示完全连接层，4表示卷积层
    def __init__(self, num_features, num_dims):
        super().__init__()
        if num_dims == 2:
            shape = (1, num_features)
        else:
            shape = (1, num_features, 1, 1)
        # 参与求梯度和迭代的拉伸参数和偏移参数，分别初始化为1和0
        self.gamma = nn.Parameter(torch.ones(shape))
        self.beta = nn.Parameter(torch.zeros(shape))
        # 非模型参数的变量初始化为0和1
        self.moving_mean = torch.zeros(shape)
        self.moving_var = torch.ones(shape)

    def forward(self, X):
        # 如果X不在内存上，则复制moving_mean和moving_var到X所在的显存上
        if self.moving_mean.device != X.device:
            self.moving_mean = self.moving_mean.to(X.device)
            self.moving_var = self.moving_var.to(X.device)
        # 保存更新过的moving_mean和moving_var
        Y, self.moving_mean, self.moving_var = batch_norm(
            X, self.gamma, self.beta, self.moving_mean, self.moving_var,
            eps=1e-5, momentum=0.9)
        return Y


# 应用BatchNorm于LeNet模型
net = nn.Sequential(
    nn.Conv2d(1, 6, kernel_size=5, padding=2), BatchNorm(6, 4),
    nn.ReLU(),
    nn.MaxPool2d(kernel_size=2, stride=2),
    nn.Conv2d(6, 16, kernel_size=5), BatchNorm(16, 4),
    nn.ReLU(),
    nn.MaxPool2d(kernel_size=2, stride=2),
    nn.Flatten(),
    nn.Linear(16 * 5 * 5, 120), BatchNorm(120, 2), nn.Dropout(0.5),
    nn.ReLU(),
    nn.Linear(120, 84), BatchNorm(84, 2), nn.Dropout(0.5),
    nn.ReLU(),
    nn.Linear(84, 10))

lr, num_epochs, batch_size = 0.05, 50, 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
d2l.plt.show()

Output

loss 0.277, train acc 0.904, test acc 0.898
39096.3 examples/sec on cuda:0