【动手学深度学习】(十一)池化层+LeNet

一、池化层

1.理论知识

二维最大池化


填充、步幅和多个通道

• 池化层与卷积层类似，都具有填充和步幅
• 没有可学习的参数
• 在每个输入通道应用池化层以获得相应的输出通道
• 输出通道数=输入通道数

平均池化层

• 最大池化层：每个窗口中最强的模式信号
• 平均池化层：将最大池化层中的“最大”操作替换为“平均”

2.代码

实现池化层的正向传播

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

def pool2d(X, pool_size, mode='max'):
    p_h, p_w = pool_size
    Y = torch.zeros((X.shape[0] - p_h + 1, X.shape[1] - p_w + 1))
    for i in range(Y.shape[0]):
        for j in range(Y.shape[1]):
            if mode == 'max':
                Y[i, j] = X[i:i + p_h, j:j+p_w].max()
            elif mode == 'avg':
                Y[i, j] = X[i:i + p_h, j:j + p_w].mean()
                
    return Y

# 验证二维最大池化层的输出
X = torch.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])
pool2d(X, (2,2))
# print(Y)

tensor([[4., 5.],
[7., 8.]])

# 验证平均池化层
pool2d(X,(2,2),'avg')

tensor([[2., 3.],
[5., 6.]])

X = torch.arange(16, dtype=torch.float32).reshape((1,1,4,4))
# X

# 深度学习框架中的步幅与池化窗口的大小相同
pool2d = nn.MaxPool2d(3)
pool2d(X)

tensor([[[[10.]]]])

# 手动指定步幅和填充
pool2d = nn.MaxPool2d(3, padding=1, stride=2)
pool2d(X)

tensor([[[[ 5., 7.],
[13., 15.]]]])

# 设定一个任意大小的矩形池化窗口
pool2d = nn.MaxPool2d((2,3), padding=(1,1), stride=(2,3))
pool2d(X)

tensor([[[[ 1., 3.],
[ 9., 11.],
[13., 15.]]]])

X = torch.cat((X, X + 1), 1)
# Y2 = torch.stack((X,X+1))
# print(Y)
# print(Y2)
X

tensor([[[[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[12., 13., 14., 15.]],
[[ 1., 2., 3., 4.],
[ 5., 6., 7., 8.],
[ 9., 10., 11., 12.],
[13., 14., 15., 16.]]]])

# print(X.shape)
pool2d = nn.MaxPool2d(3, padding=1, stride=2)
pool2d(X)

tensor([[[[ 5., 7.],
[13., 15.]],
[[ 6., 8.],
[14., 16.]]]])

二、LeNet

1.理论知识

LeNet-5的典型结构：

• 输入层：输入图像大小为32*32
• 第一层：卷积核大小为5*5，输出通道数为6
• 第二层：大小为2*2的平均池化层，步幅为2
• 第三层：卷积核大小为5，输出通道为16
• 第四层：大小为2*2的平均池化层，步幅为2
• 第五层：120个神经元的全连接层
• 第六层：84个神经元的全连接层
• 输出层：10个神经元，对应于10个类别
  

2.代码实现

LeNet由两个部分组成：卷积编码器和全连接层密集块

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(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)
)
# print(net)

检查模型

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)

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

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
train_iter.num_workers = 0
test_iter.num_workers = 0

对evaluate_accuracy函数进行改进

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)
#       将当前批次的正确预测数量和总样本数
        metric.add(d2l.accuracy(net(X), y), y.numel())
    return metric[0] / metric[1]

为了使用GPU，我们还需要修改

def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
    """用GPU训练模型"""
#   初始化神经网络的权重
    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):
#       训练损失之和，训练准确率之和，样本数
        metric = d2l.Accumulator(3)
#     将神经网络设置为训练模式
        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()
#           计算平均训练损失和平均训练准确率
            train_l = metric[0] / metric[2]
            train_acc = metric[1] / metric[2]
#         控制输出频率，确保训练信息在每个 epoch的五分之一处和最后一个迭代时被输出
            if(i+1) % (num_batches // 5) == 0 or i == num_batches - 1:
                animator.add(epoch + (i + 1) / num_batches,
                            (train_l, train_acc, None))
#       在测试数据集上评估模型的准确率  
        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
torch.cuda.set_device(0)
lr, num_epochs = 0.9, 10
train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())

loss 0.461, train acc 0.827, test acc 0.818
23915.6 examples/sec on cuda:0

【相关总结】

nn.MaxPool2d()

torch.nn.MaxPool2d(kernel_size, [stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False])

• kernel_size:池化窗口大小，当为一个整数时，表示为一个方形，否则需要输入一个包含长宽的元组。
• stride:窗口移动的步长，！！！默认是kernel_size

import torch
import torch.nn as nn

# 定义一个最大池化层，窗口大小为 3x3
max_pool_layer = nn.MaxPool2d(3)

# 创建一个输入张量（假设是一张图像）
input_data = torch.rand(1, 1, 5, 5)  # (batch_size, channels, height, width)

# 使用最大池化层进行池化操作
output_data = max_pool_layer(input_data)

print("Input data:")
print(input_data)

print("\nOutput data after max pooling:")
print(output_data)

Input data:
tensor([[[[0.0636, 0.8813, 0.3543, 0.8072, 0.7034],
[0.0906, 0.2161, 0.3276, 0.7605, 0.5871],
[0.3102, 0.9458, 0.7694, 0.7519, 0.5355],
[0.0510, 0.6437, 0.4188, 0.0824, 0.0427],
[0.5253, 0.1354, 0.7783, 0.6787, 0.4483]]]])

Output data after max pooling:
tensor([[[[0.9458]]]])