动手学习深度学习（13）现代卷积神经网络（2）

茴香豆 Lv5
  2022-11-01 09:35:42 2022-11-01 09:35:42 Created   2022-11-04 15:25:29 2022-11-04 15:25:29 Updated      

训练深层神经网络是十分困难的，特别是在较短的时间内使他们收敛更加棘手。 在本节中，我们将介绍批量规范化（batch normalization），这是一种流行且有效的技术，可持续加速深层网络的收敛速度。

批量归一化

固定小批量里面的均值和方差，批量归一化是线性变换
MATHJAX-SSR-6

\mathrm{BN}(\mathbf{x}) = \boldsymbol{\gamma} \odot \frac{\mathbf{x} - \hat{\boldsymbol{\mu}}_\mathcal{B}}{\hat{\boldsymbol{\sigma}}_\mathcal{B}} + \boldsymbol{\beta}.

均值 \beta 和方差 \gamma 为学习参数。

作用在

  • 全连接层和卷积层输出上，激活函数前
  • 全连接层和卷积层输入上

全连接层，作用在特征维；卷积层，作用在通道维。

可以加速收敛速度（通过匀速更大的学习率），但一般不改变模型精度。

从零实现

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
import torch
from torch import nn
from d2l import torch as d2l

def batch_norm(X, gamma, beta, moving_mean, moving_var, eps, momentum):
    # 通过is_grad_enabled来判断当前模式是训练模式还是预测模式
    if not torch.is_grad_enabled():
        # 如果是在预测模式下，直接使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)
        # 训练模式下，用当前的均值和方差做标准化
        X_hat = (X - mean) / torch.sqrt(var + eps)
        # 更新移动平均的均值和方差
        moving_mean = momentum * moving_mean + (1.0 - momentum) * mean
        moving_var = momentum * moving_var + (1.0 - momentum) * var
    Y = gamma * X_hat + beta  # 缩放和移位
    return Y, moving_mean.data, moving_var.data

创建一个正确的BatchNorm图层

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
class BatchNorm(nn.Module):
    # num_features：完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和偏移参数，分别初始化成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，将moving_mean和moving_var
        # 复制到X所在显存上
        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

1
2
3
4
5
6
7
8
net = nn.Sequential(
    nn.Conv2d(1, 6, kernel_size=5), BatchNorm(6, num_dims=4), nn.Sigmoid(),
    nn.AvgPool2d(kernel_size=2, stride=2),
    nn.Conv2d(6, 16, kernel_size=5), BatchNorm(16, num_dims=4), nn.Sigmoid(),
    nn.AvgPool2d(kernel_size=2, stride=2), nn.Flatten(),
    nn.Linear(16*4*4, 120), BatchNorm(120, num_dims=2), nn.Sigmoid(),
    nn.Linear(120, 84), BatchNorm(84, num_dims=2), nn.Sigmoid(),
    nn.Linear(84, 10))

在Fashion-MNIST数据集上的效果

1
2
3
4
5
6
lr, num_epochs, batch_size = 1.0, 10, 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())
# output
loss 0.268, train acc 0.900, test acc 0.831
38739.6 examples/sec on cuda:0

简洁实现

1
2
3
4
5
6
7
8
9
10
11
12
net = nn.Sequential(
    nn.Conv2d(1, 6, kernel_size=5), nn.BatchNorm2d(6), nn.Sigmoid(),
    nn.AvgPool2d(kernel_size=2, stride=2),
    nn.Conv2d(6, 16, kernel_size=5), nn.BatchNorm2d(16), nn.Sigmoid(),
    nn.AvgPool2d(kernel_size=2, stride=2), nn.Flatten(),
    nn.Linear(256, 120), nn.BatchNorm1d(120), nn.Sigmoid(),
    nn.Linear(120, 84), nn.BatchNorm1d(84), nn.Sigmoid(),
    nn.Linear(84, 10))
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
# output
loss 0.269, train acc 0.901, test acc 0.853
64557.2 examples/sec on cuda:0

ResNet残差网络

残差网络 ResNet【动手学深度学习v2】

通过视频可以更直观的理解残差网络的作用和改进之处。

残差块的实现

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l


class Residual(nn.Module):  #@save
    def __init__(self, input_channels, num_channels,
                 use_1x1conv=False, strides=1):
        super().__init__()
        self.conv1 = nn.Conv2d(input_channels, num_channels,
                               kernel_size=3, padding=1, stride=strides)
        self.conv2 = nn.Conv2d(num_channels, num_channels,
                               kernel_size=3, padding=1)
        if use_1x1conv:
            self.conv3 = nn.Conv2d(input_channels, num_channels,
                                   kernel_size=1, stride=strides)
        else:
            self.conv3 = None
        self.bn1 = nn.BatchNorm2d(num_channels)
        self.bn2 = nn.BatchNorm2d(num_channels)

    def forward(self, X):
        Y = F.relu(self.bn1(self.conv1(X)))
        Y = self.bn2(self.conv2(Y))
        if self.conv3:
            X = self.conv3(X)
        Y += X
        return F.relu(Y)

查看输入和输出形状一致的情况

1
2
3
4
5
6
blk = Residual(3,3)
X = torch.rand(4, 3, 6, 6)
Y = blk(X)
print(Y.shape)
# output
torch.Size([4, 3, 6, 6])

我们也可以在增加输出通道数的同时，减半输出的高和宽。

1
2
3
4
blk = Residual(3,6, use_1x1conv=True, strides=2)
print(blk(X).shape)
# output
torch.Size([4, 6, 3, 3])

ResNet模型

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),
                   nn.BatchNorm2d(64), nn.ReLU(),
                   nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
# 注意我们对第一个模块做了特别处理
def resnet_block(input_channels, num_channels, num_residuals,
                 first_block=False):
    blk = []
    for i in range(num_residuals):
        if i == 0 and not first_block:
            blk.append(Residual(input_channels, num_channels,
                                use_1x1conv=True, strides=2))
        else:
            blk.append(Residual(num_channels, num_channels))
    return blk
# 接着在ResNet加入所有残差块，每个模块使用2个残差块
b2 = nn.Sequential(*resnet_block(64, 64, 2, first_block=True))
b3 = nn.Sequential(*resnet_block(64, 128, 2))
b4 = nn.Sequential(*resnet_block(128, 256, 2))
b5 = nn.Sequential(*resnet_block(256, 512, 2))
# 在ResNet中加入全剧平均汇聚层，以及全连接输出。
net = nn.Sequential(b1, b2, b3, b4, b5,
                    nn.AdaptiveAvgPool2d((1,1)),
                    nn.Flatten(), nn.Linear(512, 10))

在训练ResNet之前，让我们观察一下ResNet中不同模块的输入形状是如何变化的。 在之前所有架构中，分辨率降低，通道数量增加，直到全局平均汇聚层聚集所有特征。

1
2
3
4
5
6
7
8
9
10
11
12
13
X = torch.rand(size=(1, 1, 224, 224))
for layer in net:
    X = layer(X)
    print(layer.__class__.__name__,'output shape:\t', X.shape)
# output
Sequential output shape:     torch.Size([1, 64, 56, 56])
Sequential output shape:     torch.Size([1, 64, 56, 56])
Sequential output shape:     torch.Size([1, 128, 28, 28])
Sequential output shape:     torch.Size([1, 256, 14, 14])
Sequential output shape:     torch.Size([1, 512, 7, 7])
AdaptiveAvgPool2d output shape:      torch.Size([1, 512, 1, 1])
Flatten output shape:        torch.Size([1, 512])
Linear output shape:         torch.Size([1, 10])

训练模型

1
2
3
4
5
6
lr, num_epochs, batch_size = 0.05, 10, 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=96)
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
# output
loss 0.011, train acc 0.997, test acc 0.915
4701.1 examples/sec on cuda:0
  • Title: 动手学习深度学习（13）现代卷积神经网络（2）
  • Author: 茴香豆
  • Created at : 2022-11-01 09:35:42
  • Updated at : 2022-11-04 15:25:29
  • Link: https://hxiangdou.github.io/2022/11/01/DL_13/
  • License: This work is licensed under CC BY-NC-SA 4.0.
Comments
On this page
动手学习深度学习（13）现代卷积神经网络（2）
  1. 批量归一化
    1. 从零实现
    2. 简洁实现
  2. ResNet残差网络
    1. ResNet模型