PyTorch学习笔记（27） Batch Normalization

Batch Normalization

Batch Normalization : 批标准化

批：一批数据，通常为mini-batch
标准化：0均值，1方差
优点：
1.可以用更大学习率，加速模型收敛
2.可以不用精心设计权值初始化
3.可以不用dropout或较小的dropout
4.可以不用L2或者较小的weight decay
5.可以不用LRN(local response normalization)

Internal Covariate Shift(ICS)

$\begin{aligned} \mathrm{H}_{11}=& \sum_{i=0}^{n} X_{i} * W_{1 i} \\ \mathrm{D}\left(\mathrm{H}_{11}\right) &=\sum_{i=0}^{n} D\left(X_{i}\right) * D\left(W_{1 i}\right) \\ &=n *(1 * 1) \\ &=n \end{aligned}$
$\begin{array}{l} \operatorname{std}\left(\mathrm{H}_{11}\right)=\sqrt{\mathbf{D}\left(\mathrm{H}_{11}\right)}=\sqrt{n} \\ \mathbf{D}\left(\mathrm{H}_{1}\right)=\boldsymbol{n} * \boldsymbol{D}(\boldsymbol{X}) * \boldsymbol{D}(\boldsymbol{W})=\mathbf{1} \end{array}$
$D(W)=\frac{1}{n} \Rightarrow \operatorname{std}(W)=\sqrt{\frac{1}{n}}$

_BatchNorm

nn.BatchNorm1d
nn.BatchNorm2d
nn.BatchNorm3d

参数

num_features 一个样本特征数量(最重要)
eps 分母修正项
momentum 指数加权平均估计当前mean/var
affine 是否需要affine transform
track_running_stats 是训练状态，还是测试状态

主要属性

running_mean 均值
running_var 方差
weight affine transform 中的gamma
bias affine transform 中的beta
$\widehat{x}_{i} \leftarrow \frac{x_{i}-\mu_{\mathcal{B}}}{\sqrt{\sigma_{\mathcal{B}}^{2}+\epsilon}}$
$y_{i} \leftarrow \gamma \widehat{x}_{i}+\beta \equiv \mathrm{B} \mathrm{N}_{\gamma, \beta}\left(x_{i}\right)$

训练 均值和方差采用指数加权平均计算
测试 当前统计值

对数据的要求
nn.BatchNorm1d input = B * 特征数 * 1d特征
nn.BatchNorm2d input = B * 特征数 * 2d特征
nn.BatchNorm3d input = B * 特征数 * 3d特征

import torch
import numpy as np
import torch.nn as nn
from tools.common_tools import set_seed

set_seed(1)  # 设置随机种子


class MLP(nn.Module):
    def __init__(self, neural_num, layers=100):
        super(MLP, self).__init__()
        self.linears = nn.ModuleList([nn.Linear(neural_num, neural_num, bias=False) for i in range(layers)])
        # 采用ModuleList 构建BN层
        self.bns = nn.ModuleList([nn.BatchNorm1d(neural_num) for i in range(layers)])
        self.neural_num = neural_num

    def forward(self, x):

        for (i, linear), bn in zip(enumerate(self.linears), self.bns):
            x = linear(x)
            x = bn(x)
            x = torch.relu(x)

            if torch.isnan(x.std()):
                print("output is nan in {} layers".format(i))
                break

            print("layers:{}, std:{}".format(i, x.std().item()))

        return x

    def initialize(self):
        for m in self.modules():
            if isinstance(m, nn.Linear):

                # method 1
                # 权值初始化
                # nn.init.normal_(m.weight.data, std=1)    # normal: mean=0, std=1

                # method 2 kaiming
                nn.init.kaiming_normal_(m.weight.data)


neural_nums = 256
layer_nums = 100
batch_size = 16

net = MLP(neural_nums, layer_nums)
net.initialize()

inputs = torch.randn((batch_size, neural_nums))  # normal: mean=0, std=1

output = net(inputs)
print(output)

# -*- coding:utf-8 -*-

import os
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import torchvision.transforms as transforms
from torch.utils.tensorboard import SummaryWriter
from torch.utils.data import DataLoader
from matplotlib import pyplot as plt
from model.lenet import LeNet, LeNet_bn
from tools.my_dataset import RMBDataset
from tools.common_tools import set_seed


class LeNet_bn(nn.Module):
    def __init__(self, classes):
        super(LeNet_bn, self).__init__()
        self.conv1 = nn.Conv2d(3, 6, 5)
        self.bn1 = nn.BatchNorm2d(num_features=6)

        self.conv2 = nn.Conv2d(6, 16, 5)
        self.bn2 = nn.BatchNorm2d(num_features=16)

        self.fc1 = nn.Linear(16 * 5 * 5, 120)
        self.bn3 = nn.BatchNorm1d(num_features=120)

        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, classes)

    def forward(self, x):
        out = self.conv1(x)
        out = self.bn1(out)
        out = F.relu(out)

        out = F.max_pool2d(out, 2)

        out = self.conv2(out)
        out = self.bn2(out)
        out = F.relu(out)

        out = F.max_pool2d(out, 2)

        out = out.view(out.size(0), -1)

        out = self.fc1(out)
        out = self.bn3(out)
        out = F.relu(out)

        out = F.relu(self.fc2(out))
        out = self.fc3(out)
        return out

    def initialize_weights(self):
        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                nn.init.xavier_normal_(m.weight.data)
                if m.bias is not None:
                    m.bias.data.zero_()
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_()
            elif isinstance(m, nn.Linear):
                nn.init.normal_(m.weight.data, 0, 1)
                m.bias.data.zero_()


set_seed(1)  # 设置随机种子
rmb_label = {"1": 0, "100": 1}

# 参数设置
MAX_EPOCH = 10
BATCH_SIZE = 16
LR = 0.01
log_interval = 10
val_interval = 1

# ============================ step 1/5 数据 ============================

split_dir = os.path.join("data", "rmb_split")
train_dir = os.path.join(split_dir, "train")
valid_dir = os.path.join(split_dir, "valid")

norm_mean = [0.485, 0.456, 0.406]
norm_std = [0.229, 0.224, 0.225]

train_transform = transforms.Compose([
    transforms.Resize((32, 32)),
    transforms.RandomCrop(32, padding=4),
    transforms.RandomGrayscale(p=0.8),
    transforms.ToTensor(),
    transforms.Normalize(norm_mean, norm_std),
])

valid_transform = transforms.Compose([
    transforms.Resize((32, 32)),
    transforms.ToTensor(),
    transforms.Normalize(norm_mean, norm_std),
])

# 构建MyDataset实例
train_data = RMBDataset(data_dir=train_dir, transform=train_transform)
valid_data = RMBDataset(data_dir=valid_dir, transform=valid_transform)

# 构建DataLoder
train_loader = DataLoader(dataset=train_data, batch_size=BATCH_SIZE, shuffle=True)
valid_loader = DataLoader(dataset=valid_data, batch_size=BATCH_SIZE)

# ============================ step 2/5 模型 ============================

# net = LeNet_bn(classes=2)
net = LeNet(classes=2)
# net.initialize_weights()

# ============================ step 3/5 损失函数 ============================
criterion = nn.CrossEntropyLoss()                                                   # 选择损失函数

# ============================ step 4/5 优化器 ============================
optimizer = optim.SGD(net.parameters(), lr=LR, momentum=0.9)                        # 选择优化器
scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.1)     # 设置学习率下降策略

# ============================ step 5/5 训练 ============================
train_curve = list()
valid_curve = list()

iter_count = 0
# 构建 SummaryWriter
writer = SummaryWriter(comment='test_your_comment', filename_suffix="_test_your_filename_suffix")

for epoch in range(MAX_EPOCH):

    loss_mean = 0.
    correct = 0.
    total = 0.

    net.train()
    for i, data in enumerate(train_loader):

        iter_count += 1

        # forward
        inputs, labels = data
        outputs = net(inputs)

        # backward
        optimizer.zero_grad()
        loss = criterion(outputs, labels)
        loss.backward()

        # update weights
        optimizer.step()

        # 统计分类情况
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).squeeze().sum().numpy()

        # 打印训练信息
        loss_mean += loss.item()
        train_curve.append(loss.item())
        if (i+1) % log_interval == 0:
            loss_mean = loss_mean / log_interval
            print("Training:Epoch[{:0>3}/{:0>3}] Iteration[{:0>3}/{:0>3}] Loss: {:.4f} Acc:{:.2%}".format(
                epoch, MAX_EPOCH, i+1, len(train_loader), loss_mean, correct / total))
            loss_mean = 0.

        # 记录数据，保存于event file
        writer.add_scalars("Loss", {"Train": loss.item()}, iter_count)
        writer.add_scalars("Accuracy", {"Train": correct / total}, iter_count)

    scheduler.step()  # 更新学习率

    # validate the model
    if (epoch+1) % val_interval == 0:

        correct_val = 0.
        total_val = 0.
        loss_val = 0.
        net.eval()
        with torch.no_grad():
            for j, data in enumerate(valid_loader):
                inputs, labels = data
                outputs = net(inputs)
                loss = criterion(outputs, labels)

                _, predicted = torch.max(outputs.data, 1)
                total_val += labels.size(0)
                correct_val += (predicted == labels).squeeze().sum().numpy()

                loss_val += loss.item()

            valid_curve.append(loss.item())
            print("Valid:\t Epoch[{:0>3}/{:0>3}] Iteration[{:0>3}/{:0>3}] Loss: {:.4f} Acc:{:.2%}".format(
                epoch, MAX_EPOCH, j+1, len(valid_loader), loss_val, correct / total))

            # 记录数据，保存于event file
            writer.add_scalars("Loss", {"Valid": loss.item()}, iter_count)
            writer.add_scalars("Accuracy", {"Valid": correct / total}, iter_count)

train_x = range(len(train_curve))
train_y = train_curve

train_iters = len(train_loader)
valid_x = np.arange(1, len(valid_curve)+1) * train_iters*val_interval # 由于valid中记录的是epochloss，需要对记录点进行转换到iterations
valid_y = valid_curve

plt.plot(train_x, train_y, label='Train')
plt.plot(valid_x, valid_y, label='Valid')

plt.legend(loc='upper right')
plt.ylabel('loss value')
plt.xlabel('Iteration')
plt.show()