21Batch Normalization

一、Batch Normalization概念

1.1 Batch Normalization概念

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)

《 Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift》

计算方式：

输入：一个mini-batch数据(m个)，两个待学习的参数$\gamma,\beta$γ,β

输出：

• 求取mini-batch数据的均值和方差
• 对mini-batch中的每个数据标准化，$\epsilon$ϵ是修正项，防止分母为0
• 对上一步数据进行affine transfrom，可理解为缩放和平移，增强Capacity

1.2 Internal Covariate Shift (ICS)

ICS：可以简单理解为数据尺度或分布的变化

由上图中的D(H1)=n*D(x)*D(W)=1可知，第一个隐藏层的输出等于上一层的输入的方差和二者之间权重的方差的连乘，所以如果数据的方差发生微小变化，那么随着网络的加深，这个变化会越来越明显，从而导致梯度消失或梯度爆炸
所以数据尺度或分布发生变化，则会导致模型难以训练
而Batch Normalization就是为了解决这个问题而推出来的

1.3 Batch Normalization应用

1.3.1 使用BN，可以不用权值初始化

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

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)])
        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)          # 在**函数之前使用BN层
            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
                # 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)

可以从上图看到，当使用了BN，不使用权值初始化，每层的标准差依然保持的很好

1.3.2 BN应用二分类模型

# -*- coding:utf-8 -*-
"""
@file name  : bn_application.py
# @author   : TingsongYu https://github.com/TingsongYu
@date       : 2019-11-01
@brief      : nn.BatchNorm使用
"""
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
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()

从上图可以看到，在训练时，因为没有经过权值初始化，在80到100个iteration时，loss会发生激增

在使用了权值初始化后，可以看到，在第20到40个iteration时会出现激增，而往后，Loss趋于减小，并逐渐到了一个很好的结果

可以看到在加入了BN层后，虽然loss也会出现激增，但是幅度小，而且始终保持在一个良好尺度范围内

二、PyTorch的Batch Normalization 1d/2d/3d实现

2.1 基类——_BatchNorm

__init__(self, 
		 num_features,
		 eps=1e-5,
	     momentum=0.1,
	     affine=True,
         track_running_stats=True)

_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

2.2 nn.BatchNorm1d/2d/3d

• nn.BatchNorm1d
• nn.BatchNorm2d
• nn.BatchNorm3d
  

主要属性：

• running_mean：均值
• running_var：方差
• weight： affine transform中的gamma
• bias： affine transform中的beta

训练时：均值和方差采用指数加权平均计算
running_mean = (1 - momentum) * pre_running_mean + momentum * mean_t
running_var = (1 - momentum) * pre_running_var + momentum * var_t

测试时：当前统计值

代码示例：

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

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

# ======================================== nn.BatchNorm1d
flag = 1
# flag = 0
if flag:

    batch_size = 3
    num_features = 5
    momentum = 0.3

    features_shape = (1)

    feature_map = torch.ones(features_shape)                                                    # 1D
    feature_maps = torch.stack([feature_map*(i+1) for i in range(num_features)], dim=0)         # 2D
    feature_maps_bs = torch.stack([feature_maps for i in range(batch_size)], dim=0)             # 3D
    print("input data:\n{} shape is {}".format(feature_maps_bs, feature_maps_bs.shape))

    bn = nn.BatchNorm1d(num_features=num_features, momentum=momentum)

    running_mean, running_var = 0, 1

    for i in range(2):
        outputs = bn(feature_maps_bs)

        print("\niteration:{}, running mean: {} ".format(i, bn.running_mean))
        print("iteration:{}, running var:{} ".format(i, bn.running_var))

        mean_t, var_t = 2, 0

        running_mean = (1 - momentum) * running_mean + momentum * mean_t
        running_var = (1 - momentum) * running_var + momentum * var_t

        print("iteration:{}, 第二个特征的running mean: {} ".format(i, running_mean))
        print("iteration:{}, 第二个特征的running var:{}".format(i, running_var))

这里当前用来对数据进行标准化的均值和方差，不是只是计算当前mini-batch所计算的，而是会考虑之前mini-batch数据的信息，综合考虑去估计去均值和方差

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

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
# ======================================== nn.BatchNorm2d
flag = 1
# flag = 0
if flag:

    batch_size = 3
    num_features = 6
    momentum = 0.3
    
    features_shape = (2, 2)

    feature_map = torch.ones(features_shape)                                                    # 2D
    feature_maps = torch.stack([feature_map*(i+1) for i in range(num_features)], dim=0)         # 3D
    feature_maps_bs = torch.stack([feature_maps for i in range(batch_size)], dim=0)             # 4D

    print("input data:\n{} shape is {}".format(feature_maps_bs, feature_maps_bs.shape))

    bn = nn.BatchNorm2d(num_features=num_features, momentum=momentum)

    running_mean, running_var = 0, 1

    for i in range(2):
        outputs = bn(feature_maps_bs)

        print("\niter:{}, running_mean.shape: {}".format(i, bn.running_mean.shape))
        print("iter:{}, running_var.shape: {}".format(i, bn.running_var.shape))

        print("iter:{}, weight.shape: {}".format(i, bn.weight.shape))
        print("iter:{}, bias.shape: {}".format(i, bn.bias.shape))

由上图可知，BN是在特征的数量上计算的

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

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


# ======================================== nn.BatchNorm3d
flag = 1
# flag = 0
if flag:

    batch_size = 3
    num_features = 4
    momentum = 0.3

    features_shape = (2, 2, 3)

    feature = torch.ones(features_shape)                                                # 3D
    feature_map = torch.stack([feature * (i + 1) for i in range(num_features)], dim=0)  # 4D
    feature_maps = torch.stack([feature_map for i in range(batch_size)], dim=0)         # 5D

    print("input data:\n{} shape is {}".format(feature_maps, feature_maps.shape))

    bn = nn.BatchNorm3d(num_features=num_features, momentum=momentum)

    running_mean, running_var = 0, 1

    for i in range(2):
        outputs = bn(feature_maps)

        print("\niter:{}, running_mean.shape: {}".format(i, bn.running_mean.shape))
        print("iter:{}, running_var.shape: {}".format(i, bn.running_var.shape))

        print("iter:{}, weight.shape: {}".format(i, bn.weight.shape))
        print("iter:{}, bias.shape: {}".format(i, bn.bias.shape))