深度学习——批标准化Batch Normalization

什么是批标准化？

批标准化（Batch Normalization）是深度学习中常用的一种技术，旨在加速神经网络的训练过程并提高模型的收敛速度。
批标准化通过在神经网络的每一层中对输入数据进行标准化来实现。具体而言，对于每个输入样本，在每一层的前向传播过程中，都会计算其均值和方差，并使用批量内的均值和方差对输入进行标准化。标准化后的数据会经过缩放和平移操作，使得网络可以学习到适合当前任务的特定数据分布。这样做的好处包括：
1.收敛速度更快：批标准化有助于避免梯度消失和梯度爆炸问题，使得神经网络在训练过程中更快地收敛。
2.允许更高的学习率：标准化输入可以使学习率的选择更加宽松，使得学习过程更加稳定。
3.正则化作用：批标准化在一定程度上具有正则化的效果，有助于防止过拟合。
4.不那么依赖初始化：由于标准化的存在，对网络的初始权重设置并不像传统网络那样敏感，这简化了网络的初始化过程。

对比使用批标准化和不使用批标准化

import torch
from torch import nn
from torch.nn import init
import torch.utils.data as Data
import matplotlib.pyplot as plt
import numpy as np# 用于可复现
# torch.manual_seed(1)    # reproducible
# np.random.seed(1)# Hyper parameters
# 样本点
N_SAMPLES = 2000
# 批大小
BATCH_SIZE = 64
# 轮次
EPOCH = 12
# 学习率
LR = 0.03
# 隐藏层层数
N_HIDDEN = 8
# 激活函数
ACTIVATION = torch.tanh
B_INIT = -0.2   # use a bad bias constant initializer# training data
# 生成-7到10之间的N_SAMPLES个值的等差数列，并将其转化为一个二维列向量
x = np.linspace(-7, 10, N_SAMPLES)[:, np.newaxis]
# 生成一个均值为0，标准差为2的和x相同形状的噪声数据
noise = np.random.normal(0, 2, x.shape)
# 生成x对应的y值
y = np.square(x) - 5 + noise# test data
test_x = np.linspace(-7, 10, 200)[:, np.newaxis]
noise = np.random.normal(0, 2, test_x.shape)
test_y = np.square(test_x) - 5 + noisetrain_x = torch.from_numpy(x).float()
train_y = torch.from_numpy(y).float()
test_x = torch.from_numpy(test_x).float()
test_y = torch.from_numpy(test_y).float()train_dataset = Data.TensorDataset(train_x, train_y)
train_loader = Data.DataLoader(dataset=train_dataset, batch_size=BATCH_SIZE, shuffle=True, num_workers=2,)# show data
# plt.scatter(train_x.numpy(), train_y.numpy(), c='#FF9359', s=50, alpha=0.2, label='train')
# plt.scatter(test_x.numpy(), test_y.numpy(), c='blue', s=50, alpha=0.2, label='test')
# plt.legend(loc='best')class Net(nn.Module):def __init__(self, batch_normalization=False):super(Net, self).__init__()# 是否进行批标准化self.do_bn = batch_normalization# 全连接层的列表self.fcs = []# 批标准化层的列表self.bns = []self.bn_input = nn.BatchNorm1d(1, momentum=0.5)   # for input datafor i in range(N_HIDDEN):               # build hidden layers and BN layers# 如果是第一层，输入神经元个数为1，其余为10个input_size = 1 if i == 0 else 10# 全连接层fc = nn.Linear(input_size, 10)# 将全连接层重新命名然后设置为类属性setattr(self, 'fc%i' % i, fc)       # IMPORTANT set layer to the Module# 对全连接层的参数进行初始化self._set_init(fc)                  # parameters initialization# 添加到列表中self.fcs.append(fc)if self.do_bn:bn = nn.BatchNorm1d(10, momentum=0.5)setattr(self, 'bn%i' % i, bn)   # IMPORTANT set layer to the Moduleself.bns.append(bn)self.predict = nn.Linear(10, 1)         # output layerself._set_init(self.predict)            # parameters initializationdef _set_init(self, layer):init.normal_(layer.weight, mean=0., std=.1)init.constant_(layer.bias, B_INIT)# 前向传播def forward(self, x):pre_activation = [x]if self.do_bn:x = self.bn_input(x)     # input batch normalizationlayer_input = [x]for i in range(N_HIDDEN):x = self.fcs[i](x)pre_activation.append(x)if self.do_bn: x = self.bns[i](x)   # batch normalizationx = ACTIVATION(x)layer_input.append(x)out = self.predict(x)# 返回预测值、每个隐藏层的输入、激活函数的输出return out, layer_input, pre_activationnets = [Net(batch_normalization=False), Net(batch_normalization=True)]# print(*nets)    # print net architecture# 优化器
opts = [torch.optim.Adam(net.parameters(), lr=LR) for net in nets]
# MSE作为损失函数
loss_func = torch.nn.MSELoss()def plot_histogram(l_in, l_in_bn, pre_ac, pre_ac_bn):for i, (ax_pa, ax_pa_bn, ax, ax_bn) in enumerate(zip(axs[0, :], axs[1, :], axs[2, :], axs[3, :])):[a.clear() for a in [ax_pa, ax_pa_bn, ax, ax_bn]]if i == 0:p_range = (-7, 10);the_range = (-7, 10)else:p_range = (-4, 4);the_range = (-1, 1)ax_pa.set_title('L' + str(i))ax_pa.hist(pre_ac[i].data.numpy().ravel(), bins=10, range=p_range, color='#FF9359', alpha=0.5);ax_pa_bn.hist(pre_ac_bn[i].data.numpy().ravel(), bins=10, range=p_range, color='#74BCFF', alpha=0.5)ax.hist(l_in[i].data.numpy().ravel(), bins=10, range=the_range, color='#FF9359');ax_bn.hist(l_in_bn[i].data.numpy().ravel(), bins=10, range=the_range, color='#74BCFF')for a in [ax_pa, ax, ax_pa_bn, ax_bn]: a.set_yticks(());a.set_xticks(())ax_pa_bn.set_xticks(p_range);ax_bn.set_xticks(the_range)axs[0, 0].set_ylabel('PreAct');axs[1, 0].set_ylabel('BN PreAct');axs[2, 0].set_ylabel('Act');axs[3, 0].set_ylabel('BN Act')plt.pause(0.01)if __name__ == "__main__":f, axs = plt.subplots(4, N_HIDDEN + 1, figsize=(10, 5))# 开启动态绘制plt.ion()  # something about plottingplt.show()# traininglosses = [[], []]  # recode loss for two networksfor epoch in range(EPOCH):print('Epoch: ', epoch)layer_inputs, pre_acts = [], []# 训练两个网络for net, l in zip(nets, losses):net.eval()              # set eval mode to fix moving_mean and moving_varpred, layer_input, pre_act = net(test_x)l.append(loss_func(pred, test_y).data.item())layer_inputs.append(layer_input)pre_acts.append(pre_act)net.train()             # free moving_mean and moving_varplot_histogram(*layer_inputs, *pre_acts)     # plot histogramfor step, (b_x, b_y) in enumerate(train_loader):for net, opt in zip(nets, opts):     # train for each network# 获取到预测值pred, _, _ = net(b_x)# 计算lossloss = loss_func(pred, b_y)# 梯度清零opt.zero_grad()# 误差反向传播loss.backward()# 逐步优化网络参数opt.step()    # it will also learns the parameters in Batch Normalization# 关闭动态绘制plt.ioff()# plot training loss# 绘制loss图plt.figure(2)plt.plot(losses[0], c='#FF9359', lw=3, label='Original')plt.plot(losses[1], c='#74BCFF', lw=3, label='Batch Normalization')plt.xlabel('step')plt.ylabel('test loss')plt.ylim((0, 2000))plt.legend(loc='best')# evaluation# set net to eval mode to freeze the parameters in batch normalization layers[net.eval() for net in nets]    # set eval mode to fix moving_mean and moving_varpreds = [net(test_x)[0] for net in nets]plt.figure(3)# 测试拟合效果plt.plot(test_x.data.numpy(), preds[0].data.numpy(), c='#FF9359', lw=4, label='Original')plt.plot(test_x.data.numpy(), preds[1].data.numpy(), c='#74BCFF', lw=4, label='Batch Normalization')plt.scatter(test_x.data.numpy(), test_y.data.numpy(), c='r', s=50, alpha=0.2, label='train')plt.legend(loc='best')plt.show()