PyTorch学习笔记（15）权值初始化

权值初始化

梯度消失 梯度爆炸

两个相互独立的随机变量乘积的期望 等于 他们各自期望的乘积

$$\text{ 1. }\mathrm{E}(\mathbf{X}\ast \mathbf{Y})=\mathbf{E}(\mathbf{X})\ast \mathbf{E}(\mathbf{Y})$$
方差的公式

$$\text{ 2. }D(X)=E\left(X^2\right)-[E(X){]}^2$$

两个相互独立的随机变量之和的方差 等于 他们各自方差的和
$$\text{ 3. }\mathrm{D}(X+Y)=D(X)+D(Y)$$
由1.2.3.式可得
$$1.2.3\Rightarrow \mathrm{D}(\mathrm{X}+\mathrm{Y})=\mathrm{D}(\mathrm{X})\ast \mathrm{D}(\mathrm{Y})+\mathrm{D}(\mathrm{X})\ast [E(\mathrm{Y}){]}^2+\mathrm{D}(\mathrm{Y})\ast [E(X){]}^2$$
若
$$\begin{array}{rl}& E(X)=0,E(Y)=0\\ & \mathrm{D}(\mathrm{X}\ast \mathrm{Y})=\mathrm{D}(\mathrm{X})\ast \mathrm{D}(\mathrm{Y})\end{array}$$

Xavier初始化

方差一致性：保持数据尺度维持在恰当范围，通常方差为1
激活函数：饱和函数 如Sigmoid Tanh
$$\begin{array}{rl}& {\mathbf{n}}_i\ast \mathbf{D}(\mathbf{W})=1\\ & {\mathbf{n}}_{\mathbf{i}+1}\ast \mathbf{D}(\mathbf{W})=1\end{array}\Rightarrow D(W)=\frac{2}{n_i+n_{i+1}}$$

Kaiming初始化
方差一致性：保持数据尺度维持在恰当范围，通常方差为1
激活函数:ReLU及其变种

$$\mathrm{D}(W)=\frac{2}{n_i}$$

$$\mathrm{D}(W)=\frac{2}{\left(1+{\mathrm{a}}^2\right)\ast n_i}$$

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

import os
import torch
import random
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):
    # 构造100层的线性叠加 不考虑偏置
    def __init__(self, neural_num, layers):
        super(MLP, self).__init__()
        self.linears = nn.ModuleList([nn.Linear(neural_num, neural_num, bias=False) for i in range(layers)])
        self.neural_num = neural_num

    def forward(self, x):
        for (i, linear) in enumerate(self.linears):
            x = linear(x)
            x = torch.relu(x)

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

        return x

    def initialize(self):
        for m in self.modules():
            if isinstance(m, nn.Linear):
                # 判断是否是线性层 若是 对权值进行初始化 采用标准正态分布，0均值 1标准差 的分布
                nn.init.normal_(m.weight.data)
                # nn.init.normal_(m.weight.data, std=np.sqrt(1/self.neural_num))    # normal: mean=0, std=1

                # a = np.sqrt(6 / (self.neural_num + self.neural_num))
                #
                # tanh_gain = nn.init.calculate_gain('tanh')
                # a *= tanh_gain
                #
                # nn.init.uniform_(m.weight.data, -a, a)

                # nn.init.xavier_uniform_(m.weight.data, gain=tanh_gain)

                # nn.init.normal_(m.weight.data, std=np.sqrt(2 / self.neural_num))
                # nn.init.kaiming_normal_(m.weight.data)

# flag = 0
flag = 1

if flag:
    layer_nums = 100
    neural_nums = 256
    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)

# ======================================= calculate gain =======================================

flag = 0
# flag = 1

if flag:

    x = torch.randn(10000)
    out = torch.tanh(x)

    gain = x.std() / out.std()
    print('gain:{}'.format(gain))

    tanh_gain = nn.init.calculate_gain('tanh')
    print('tanh_gain in PyTorch:', tanh_gain)

十种初始化方法

Xavier均匀分布
Xavier标准正态分布
Kaiming均匀分布
Kaiming标准正态分布
均匀分布
正态分布
常数分布
正交矩阵初始化
单位矩阵初始化
稀疏矩阵初始化

nn.init.calculate_gain

主要功能：计算激活函数的方差变化尺度
主要参数
nonlinearity 激活函数名称
param 激活函数的参数 如Leaky ReLU的negative_slop