Pytorch实战入门(一):MLP

Pytorch实战入门(一):MLP
Pytorch实战入门(二):CNN与MNIST
Pytorch实战入门(三):迁移学习

前言

环境:
  Python 3.7.4
  Pytorch 1.3.1

任务:
  构建一个多层感知机(Multi-Layer Perceptron,MLP)学习随机生成的输入和输出数据。
PS:MLP好像别名挺多的其实就是全连接网络,有的也叫人工神经网络(Artificial Neural Network,ANN);其中的全连接层(Fully Connected Layers)一般搭网络时取层名为 FC;而 FCN 一般是全卷积网络(Fully Convolutional Networks)
网络输入为1000维,输出为10维,随机生成64组数据用作训练;网络包含三层:输入层(1000个神经元)、隐藏层(100个神经元)、输出层(10个神经元)。

流程:

  1. 用 numpy 构建 MLP,回顾一下原理等
  2. 逐步将代码转变为用 pytorch 写,熟悉一些常用 API 和框架套路
  3. 最后得到一个与大部分 pytorch 工程类似的代码,麻雀虽小五脏俱全

API 查询: Pytorch官网
若对神经网络基础不熟悉建议 3Blue1Brown 的深度学习视频(p1,p2,p3)

1. numpy 构建神经网络

import numpy as np

N = 64  # 训练数据数量
D_in = 1000  # 训练数据维度,也是输入层神经元个数
H = 100  # 隐藏层神经元个数
D_out = 10  # 输出层神经元个数,也是训练数据标签的维度

# 随机生成训练数据
x = np.random.randn(N, D_in)    # [64, 1000] 64个1000维的输出
y = np.random.randn(N, D_out)   # [64, 10] 64个10维的对应输出

# 随机初始化网络的权重(此网络忽略偏置 bias)
w1 = np.random.randn(D_in, H)   # [1000, 100] 输入层和隐藏层间的权重
w2 = np.random.randn(H, D_out)  # [100, 10] 隐藏层和输出层间的权重
learning_rate = 1e-6  # 设置学习率

# 开始训练网络,迭代500次
for it in range(500):
    # Forward Pass 前向传播
    z1 = x.dot(w1)              # x*w1, 输出[64, 100]
    a1 = np.maximum(z1, 0)      # 激活层 relu, 小于0取0, 大于0不变 
    y_pred = a1.dot(w2)         # a1*w2, 输出[64, 10]
    # Loss 计算损失
    loss = np.square(y_pred - y).sum()  # MSE均方误差损失
    print(it, loss)
    
    # Backward Pass 反向传播
    # Gradient 计算梯度, 暂略具体计算公式的推导, 备注中的维度变化可以简单验证计算正确性
    grad_y_pred = 2.0 * (y_pred - y)         # [64,10]
    grad_w2 = a1.T.dot(grad_y_pred)          # [100,10] = [100,64] * [64,10]
    grad_a1 = grad_y_pred.dot(w2.T)          # [64,100] = [64,10] * [10,100]
    grad_z1 = grad_a1.copy()                 
    grad_z1[z1<0] = 0                        # [64,100]
    grad_w1 = x.T.dot(grad_z1)               # [1000,100] = [1000,64] * [64,100]
    # update weights 更新权重
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2

输出:

0 36093135.37125358
1 32398017.92254483
2 30489201.634114698
3 25977952.979760103
......
497 5.757372208142832e-06
498 5.501219493141868e-06
499 5.256529222978903e-06

2. numpy 代码转 pytorch 代码

2.1 代码框架不变,单纯替换api

import torch

N = 64
D_in = 1000
H = 100
D_out = 10

# np.random.randn() 变为 torch.randn()
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)
w1 = torch.randn(D_in, H) 
w2 = torch.randn(H, D_out)
learning_rate = 1e-6

for it in range(500):
    # Forward Pass
    z1 = x.mm(w1)         # dot() 变为 mm()
    a1 = z1.clamp(min=0)  # np.maximum() 变为 .clamp(min,max), 将数值夹在设定的 min,max 之间
    y_pred = a1.mm(w2)
    # Loss
    loss = (y_pred - y).pow(2).sum().item()
    # np.square变为.pow(2), 计算完的 loss 是一个 tensor, 通过 .item() 获取数值
    print(it, loss)
    # Backward Pass
    # Gradient
    grad_y_pred = 2.0 * (y_pred - y)
    grad_w2 = a1.t().mm(grad_y_pred)          # .T变为.t()
    grad_a1 = grad_y_pred.mm(w2.t())
    grad_z1 = grad_a1.clone()                 # .copy()变为.clone()
    grad_z1[z1<0] = 0
    grad_w1 = x.t().mm(grad_z1)
    # update weights
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2

输出:

0 32200542.0
1 31099402.0
2 35729468.0
......
497 0.00011954964429605752
498 0.00011727648234227672
499 0.00011476786312414333

2.2 自动计算梯度

import torch

N = 64
D_in = 1000
H = 100
D_out = 10

x = torch.randn(N, D_in)
y = torch.randn(N, D_out)
# requires_grad 设为 True 后即可自动求导
# 在1.3.1版本默认为 False
w1 = torch.randn(D_in, H, requires_grad = True)
w2 = torch.randn(H, D_out, requires_grad = True)
learning_rate = 1e-6

for it in range(500):
    # Forward Pass
    # 自动求导不需要网络中间的输出, 一行解决前向传播
    y_pred = x.mm(w1).clamp(min=0).mm(w2)  
    # Loss
    loss = (y_pred - y).pow(2).sum()    
    print(it, loss.item())
    
    # Backward Pass
    # Gradient
    loss.backward()
    # update weights
    with torch.no_grad():
        w1 -= learning_rate * w1.grad  # .grad 即可获取对应梯度
        w2 -= learning_rate * w2.grad
        w1.grad.zero_()    # 梯度在每次使用前需要清零,不然会不断累加
        w2.grad.zero_()

2.3 构建网络和损失函数

import torch
import torch.nn as nn

N = 64
D_in = 1000
H = 100
D_out = 10

x = torch.randn(N, D_in)
y = torch.randn(N, D_out) 

# 用 nn.Sequential 直接搭建网络
model = nn.Sequential(nn.Linear(D_in, H, bias = False),
                      nn.ReLU(),
                      nn.Linear(H, D_out, bias = False))
# 权重初始化
nn.init.normal_(model[0].weight)
nn.init.normal_(model[2].weight)
# 损失函数
loss_fn = nn.MSELoss(reduction = 'sum')
learning_rate = 1e-6

for it in range(500):
    # Forward Pass
    y_pred = model(x)  # 相当于 model.forward(x)
    # Loss
    loss = loss_fn(y_pred, y)
    print(it, loss.item())
    # Backward Pass
    # Gradient
    loss.backward()
    # update weights
    with torch.no_grad():
        for param in model.parameters():
            param -= learning_rate * param.grad
    model.zero_grad()

2.4 自动做梯度下降

import torch
import torch.nn as nn

N = 64
D_in = 1000
H = 100
D_out = 10

x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

model = nn.Sequential(nn.Linear(D_in, H, bias = False),
                      nn.ReLU(),
                      nn.Linear(H, D_out, bias = False))
# 权重初始化
nn.init.normal_(model[0].weight)
nn.init.normal_(model[2].weight)
# 损失函数
loss_fn = nn.MSELoss(reduction = 'sum')
# optimizer 优化器, 用来做梯度下降
learning_rate = 1e-4    # Adam 通常用 1e-3 到 1e-4
optimizer = torch.optim.Adam(model.parameters(), lr = learning_rate)
learning_rate = 1e-6    # SGD 通常用 1e-6
optimizer = torch.optim.SGD(model.parameters(), lr = learning_rate)

for it in range(500):
    # Forward Pass
    y_pred = model(x)
    # Loss
    loss = loss_fn(y_pred, y)
    print(it, loss.item())
    # Backward Pass
    # Gradient
    loss.backward()
    # update weights
    optimizer.step()
    optimizer.zero_grad()
  • 使用 Adam 做优化器,并使用 nn.init.normal_() 初始化权重时的输出:
0 22112800.0
1 22049420.0
2 21986150.0
......
497 4801638.0
498 4786025.0
499 4770454.0
  • 使用 Adam 做优化器,并备注掉两行初始化权重时的输出:
0 665.029296875
1 648.2096557617188
2 631.8590087890625
......
497 1.3149491451258655e-07
498 1.2488904133078904e-07
499 1.1852827697111934e-07
  • 使用 SGD 做优化器,并使用 nn.init.normal_() 初始化权重时的输出:
0 30186936.0
1 27895552.0
2 28996608.0
......
497 3.768844544538297e-05
498 3.709576412802562e-05
499 3.662251037894748e-05
  • 使用 SGD 做优化器,并备注掉两行初始化权重时的输出:
0 663.9910278320312
1 663.4700927734375
2 662.9500122070312
......
497 470.6908264160156
498 470.3971252441406
499 470.1034240722656

  可以看出使用不同的优化器时,权重的初始化方式会很大程度影响网络训练的效果和速度,其中具体原理尚待补充研究。

2.5 一般项目的写法

import torch
import torch.nn as nn

N = 64
D_in = 1000
H = 100
D_out = 10

x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# 创建一个类构件模型,对构件复杂模型有很大好处
class TwoLayerNet(torch.nn.Module):
    def __init__(self, D_in, H, D_out):
        super(TwoLayerNet, self).__init__()
        self.linear1 = nn.Linear(D_in, H, bias = False)
        self.relu = nn.ReLU()
        self.linear2 = nn.Linear(H, D_out, bias = False)
        
    def forward(self, x):
        y_pred = self.linear2(self.relu(self.linear1(x)))
        return y_pred
# model
model = TwoLayerNet(D_in, H, D_out)
# loss
loss_fn = nn.MSELoss(reduction = 'sum')
# optimizer
learning_rate = 1e-4
optimizer = torch.optim.Adam(model.parameters(), lr = learning_rate)

for it in range(500):
    # Forward Pass
    y_pred = model(x)
    # Loss
    loss = loss_fn(y_pred, y)
    print(it, loss.item())
    # Backward Pass
    loss.backward()
    # update model parameters
    optimizer.step()
    optimizer.zero_grad()

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