前馈神经网络dropout实例

直接看代码。

（一）手动实现

import torch
import torch.nn as nn
import numpy as np
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt


#下载MNIST手写数据集  
mnist_train = torchvision.datasets.MNIST(root='./MNIST', train=True, download=True, transform=transforms.ToTensor())  
mnist_test = torchvision.datasets.MNIST(root='./MNIST', train=False,download=True, transform=transforms.ToTensor())  

#读取数据  
batch_size = 256 
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True,num_workers=0)  
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False,num_workers=0)  


#初始化参数  
num_inputs,num_hiddens,num_outputs =784, 256,10

num_epochs=30

lr = 0.001

def init_param():
    W1 = torch.tensor(np.random.normal(0, 0.01, (num_hiddens,num_inputs)), dtype=torch.float32)  
    b1 = torch.zeros(1, dtype=torch.float32)  
    W2 = torch.tensor(np.random.normal(0, 0.01, (num_outputs,num_hiddens)), dtype=torch.float32)  
    b2 = torch.zeros(1, dtype=torch.float32)  
    params =[W1,b1,W2,b2]
    for param in params:  
        param.requires_grad_(requires_grad=True)  
    return W1,b1,W2,b2

def dropout(X, drop_prob):
    X = X.float()
    assert 0 <= drop_prob <= 1
    keep_prob = 1 - drop_prob
    if keep_prob == 0:
        return torch.zeros_like(X)
    mask = (torch.rand(X.shape) < keep_prob).float()
    print(mask)
    return mask * X / keep_prob

def net(X, is_training=True):
    X = X.view(-1, num_inputs)
    H1 = (torch.matmul(X, W1.t()) + b1).relu()
    if is_training:
        H1 = dropout(H1, drop_prob)
    return (torch.matmul(H1,W2.t()) + b2).relu()


def train(net,train_iter,test_iter,loss,num_epochs,batch_size,lr=None,optimizer=None):
    train_ls, test_ls = [], []
    for epoch in range(num_epochs):
        ls, count = 0, 0
        for X,y in train_iter:
            l=loss(net(X),y)
            
            optimizer.zero_grad()
            l.backward()
            optimizer.step()
            
            ls += l.item()
            count += y.shape[0]
            
        train_ls.append(ls)
        
        ls, count = 0, 0
        
        for X,y in test_iter:
            
            l=loss(net(X,is_training=False),y)
            
            ls += l.item()
            count += y.shape[0]
            
        test_ls.append(ls)
        
        if(epoch+1)%10==0:
            print('epoch: %d, train loss: %f, test loss: %f'%(epoch+1,train_ls[-1],test_ls[-1]))
            
    return train_ls,test_ls


drop_probs = np.arange(0,1.1,0.1)

Train_ls, Test_ls = [], []

for drop_prob in drop_probs:

    W1,b1,W2,b2 = init_param()
    loss = nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD([W1,b1,W2,b2],lr = 0.001)
    train_ls, test_ls =  train(net,train_iter,test_iter,loss,num_epochs,batch_size,lr,optimizer)   
    Train_ls.append(train_ls)
    Test_ls.append(test_ls)
    
    
x = np.linspace(0,len(train_ls),len(train_ls))

plt.figure(figsize=(10,8))

for i in range(0,len(drop_probs)):
    plt.plot(x,Train_ls[i],label= 'drop_prob=%.1f'%(drop_probs[i]),linewidth=1.5)
    plt.xlabel('epoch')
    plt.ylabel('loss')
    
# plt.legend()
plt.legend(loc=2, bbox_to_anchor=(1.05,1.0),borderaxespad = 0.)
plt.title('train loss with dropout')
plt.show()

运行结果：

（二）torch.nn实现

import torch
import torch.nn as nn
import numpy as np
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt

mnist_train = torchvision.datasets.MNIST(root='./MNIST', train=True, download=True, transform=transforms.ToTensor())  
mnist_test = torchvision.datasets.MNIST(root='./MNIST', train=False,download=True, transform=transforms.ToTensor())  
batch_size = 256 
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True,num_workers=0)  
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False,num_workers=0)  


class LinearNet(nn.Module):
    def __init__(self,num_inputs, num_outputs, num_hiddens1, num_hiddens2, drop_prob1,drop_prob2):
        super(LinearNet,self).__init__()
        self.linear1 = nn.Linear(num_inputs,num_hiddens1)
        self.relu = nn.ReLU()
        self.drop1 = nn.Dropout(drop_prob1)
        self.linear2 = nn.Linear(num_hiddens1,num_hiddens2)
        self.drop2 = nn.Dropout(drop_prob2)
        self.linear3 = nn.Linear(num_hiddens2,num_outputs)
        self.flatten  = nn.Flatten()
    
    def forward(self,x):
        x = self.flatten(x)
        x = self.linear1(x)
        x = self.relu(x)
        x = self.drop1(x)
        x = self.linear2(x)
        x = self.relu(x)
        x = self.drop2(x)
        x = self.linear3(x)
        y = self.relu(x)
        return y
    
    
    
    
def train(net,train_iter,test_iter,loss,num_epochs,batch_size,params=None,lr=None,optimizer=None):
    train_ls, test_ls = [], []
    for epoch in range(num_epochs):
        ls, count = 0, 0
        for X,y in train_iter:
            l=loss(net(X),y)
            optimizer.zero_grad()
            l.backward()
            optimizer.step()
            ls += l.item()
            count += y.shape[0]
        train_ls.append(ls)
        ls, count = 0, 0
        for X,y in test_iter:
            l=loss(net(X),y)
            ls += l.item()
            count += y.shape[0]
        test_ls.append(ls)
        if(epoch+1)%5==0:
            print('epoch: %d, train loss: %f, test loss: %f'%(epoch+1,train_ls[-1],test_ls[-1]))
    return train_ls,test_ls    
    
    
    
    
    
num_inputs,num_hiddens1,num_hiddens2,num_outputs =784, 256,256,10
num_epochs=20
lr = 0.001
drop_probs = np.arange(0,1.1,0.1)
Train_ls, Test_ls = [], []

for drop_prob in drop_probs:
    net = LinearNet(num_inputs, num_outputs, num_hiddens1, num_hiddens2, drop_prob,drop_prob)
    for param in net.parameters():
        nn.init.normal_(param,mean=0, std= 0.01)
    loss = nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD(net.parameters(),lr)
    train_ls, test_ls = train(net,train_iter,test_iter,loss,num_epochs,batch_size,net.parameters,lr,optimizer)
    Train_ls.append(train_ls)
    Test_ls.append(test_ls)
    
    
    
    
x = np.linspace(0,len(train_ls),len(train_ls))
plt.figure(figsize=(10,8))
for i in range(0,len(drop_probs)):
    plt.plot(x,Train_ls[i],label= 'drop_prob=%.1f'%(drop_probs[i]),linewidth=1.5)
    plt.xlabel('epoch')
    plt.ylabel('loss')
plt.legend(loc=2, bbox_to_anchor=(1.05,1.0),borderaxespad = 0.)
plt.title('train loss with dropout')
plt.show()


input = torch.randn(2, 5, 5)
m = nn.Sequential(
nn.Flatten()
)
output = m(input)
output.size()

运行结果：

关于dropout的原理，网上资料很多，一般都是用一个正态分布的矩阵，比较矩阵元素和（1-dropout），大于（1-dropout）的矩阵元素值的修正为1，小于（1-dropout）的改为1，将输入的值乘以修改后的矩阵，再除以(1-dropout)。

疑问：

1. 数值经过正态分布矩阵的筛选后，还要除以 (1-dropout)，这样做的原因是什么？
2. Flatten层用来将输入“压平”，即把多维的输入一维化，常用在从卷积层到全连接层的过渡。