1 导入所需要的包
import torch import numpy as np import random from IPython import display from matplotlib import pyplot as plt import torchvision import torchvision.transforms as transforms
2 下载MNIST数据集
mnist_train = torchvision.datasets.MNIST(root='../Datasets/MNIST', train=True, download=True, transform=transforms.ToTensor()) mnist_test = torchvision.datasets.MNIST(root='../Datasets/MNIST', train=False,download=True, transform=transforms.ToTensor())
3 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)
4 初始化参数+定义隐藏层的激活函数
num_inputs,num_hiddens,num_outputs =784, 256,10
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 relu(x): x = torch.max(input=x,other=torch.tensor(0.0)) return x
5 定义模型
def net(X): X = X.view((-1,num_inputs)) H = relu(torch.matmul(X,W1.t())+b1) return torch.matmul(H,W2.t())+b2
6 定义交叉熵损失函数和优化器
loss = torch.nn.CrossEntropyLoss() def SGD(paras,lr): for param in params: param.data -= lr * param.grad
7 定义L2范数
def l2_penalty(w): return (w**2).sum()/2
8 定义训练函数
def train(net,train_iter,test_iter,loss,num_epochs,batch_size,lr=None,optimizer=None,mylambda=0): train_ls, test_ls = [], [] for epoch in range(num_epochs): ls, count = 0, 0 for X,y in train_iter : X = X.reshape(-1,num_inputs) l=loss(net(X),y)+ mylambda*l2_penalty(W1) + mylambda*l2_penalty(W2) 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: X = X.reshape(-1,num_inputs) l=loss(net(X),y) + mylambda*l2_penalty(W1) + mylambda*l2_penalty(W2) 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
9 开始训练模型
lr = 0.01 num_epochs = 20 Lamda = [0,0.1,0.2,0.3,0.4,0.5] Train_ls, Test_ls = [], [] for lamda in Lamda: print("current lambda is %f"%lamda) W1,b1,W2,b2 = init_param() loss = torch.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,lamda) Train_ls.append(train_ls) Test_ls.append(test_ls)
10 绘制训练集和测试集的loss曲线
x = np.linspace(0,len(Train_ls[1]),len(Train_ls[1])) plt.figure(figsize=(10,8)) for i in range(0,len(Lamda)): plt.plot(x,Train_ls[i],label= f'L2_Regularization:{Lamda [i]}',linewidth=1.5) plt.xlabel('different epoch') plt.ylabel('loss') plt.legend(loc=2, bbox_to_anchor=(1.1,1.0),borderaxespad = 0.) plt.title('train loss with L2_penalty') plt.show()