Softmax分类器

MNIST数据集有10个标签，如何设计网络结构？
可以使用Softmax输出预测分布。

假设$z^l\in R^K$是最后一层的输出，于是可得：
$P(y=i)=\frac{e^{z_i}}{{\sum }_{j=0}^{K-1}{e}^{z_j}},i\in \{0,\dots ,K-1\}$
例子：

交叉熵损失：

使用numpy计算交叉熵损失：

import numpy as np
y = np.array([1,0,0])
z = np.array([0.2,0.1,-0.1])
y_pred = np.exp(z) / np.exp(z).sum()
loss = (-y * np.log(y_pred)).sum()
print(loss)

输出结果：0.9729189131256584

使用PyTorch计算交叉熵损失：

import torch
y = torch.LongTensor([0])
z = torch.Tensor([[0.2,0.1,-0.1]])
criterion = torch.nn.CrossEntropyLoss()
loss = criterion(z,y)
print(loss)

输出结果：tensor(0.9729)
使用小批量来计算交叉熵损失：

import torch
criterion = torch.nn.CrossEntropyLoss()
Y = torch.LongTensor([2,0,1])
Y_pred1 = torch.Tensor([[0.1, 0.2, 0.9],
                        [1.1, 0.1, 0.2],
                        [0.2, 2.1, 0.1]])
Y_pred2 = torch.Tensor([[0.1, 0.2, 0.9],
                        [1.1, 0.1, 0.2],
                        [0.2, 2.1, 0.1]])
l1 = criterion(Y_pred1,Y)
l2 = criterion(Y_pred2,Y)
print("Batch loss1 = ",l1.data,"\nBatch Loss2 = ",l2.data)

输出结果：
Batch loss1 = tensor(0.4966)
Batch Loss2 = tensor(0.4966)

设计MNIST数据集的分类器：
1、导入各种包

import torch,torchvision
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optim

2、加载数据集，需将PIL图像转化为PyTorch张量

batch_size = 64
transform = transforms.Compose([
    transforms.ToTensor(),#将PIL图像转换为PyTorch张量
    transforms.Normalize((0.1307, ),(0.3081, ))#这两个参数是平均值和标准差
])

train_dataset = datasets.MNIST(root='../dataset/mnist/',
                                train = True,
                                download = True,
                                transform = torchvision.transforms.ToTensor())
train_loader = DataLoader(train_dataset,
                            shuffle = True,
                            batch_size = batch_size)
test_dataset = datasets.MNIST(root='../dataset/mnist/',
                                train=False,
                                download = True,
                                 transform = torchvision.transforms.ToTensor())
test_loader = DataLoader(test_dataset,
                            shuffle = False,
                            batch_size = batch_size)

3、设计模型

class Net(torch.nn.Module):
    def __init__(self):
        super(Net,self).__init__()
        self.l1 = torch.nn.Linear(784,512)
        self.l2 = torch.nn.Linear(512,256)
        self.l3 = torch.nn.Linear(256,128)
        self.l4 = torch.nn.Linear(128,64)
        self.l5 = torch.nn.Linear(64,10)
        
    def forward(self,x):
        x = x.view(-1,784)
        x = F.relu(self.l1(x))
        x = F.relu(self.l2(x))
        x = F.relu(self.l3(x))
        x = F.relu(self.l4(x))
        return self.l5(x)

model = Net()

4、构建损失和优化器

criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(),lr=0.01,momentum=0.5)

5、训练和测试

def train(epoch):
    running_loss = 0.0
    for batch_idx,data in enumerate(train_loader,0):
        inputs, target = data
        optimizer.zero_grad()
        
        #前向传播+反向传播+更新
        outputs = model(inputs)
        loss = criterion(outputs,target)
        loss.backward()
        optimizer.step()
        
        running_loss += loss.item()
        if batch_idx % 300 == 299:
            print('[%d,%5d] loss: %.3f' % (epoch+1,batch_idx+1,running_loss/300))
            running_loss = 0.0
            
def test():
    correct = 0
    total = 0
    with torch.no_grad():
        for data in test_loader:
            images,labels = data
            outputs = model(images)
            _,predicted = torch.max(outputs.data,dim=1)
            total += labels.size(0)
            correct += (predicted == labels).sum().item()
    print('Accuracy on test set: %d %%'% (100*correct/total))

for epoch in range(10):
    train(epoch)
    test()

结果：