神经网络模型底层原理与实现10-softmax的实现

import torch
from IPython import display
from d2l import torch as d2l

batch_size=256

#定义训练和验证数据集
train_iter,test_iter=d2l.load_data_fashion_mnist(batch_size)

#参数初始化,把输入图片看成长度784的向量，这个数据集有十个类别，输出为10
num_inputs=784
num_outputs=10
w=torch.normal(0,0.01,size=(num_inputs,num_outputs),requires_grad=True)
b=torch.zeros(num_outputs,requires_grad=True)

#实现softmax函数
def softmax(X):
X_exp=torch.exp(X)
partition=X_exp.sum(1,keepdim=True)#保持输出维度，使它还是一个矩阵,0是按列求和，1是按行求和

#实现softmax回归模型
def net(X):
return softmax(torch.matmul(X.reshape(-1,w.shape[0]),w)+b)#matmul是矩阵乘法

#实现交叉熵损失函数
def cross_entropy(y_hat,y):#公式是-y*log(y_hat)
return -torch.log(y_hat[range(len(y_hat)),y])#log是以e为底的对数，根据前面推的公式，【】内是取出对应元素值

#将预测类别与真实类别比较，这里开始进入测试部分
def accuracy(y_hat,y):
if len(y_hat.shape)>1 and y_hat.shape[1]>1:
y_hat=y_hat.argmax(axis=1)#选出每行中最大的，也就是分类的类别
cmp=y_hat.type(y.dtype)==y
return float(cmp.type(y.dtype).sum())

#按照accuracy的思路，可以写出模型结果准确率计算函数,分子分母不断累加正确的个数和总的个数
def evaluate_accuracy(data_iter, net):
acc_sum, n = 0.0, 0
for X, y in data_iter:
acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()#item将tensor类型转为数据类型
n += y.shape[0]
return acc_sum / n

#softmax训练过程
def train_ch3(net, train_iter, test_iter, loss, num_epochs,batch_size,params=None, lr=None, optimizer=None):#num_epochs训练次数，lr学习率
for epoch in range(num_epochs):
train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
for X, y in train_iter:
y_hat = net(X)#进入网络
l = loss(y_hat, y).sum()#求损失

# 梯度清零
if optimizer is not None:
optimizer.zero_grad()
elif params is not None and params[0].grad is not None:
for param in params:
param.grad.data.zero_()

l.backward()#反向传播
if optimizer is None:
d2l.sgd(params, lr, batch_size)
else:
optimizer.step()
train_l_sum += l.item()
train_acc_sum += (y_hat.argmax(dim=1) ==y).sum().item()
n += y.shape[0]
test_acc = evaluate_accuracy(test_iter, net)
print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'% (epoch + 1, train_l_sum / n, train_acc_sum / n,test_acc))