softmax回归是一个多分类模型，但是他跟线性回归一样将输入特征与权重做线性叠加，与线性不同的是他有多个输出，输出的个数对应分类标签的个数，比如四个特征和三种输出动物类别，则权重包含12个标量（带下标的w），偏差包含三个标量（带下标的b），且对每个输入计算o1,o2,o3

然后再对这些输出值进行softmax‘运算，softmax也是单层模型

import torch
from IPython import display
from d2l import torch as d2lbatch_size=256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)#初始化模型参数
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)X = torch.tensor([[1.,2.,3.],[4.,5.,6.]])
X.sum(0,keepdim=True),X.sum(1,keepdim=True)Output:  (tensor([[5., 7., 9.]]),tensor([[ 6.],[15.]]))#定义softmax回归
def softmax(X):X_exp = torch.exp(X)partition = X_exp.sum(1,keepdim=True)return X_exp/partition#这里应用了广播机制x= torch.normal(0,1,(2,5))
x_prob= softmax(x)
x_prob,x_prob.sum(1)Output:   (tensor([[0.0902, 0.0850, 0.2683, 0.1946, 0.3619],[0.0551, 0.4104, 0.2667, 0.1486, 0.1192]]),tensor([1., 1.]))#实现softmax回归
def net(X):return softmax(torch.matmul(X.reshape((-1,w.shape[0])),w)+b)y = torch.tensor([0,2])
y_hat= torch.tensor([[0.1,0.3,0.6],[0.3,0.3,0.5]])
y_hat[[0,1],y]Output:   tensor([0.1000, 0.5000])#定义损失函数
def cross_entropy(y_hat,y):return -torch.log(y_hat[range(len(y_hat)),y])
cross_entropy(y_hat,y)Output:  tensor([2.3026, 0.6931])#分类精度
def accuracy(y_hat,y):if(len(y_hat.shape)>1 and y_hat.shape[0]>1):y_hat=y_hat.argmax(axis=1)cmp = y_hat.type(y.dtype) ==yreturn float(cmp.type(y.dtype).sum())
accuracy(y_hat,y)/len(y)Output:  0.5#我们可以评估任意模型的net的准确率
def evaluate_accuracy(net,data_iter):if isinstance(net,torch.nn.Module):net.eval()#将模型设置为评估模式metric = Accumulator(2)#正确预测数，预测总数，是一个累加的迭代器for X,y in data_iter:metric.add(accuracy(net(X),y),y.numel())return metric[0]/metric[1]class Accumulator:def __init__(self,n):self.data=[0.0]*ndef add(self,*args):self.data=[a+float(b) for a,b in zip(self.data,args)]def reset(self):self.data=[0.0]*len(self.data)def __getitem__(self,idx):return self.data[idx]
evaluate_accuracy(net,test_iter)Output:  0.1196def train_epoch_ch3(net, train_iter, loss, updater):  #@save"""训练模型一个迭代周期（定义见第3章）"""# 将模型设置为训练模式if isinstance(net, torch.nn.Module):net.train()# 训练损失总和、训练准确度总和、样本数metric = Accumulator(3)for X, y in train_iter:# 计算梯度并更新参数y_hat = net(X)l = loss(y_hat, y)if isinstance(updater, torch.optim.Optimizer):# 使用PyTorch内置的优化器和损失函数updater.zero_grad()l.mean().backward()updater.step()else:# 使用定制的优化器和损失函数l.sum().backward()updater(X.shape[0])metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())# 返回训练损失和训练精度return metric[0] / metric[2], metric[1] / metric[2]class Animator:  #@save"""在动画中绘制数据"""def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,ylim=None, xscale='linear', yscale='linear',fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,figsize=(3.5, 2.5)):# 增量地绘制多条线if legend is None:legend = []d2l.use_svg_display()self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)if nrows * ncols == 1:self.axes = [self.axes, ]# 使用lambda函数捕获参数self.config_axes = lambda: d2l.set_axes(self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)self.X, self.Y, self.fmts = None, None, fmtsdef add(self, x, y):# 向图表中添加多个数据点if not hasattr(y, "__len__"):y = [y]n = len(y)if not hasattr(x, "__len__"):x = [x] * nif not self.X:self.X = [[] for _ in range(n)]if not self.Y:self.Y = [[] for _ in range(n)]for i, (a, b) in enumerate(zip(x, y)):if a is not None and b is not None:self.X[i].append(a)self.Y[i].append(b)self.axes[0].cla()for x, y, fmt in zip(self.X, self.Y, self.fmts):self.axes[0].plot(x, y, fmt)self.config_axes()display.display(self.fig)display.clear_output(wait=True)#训练函数
def train_ch3(net,train_iter,test_iter,loss,num_epochs,updater):animator = Animator(xlabel='epoch',xlim=[1,num_epochs],ylim=[0.3,0.9],legend=['train loss','train acc','test acc'])for epoch in range(num_epochs):train_metrics = train_epoch_ch3(net,train_iter,loss,updater)test_acc=evaluate_accuracy(net,test_iter)animator.add(epoch+1,train_metrics+(test_acc,))train_loss,train_acc = train_metrics
#     assert train_loss<0.5,train_loss
#     assert train_acc <=1 and train_acc>0.7,train_acc
#     assert test_acc <=1 and test_acc>0.7,test_acclr = 0.1
#设置优化函数
def updater(batch_size):return d2l.sgd([w,b],lr,batch_size)num_epochs =10
train_ch3(net,train_iter,test_iter,cross_entropy,num_epochs,updater)

Output:

#预测
def predict_ch3(net,test_iter, n=6):for X,y in test_iter:breaktrues = d2l.get_fashion_mnist_labels(y)preds=d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))titles = [true + '\n'+pred for true,pred in zip(trues,preds)]d2l.show_images(X[0:n].reshape((n,28,28)),1,n,titles=titles[0:n])
predict_ch3(net,test_iter)

output: