动手深度学习4月17日

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权重衰减

%matplotlib inline
import torch
from torch import nn
from d2l import torch as

像以前一样生成一些数据，生成公式如下：

n_train, n_test, num_inputs, batch_size = 20, 100, 200, 5
true_w, true_b = torch.ones((num_inputs,1)) * 0.01, 0.05
train_data = d2l.synthetic_data(true_w, true_b, n_train)
train_iter = d2l.load_array(train_data, batch_size)
test_data = d2l.synthetic_data(true_w, true_b, n_test)
test_iter = d2l.load_array(test_data, batch_size, is_train=False)

初始化模型参数

def init_params():
    w = torch.normal(0,1, size=(num_inputs,1), requires_grad=True)
    b = torch.zeros(1, requires_grad=True)
    return [w, b]

定义 L 2 L_2 L2​范数惩罚

def l2_penalty(w):
    return torch.sum(w.pow(2)) / 2

定义 L 1 L_1 L1​范数惩罚

def l1_penalty(w):
    return torch.sum(torch.abs(w))

定义训练代码实现

def train(lambd):
    w, b = init_params()
    net, loss = lambda X: d2l.linreg(X, w, b), d2l.squared_loss
    num_epochs, lr = 100, 0.003
    animator = d2l.Animator(xlabel='epochs', ylabel='loss', yscale='log',
                            xlim=[5, num_epochs], legend=['train', 'test'])
    for epoch in range(num_epochs):
        for X, y in train_iter:
            with torch.enable_grad():
                # 增加了L2范数惩罚项，广播机制使l2_penalty(w)成为一个长度为`batch_size`的向量。
                l = loss(net(X), y) + lambd * l2_penalty(w)
            l.sum().backward()
            d2l.sgd([w, b], lr, batch_size)
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1, (d2l.eval（net, train_iter, loss),
                                     d2l.eval（net, test_iter, loss)))
    print('w的L2范数是：', torch.norm(w).item())

忽略正则化直接训练

train(lambd=0)

w的L2范数是： 13.606081008911133

使用权重衰减

train(lambd=3)

w的L2范数是： 0.38097628951072693

train(lambd=6)

w的L2范数是： 0.0328742153942585

train(lambd=9)

w的L2范数是： 0.02456110343337059

简洁实现

def train_concise(wd):
    net = nn.Sequential(nn.Linear(num_inputs, 1))
    for param in net.parameters():
        param.data.normal_()
    loss = nn.MSELoss()
    num_epochs, lr = 100, 0.003
    # 偏置参数没有衰减。
    trainer = torch.optim.SGD([{
        "params": net[0].weight,
        'weight_decay': wd}, {
            "params": net[0].bias}], lr=lr)
    animator = d2l.Animator(xlabel='epochs', ylabel='loss', yscale='log',
                            xlim=[5, num_epochs], legend=['train', 'test'])
    for epoch in range(num_epochs):
        for X, y in train_iter:
            with torch.enable_grad():
                trainer.zero_grad()
                l = loss(net(X), y)
            l.backward()
            trainer.step()
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1, (d2l.eval（net, train_iter, loss),
                                     d2l.eval（net, test_iter, loss)))
    print('w的L2范数：', net[0].weight.norm().item())

train_concise(0)

w的L2范数： 12.51321029663086

train_concise(5)

w的L2范数： 0.04912784695625305

Dropout

import torch 
from torch import nn
from d2l import torch as d2l

def dropout_layer(X, dropout):
    assert 0 <= dropout <= 1
    if dropout == 1:
        return torch.zeros_like(X)
    if dropout == 0:
        return X
    mask = (torch.randn(X.shape) > dropout).float()
    return mask * X / (1.0 - dropout)

测试​​dropout_layer​​函数

X = torch.arange(16, dtype=torch.float32).reshape((2,8))
print(X)
print(dropout_layer(X, 0.))
print(dropout_layer(X, 0.5))
print(dropout_layer(X, 1.))

tensor([[ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11., 12., 13., 14., 15.]])
tensor([[ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11., 12., 13., 14., 15.]])
tensor([[ 0.,  0.,  0.,  6.,  0.,  0.,  0., 14.],
        [ 0.,  0.,  0., 22.,  0.,  0., 28.,  0.]])
tensor([[0., 0., 0., 0., 0., 0., 0., 0.],
        [0., 0., 0., 0., 0., 0., 0., 0.]])

定义具有两个隐藏层的多层感知机，每个隐藏层包含256个单元

num_inputs, num_outputs, num_hiddens1, num_hiddens2 = 784, 10, 256, 256
dropout1, dropout2 = 0.2, 0.5

class Net(nn.Module):
    def __init__(self, num_inputs, num_outputs, num_hiddens1, num_hiddens2,
                 is_training=True):
        super(Net, self).__init__()

        self.num_inputs = num_inputs
        self.training = is_training

        self.lin1 = nn.Linear(num_inputs, num_hiddens1)
        self.lin2 = nn.Linear(num_hiddens1, num_hiddens2)
        self.lin3 = nn.Linear(num_hiddens2, num_outputs)

        self.relu = nn.ReLU()

    def forward(self, X):
        H1 = self.relu(self.lin1(X.reshape((-1, self.num_inputs))))
        # 只有在训练模型时才使用dropout
        if self.training == True:
            # 在第一个全连接层之后添加一个dropout层
            H1 = dropout_layer(H1, dropout1)
        H2 = self.relu(self.lin2(H1))
        if self.training == True:
            # 在第二个全连接层之后添加一个dropout层
            H2 = dropout_layer(H2, dropout2)
        out = self.lin3(H2)
        return out

net = Net(num_inputs, num_outputs, num_hiddens1, num_hiddens2)

训练和测试

num_epochs, lr, batch_size = 10, 0.5, 256
loss = nn.CrossEntropyLoss()
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
trainer = torch.optim.SGD(net.parameters(), lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

简洁实现

net = nn.Sequential(nn.Flatten(), nn.Linear(784, 256), nn.ReLU(),
                    # 在第一个全连接层之后添加一个dropout层
                    nn.Dropout(dropout1), nn.Linear(256, 256), nn.ReLU(),
                    # 在第二个全连接层之后添加一个dropout层
                    nn.Dropout(dropout2), nn.Linear(256, 10))

def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01)

net.apply(init_weights);

对模型进行训练和测试

trainer = torch.optim.SGD(net.parameters(), lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)