深度学习_多层感知机

%matplotlib inline
import torch
from d2l import torch as d2l

x = torch.arange(-8.0, 8.0, 0.1, requires_grad=True) 
y = torch.relu(x)
d2l.plot(x.detach(), y.detach(), 'x', 'relu(x)', figsize=(5, 2.5))

y.backward(torch.ones_like(x), retain_graph=True)
d2l.plot(x.detach(), x.grad, 'x', 'grad of relu', figsize=(5, 2.5))

y = torch.sigmoid(x)
d2l.plot(x.detach(), y.detach(), 'x', 'sigmoid(x)', figsize=(5, 2.5))

# 清除以前的梯度
x.grad.data.zero_()
y.backward(torch.ones_like(x),retain_graph=True)
d2l.plot(x.detach(), x.grad, 'x', 'grad of sigmoid', figsize=(5, 2.5))

y = torch.tanh(x)
d2l.plot(x.detach(), y.detach(), 'x', 'tanh(x)', figsize=(5, 2.5))

# 清除以前的梯度
x.grad.data.zero_()
y.backward(torch.ones_like(x),retain_graph=True)
d2l.plot(x.detach(), x.grad, 'x', 'grad of tanh', figsize=(5, 2.5))

多层感知机的从零开始实现

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

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

num_inputs, num_outputs, num_hiddens = 784, 10, 256
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))
W2 = nn.Parameter(torch.randn(
num_hiddens, num_outputs, requires_grad=True) * 0.01)

b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))
params = [W1, b1, W2, b2]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    return (H@W2 + b2)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.1
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

d2l.predict_ch3(net, test_iter)

在所有其他参数保持不变的情况下，更改超参数num_hiddens的值，并查看此超参数的变化对结果有 何影响。确定此超参数的最佳值。

num_inputs, num_outputs, num_hiddens128 = 784, 10, 128
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens128, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens128, requires_grad=True))
W2 = nn.Parameter(torch.randn(
num_hiddens128, num_outputs, requires_grad=True) * 0.01)

b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))
params = [W1, b1, W2, b2]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    return (H@W2 + b2)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.1
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

num_inputs, num_outputs, num_hiddens512 = 784, 10, 512
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens512, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens512, requires_grad=True))
W2 = nn.Parameter(torch.randn(
num_hiddens512, num_outputs, requires_grad=True) * 0.01)

b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))
params = [W1, b1, W2, b2]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    return (H@W2 + b2)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.1
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

尝试添加更多的隐藏层，并查看它对结果有何影响。

num_inputs, num_outputs, num_hiddens512, num_hiddens= 784, 10, 512, 256
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens512, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens512, requires_grad=True))

W2 = nn.Parameter(torch.randn(
num_hiddens512, num_hiddens, requires_grad=True) * 0.01)
b2 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))

W3 = nn.Parameter(torch.randn(
num_hiddens, num_outputs, requires_grad=True) * 0.01)
b3 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))


params = [W1, b1, W2, b2, W3, b3]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H1 = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    H2 = relu(H1@W2 + b2)
    return (H2@W3 + b3)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.1
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

改变学习速率会如何影响结果？保持模型架构和其他超参数（包括轮数）不变，学习率设置为多少会带 来最好的结果？

num_inputs, num_outputs, num_hiddens = 784, 10, 256
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))
W2 = nn.Parameter(torch.randn(
num_hiddens, num_outputs, requires_grad=True) * 0.01)

b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))
params = [W1, b1, W2, b2]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    return (H@W2 + b2)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.05
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

num_inputs, num_outputs, num_hiddens = 784, 10, 256
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))
W2 = nn.Parameter(torch.randn(
num_hiddens, num_outputs, requires_grad=True) * 0.01)

b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))
params = [W1, b1, W2, b2]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    return (H@W2 + b2)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.5
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

通过对所有超参数（学习率、轮数、隐藏层数、每层的隐藏单元数）进⾏联合优化，可以得到的最佳结 果是什么？

num_inputs, num_outputs, num_hiddens512, num_hiddens= 784, 10, 512, 256
W1 = nn.Parameter(torch.randn(
num_inputs, num_hiddens512, requires_grad=True) * 0.01)
b1 = nn.Parameter(torch.zeros(num_hiddens512, requires_grad=True))

W2 = nn.Parameter(torch.randn(
num_hiddens512, num_hiddens, requires_grad=True) * 0.01)
b2 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))

W3 = nn.Parameter(torch.randn(
num_hiddens, num_outputs, requires_grad=True) * 0.01)
b3 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))


params = [W1, b1, W2, b2, W3, b3]

def relu(X):
    a = torch.zeros_like(X)
    return torch.max(X, a)

def net(X):
    X = X.reshape((-1, num_inputs))
    H1 = relu(X@W1 + b1) # 这⾥“@”代表矩阵乘法
    H2 = relu(H1@W2 + b2)
    return (H2@W3 + b3)

loss = nn.CrossEntropyLoss(reduction='none')

num_epochs, lr = 10, 0.5
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

多层感知机的简洁实现

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

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.ReLU(),
                    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)

batch_size, lr, num_epochs = 256, 0.1, 10
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

尝试添加不同数量的隐藏层（也可以修改学习率），怎么样设置效果最好？

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 512),
                    nn.ReLU(),
                    nn.Linear(512,256),
                    nn.ReLU(),
                    nn.Linear(256,128),
                    nn.ReLU(),
                    nn.Linear(128, 10))
def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01)
net.apply(init_weights)

batch_size, lr, num_epochs = 256, 0.1, 10
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.Tanh(),
                    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)

batch_size, lr, num_epochs = 256, 0.1, 10
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.Sigmoid(),
                    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)

batch_size, lr, num_epochs = 256, 0.1, 10
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

尝试不同的⽅案来初始化权重，什么⽅法效果最好？

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.ReLU(),
                    nn.Linear(256, 10))
def init_weights(m):
    if type(m) == nn.Linear:
#         nn.init.normal_(m.weight, std=0.01)
          nn.init.zeros_(m.weight)
net.apply(init_weights)

batch_size, lr, num_epochs = 256, 0.1, 10
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.ReLU(),
                    nn.Linear(256, 10))
def init_weights(m):
    if type(m) == nn.Linear:
#         nn.init.normal_(m.weight, std=0.01)
#           nn.init.zeros_(m.weight)
            nn.init.ones_(m.weight)
    
net.apply(init_weights)

batch_size, lr, num_epochs = 256, 0.1, 10
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

模型选择、欠拟合和过拟合

import math
import numpy as np
import torch
from torch import nn
from d2l import torch as d2l

max_degree = 20 # 多项式的最⼤阶数
n_train, n_test = 100, 100 # 训练和测试数据集⼤⼩
true_w = np.zeros(max_degree) # 分配⼤量的空间
true_w[0:4] = np.array([5, 1.2, -3.4, 5.6])

features = np.random.normal(size=(n_train + n_test, 1))
np.random.shuffle(features)
poly_features = np.power(features, np.arange(max_degree).reshape(1, -1))
for i in range(max_degree):
    poly_features[:, i] /= math.gamma(i + 1) # gamma(n)=(n-1)!
# labels的维度:(n_train+n_test,)
labels = np.dot(poly_features, true_w)
labels += np.random.normal(scale=0.1, size=labels.shape)

# NumPy ndarray转换为tensor
true_w, features, poly_features, labels = [torch.tensor(x, dtype=
    torch.float32) for x in [true_w, features, poly_features, labels]]

features[:2], poly_features[:2, :], labels[:2]

def evaluate_loss(net, data_iter, loss): #@save
    """评估给定数据集上模型的损失"""
    metric = d2l.Accumulator(2) # 损失的总和,样本数量
    for X, y in data_iter:
        out = net(X)
        y = y.reshape(out.shape)
        l = loss(out, y)
        metric.add(l.sum(), l.numel())
    return metric[0] / metric[1]

def train(train_features, test_features, train_labels, test_labels,
            num_epochs=400):
    loss = nn.MSELoss(reduction='none')
    input_shape = train_features.shape[-1] # 不设置偏置，因为我们已经在多项式中实现了它
    net = nn.Sequential(nn.Linear(input_shape, 1, bias=False))
    batch_size = min(10, train_labels.shape[0])
    train_iter = d2l.load_array((train_features, train_labels.reshape(-1,1)),
                                    batch_size)
    test_iter = d2l.load_array((test_features, test_labels.reshape(-1,1)),
                                    batch_size, is_train=False)
    trainer = torch.optim.SGD(net.parameters(), lr=0.01)
    animator = d2l.Animator(xlabel='epoch', ylabel='loss', yscale='log',
                            xlim=[1, num_epochs], ylim=[1e-3, 1e2],
                            legend=['train', 'test'])
    for epoch in range(num_epochs):
        d2l.train_epoch_ch3(net, train_iter, loss, trainer)
        if epoch == 0 or (epoch + 1) % 20 == 0:
            animator.add(epoch + 1, (evaluate_loss(net, train_iter, loss),
                                    evaluate_loss(net, test_iter, loss)))
    print('weight:', net[0].weight.data.numpy())

# 从多项式特征中选择前4个维度，即1,x,x^2/2!,x^3/3!
train(poly_features[:n_train, :4], poly_features[n_train:, :4],
        labels[:n_train], labels[n_train:])

# 从多项式特征中选择前2个维度，即1和x
train(poly_features[:n_train, :2], poly_features[n_train:, :2],
        labels[:n_train], labels[n_train:])

# 从多项式特征中选取所有维度
train(poly_features[:n_train, :], poly_features[n_train:, :],
        labels[:n_train], labels[n_train:], num_epochs=1500)

权重衰减

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

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)

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]

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

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:
            # 增加了L2范数惩罚项，
            # ⼴播机制使l2_penalty(w)成为⼀个⻓度为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.evaluate_loss(net, train_iter, loss),
                                        d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数是：', torch.norm(w).item())

train(lambd=0)

train(lambd=3)

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(reduction='none')
    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:
            trainer.zero_grad()
            l = loss(net(X), y)
            l.mean().backward()
            trainer.step()
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1,
                            (d2l.evaluate_loss(net, train_iter, loss),
                            d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数：', net[0].weight.norm().item())

train_concise(0)

train_concise(3)

在本节的估计问题中使⽤λ的值进⾏实验。绘制训练和测试精度关于λ的函数。你观察到了什么？

def train_concise(wd):
    net = nn.Sequential(nn.Linear(num_inputs, 1))
    
    for param in net.parameters():
        for wd in range(0,20):
            param.data.normal_()
        loss = nn.MSELoss(reduction='none')
        num_epochs, lr = 20, 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_lamda = d2l.Animator(xlabel='lamdas', ylabel='loss', yscale='log',
                                xlim=[5, num_epochs], legend=['train', 'test'])
        for lamda in range(0,20):
            for X, y in train_iter:
                trainer.zero_grad()
                l = loss(net(X), y)
                l.mean().backward()
                trainer.step()
            if (lamda + 1) % 5 == 0:
                animator_lamda.add(lamda + 1,
                                (d2l.evaluate_loss(net, train_iter, loss),
                                d2l.evaluate_loss(net, test_iter, loss)))
        print('w的L2范数：', net[0].weight.norm().item())

    

train_concise(0)

如果我们使⽤∑i |wi|作为我们选择的惩罚（L1正则化），那么更新⽅程会是什么样⼦？

def train_conciseL1(wd):
    net = nn.Sequential(nn.Linear(num_inputs, 1))
    for param in net.parameters():
        param.data.normal_()
    loss = nn.L1Loss(reduction='none')
    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:
            trainer.zero_grad()
            l = loss(net(X), y)
            l.mean().backward()
            trainer.step()
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1,
                            (d2l.evaluate_loss(net, train_iter, loss),
                            d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L1范数：', net[0].weight.norm().item())

train_conciseL1(0)

4.6 暂退法（Dropout）

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

def dropout_layer(X, dropout):
    assert 0 <= dropout <= 1 # 在本情况中，所有元素都被丢弃
    if dropout == 1:
        return torch.zeros_like(X)
    # 在本情况中，所有元素都被保留
    if dropout == 0:
        return X
    mask = (torch.rand(X.shape) > dropout).float()
    return mask * X / (1.0 - dropout)

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.))

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)

num_epochs, lr, batch_size = 10, 0.5, 256
loss = nn.CrossEntropyLoss(reduction='none')
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)

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

如果更改第⼀层和第⼆层的暂退法概率，会发⽣什么情况？具体地说，如果交换这两个层，会发⽣什么 情况？设计⼀个实验来回答这些问题，定量描述你的结果，并总结定性的结论。

dropout1, dropout2 = 0.2, 0.5
dropoutX1, dropoutX2 = 0.4, 0.8

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(dropoutX1),
        nn.Linear(256, 256),
        nn.ReLU(),
        # 在第⼆个全连接层之后添加⼀个dropout层
        nn.Dropout(dropoutX2),
        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)
trainer = torch.optim.SGD(net.parameters(), lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

dropout1, dropout2 = 0.2, 0.5
dropoutX1, dropoutX2 = 0.4, 0.8

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(dropout2),
        nn.Linear(256, 256),
        nn.ReLU(),
        # 在第⼆个全连接层之后添加⼀个dropout层
        nn.Dropout(dropout1),
        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)
trainer = torch.optim.SGD(net.parameters(), lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

增加训练轮数，并将使⽤暂退法和不使⽤暂退法时获得的结果进⾏⽐较。

num_epochsX, lr, batch_size = 20, 0.5, 256
dropoutX3, dropoutX4 = 0, 0

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(dropoutX3),
        nn.Linear(256, 256),
        nn.ReLU(),
        # 在第⼆个全连接层之后添加⼀个dropout层
        nn.Dropout(dropoutX4),
        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)
trainer = torch.optim.SGD(net.parameters(), lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochsX, trainer)

李沐动手学深度学习 https://zh-v2.d2l.ai/chapter_introduction/index.html