使用 python3.11 与 pycharm 进行实验
未包含实战Kaggle比赛

pycharm画图请自行引入，下文不再赘述
—头文件 from matplotlib import pyplot as plt
—main函数尾 plt.show()

新版d2l包函数缺失，可以自行网络搜索导入或选用旧版包，图省事可以到”深度学习-代码-1-线性神经网络”把直接粘贴代码过来用

如果提示缺包就按提示直接引入即可，都是前面用过的不需下载
所有代码都已测试过可以正常在pycharm中显示图像与数据

多层感知机(MLP, Multi-Layer Perceptron)

隐藏层

线性意味着单调假设： 任何特征的线性变化都会导致模型输出对应的线性变化，难以通过简单的预处理来解决个问题。
可以通过在网络中加入一个或多个隐藏层来克服线性模型的限制， 使其能处理更普遍的函数关系类型。

如果隐藏层只做仿射变换，且没有任何非线性激活函数，模型的表现并不会比简单的线性模型好。因为仿射函数的组合本质上还是一个仿射函数，多个仿射函数相叠加依然是仿射函数。因此，如果模型只用仿射函数，实际上不会增加模型的表达能力，效果和简单的线性模型没有区别。

隐藏层的作用在于添加非线性激活函数。只有在每个层使用非线性激活函数(如 ReLU、Sigmoid 等)后，神经网络才能变得更复杂，能够表示复杂的映射关系。否则，即使有多层，神经网络也只能表示线性变换。

通用近似定理

一个含有至少一个隐藏层的前馈神经网络(如 MLP)，只要有足够多的神经元和适当的激活函数(如 Sigmoid 或 ReLU)，它就能够近似任意连续的函数。

激活函数

头文件

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import torch
from d2l import torch as d2l

ReLU函数图像

$$
\text{ReLU}(x) = \max(0, x)
$$

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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))
# detach() 的作用是将一个张量从计算图中分离出来，避免不必要的梯度计算，不分也可以

ReLU函数导数图像

分段线性也是非线性。
当输入为负时，ReLU函数的导数为0，而当输入为正时，ReLU函数的导数为1。使用ReLU的原因是，它求导表现得特别好：要么让参数消失，要么让参数通过。 这使得优化表现得更好，并且ReLU减轻了困扰以往神经网络的梯度消失问题。

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

sigmoid函数图像

$$
\text{sigmoid}(x) = \frac{1}{1 + e^{-x}}
$$

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

sigmoid函数导数图像

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# 默认情况下，PyTorch 会累积梯度，需要清除以前的梯度
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))

tanh函数

$$
\tanh(x) = \frac{1 - e^{-2x}}{1 + e^{-2x}}
$$

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

tanh函数导数图像

.

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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

需旧d2l包，rgba(255
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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)  
    return (H@W2 + b2)

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

def main():
    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)
    
if __name__ == '__main__':
    main()

图像分类数据集

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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)

初始化模型参数 (待修)

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num_inputs, num_outputs, num_hiddens = 784, 10, 256

# Parameter 是 PyTorch 中的一个特殊类，继承张量，专门用于存储需要训练的参数
# 从存储结构和计算属性上，Parameter 其实就是普通张量，只是多了被自动注册到模型参数中的“标签”
W1 = nn.Parameter(torch.randn(
    num_inputs, num_hiddens, requires_grad=True) * 0.01)
    # 乘以0.01 是一种手工调整的权重初始化的方法
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]

激活函数

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

模型

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def net(X):
    # 一次传入多个1xnum_inputs向量
    X = X.reshape((-1, num_inputs))
    H = relu(X@W1 + b1)  
    return (H@W2 + b2)

损失函数

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

训练

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num_epochs, lr = 10, 0.1  # 训练次数和学习率
updater = torch.optim.SGD(params, lr=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)
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d2l.predict_ch3(net, test_iter)  # 评估

多层感知机的简洁实现

需旧d2l包
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import matplotlib.pyplot as plt
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)

def main():
    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)
    plt.show()

if __name__ == '__main__':
    main()

模型

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# nn.Sequential 是 PyTorch 中用于按顺序串联多个层的容器，输入数据会依次通过每个层
# Flatten 是展平层，把多维输入张量展平成二维张量，方便全连接层处理
net = nn.Sequential(nn.Flatten(),
                    nn.Linear(784, 256),
                    nn.ReLU(),
                    nn.Linear(256, 10))

# 原地正态分布随机填充权重参数
def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01)
        # nn.init是torch.nn.init包

# 完整的神经网络模型
net.apply(init_weights)
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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

完整代码
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import math
import matplotlib.pyplot as plt
import numpy as np
import torch
from torch import nn
from d2l import torch as d2l

def evaluate_loss(net, data_iter, loss):  
    metric = d2l.Accumulator(2) 
    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_epoch_ch3(net, train_iter, loss, trainer):
    for X, y in train_iter:
        out = net(X)
        y = y.reshape(out.shape)
        l = loss(out, y)  
        trainer.zero_grad()
        l.mean().backward() 
        trainer.step()

def train(train_features, test_features, train_labels, test_labels,
          num_epochs=400):
    loss = nn.MSELoss(reduction='none')
    input_shape = train_features.shape[-1]
    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):
        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())

def main():
    max_degree = 20  
    n_train, n_test = 100, 100  
    true_w = np.zeros(max_degree)  
    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) 打乱了 features，并没有重新生成后续两个变量，导致特征与标签不再一一对应。也就是 X 和 y 错位了!!!d2l外的地方不能加上这个

    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) 
    labels = np.dot(poly_features, true_w)
    labels += np.random.normal(scale=0.1, size=labels.shape)

    true_w, features, poly_features, labels = [torch.tensor(x, dtype=
    torch.float32) for x in [true_w, features, poly_features, labels]]
    print(features[:2], poly_features[:2, :], labels[:2])


    #三选一，顺序对应正常、欠拟合、过拟合，

    # train(poly_features[:n_train, :4], poly_features[n_train:, :4],
    #       labels[:n_train], labels[n_train:])
    # train(poly_features[:n_train, :2], poly_features[n_train:, :2],
    #       labels[:n_train], labels[n_train:])
    train(poly_features[:n_train, :], poly_features[n_train:, :],
          labels[:n_train], labels[n_train:], num_epochs=1500)
    plt.show()

if __name__ == '__main__':
    main()

头文件

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

生成数据集

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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)
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# 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]

对模型进行训练和测试

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def evaluate_loss(net, data_iter, loss): 
    """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]
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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())

三阶多项式函数拟合(正常)

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# 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:])

线性函数拟合(欠拟合)

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# 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:])

高阶多项式函数拟合(过拟合)

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# 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

完整代码
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import torch
from matplotlib import pyplot as plt
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:
            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())


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
    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())

def main():
    train_concise(3)
    plt.show()

if __name__ == '__main__':
    main()

高维线性回归

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

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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L2范数惩罚

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

定义训练代码实现

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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.evaluate_loss(net, train_iter, loss),
                                     d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数是：', torch.norm(w).item())

忽略正则化直接训练

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train(lambd=0)

使用权重衰减

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train(lambd=3)

简洁实现

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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())
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train_concise(0)
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train_concise(3)

暂退法

需旧d2l包
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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)

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)

def main():
    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_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)

if __name__ == '__main__':
    main()
简洁实现版-需旧d2l包-未实际测试
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import torch
from torch import nn
from d2l import torch as d2l

dropout1, dropout2 = 0.2, 0.5

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)

def main():
    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)

if __name__ == '__main__':
    main()

从零开始实现

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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)
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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.))

定义模型参数

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num_inputs, num_outputs, num_hiddens1, num_hiddens2 = 784, 10, 256, 256

定义模型

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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

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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)

简洁实现

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

数值稳定性和模型初始化

梯度消失

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import torch
from d2l import torch as d2l
from matplotlib import pyplot as plt

x = torch.arange(-8.0, 8.0, 0.1, requires_grad=True)
y = torch.sigmoid(x)
y.backward(torch.ones_like(x))

def main():
    d2l.plot(x.detach().numpy(), [y.detach().numpy(), x.grad.numpy()],
             legend=['sigmoid', 'gradient'], figsize=(4.5, 2.5))
    plt.show()

if __name__ == '__main__':
    main()

梯度爆炸

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M = torch.normal(0, 1, size=(4,4))
print('一个矩阵 \n',M)
for i in range(100):
    M = torch.mm(M,torch.normal(0, 1, size=(4, 4)))
print('乘以100个矩阵后\n', M)