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使用示例学习 PyTorch

作者: Justin Johnson

注意

这是我们较旧的 PyTorch 教程之一。您可以在 学习基础知识 中查看我们最新的初学者内容。

本教程通过自包含的示例介绍了 PyTorch 的基本概念。

PyTorch 的核心提供了两个主要功能

  • n 维张量，类似于 numpy，但可以在 GPU 上运行

  • 用于构建和训练神经网络的自动微分

我们将使用用三阶多项式拟合 \(y=\sin(x)\) 的问题作为我们的运行示例。该网络将有四个参数，并将使用梯度下降进行训练，以通过最小化网络输出与真实输出之间的欧几里得距离来拟合随机数据。

注意

您可以在 此页面末尾 浏览各个示例。

张量

热身：numpy

在介绍 PyTorch 之前，我们首先将使用 numpy 实现网络。

Numpy 提供了一个 n 维数组对象，以及许多用于操作这些数组的函数。Numpy 是一个通用的科学计算框架；它对计算图、深度学习或梯度一无所知。但是，我们可以很容易地使用 numpy 将三阶多项式拟合到正弦函数，方法是手动使用 numpy 操作实现网络的前向和反向传递

# -*- coding: utf-8 -*-
import numpy as np
import math

# Create random input and output data
x = np.linspace(-math.pi, math.pi, 2000)
y = np.sin(x)

# Randomly initialize weights
a = np.random.randn()
b = np.random.randn()
c = np.random.randn()
d = np.random.randn()

learning_rate = 1e-6
for t in range(2000):
    # Forward pass: compute predicted y
    # y = a + b x + c x^2 + d x^3
    y_pred = a + b * x + c * x ** 2 + d * x ** 3

    # Compute and print loss
    loss = np.square(y_pred - y).sum()
    if t % 100 == 99:
        print(t, loss)

    # Backprop to compute gradients of a, b, c, d with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_a = grad_y_pred.sum()
    grad_b = (grad_y_pred * x).sum()
    grad_c = (grad_y_pred * x ** 2).sum()
    grad_d = (grad_y_pred * x ** 3).sum()

    # Update weights
    a -= learning_rate * grad_a
    b -= learning_rate * grad_b
    c -= learning_rate * grad_c
    d -= learning_rate * grad_d

print(f'Result: y = {a} + {b} x + {c} x^2 + {d} x^3')

PyTorch：张量

NumPy 是一个很棒的框架，但它无法利用 GPU 来加速其数值计算。对于现代深度神经网络，GPU 通常可以提供50 倍或更高的加速，因此不幸的是，NumPy 不足以满足现代深度学习的需求。

在这里，我们介绍 PyTorch 最基本的概念：**张量 (Tensor)**。PyTorch 张量在概念上与 NumPy 数组相同：张量是一个 n 维数组，PyTorch 提供了许多用于操作这些张量的函数。在幕后，张量可以跟踪计算图和梯度，但它们也可用作科学计算的通用工具。

此外，与 NumPy 不同，PyTorch 张量可以利用 GPU 来加速其数值计算。要在 GPU 上运行 PyTorch 张量，您只需要指定正确的设备即可。

在这里，我们使用 PyTorch 张量将三次多项式拟合到正弦函数。与上面的 NumPy 示例一样，我们需要手动实现网络的前向和反向传递。

# -*- coding: utf-8 -*-

import torch
import math


dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# Create random input and output data
x = torch.linspace(-math.pi, math.pi, 2000, device=device, dtype=dtype)
y = torch.sin(x)

# Randomly initialize weights
a = torch.randn((), device=device, dtype=dtype)
b = torch.randn((), device=device, dtype=dtype)
c = torch.randn((), device=device, dtype=dtype)
d = torch.randn((), device=device, dtype=dtype)

learning_rate = 1e-6
for t in range(2000):
    # Forward pass: compute predicted y
    y_pred = a + b * x + c * x ** 2 + d * x ** 3

    # Compute and print loss
    loss = (y_pred - y).pow(2).sum().item()
    if t % 100 == 99:
        print(t, loss)

    # Backprop to compute gradients of a, b, c, d with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_a = grad_y_pred.sum()
    grad_b = (grad_y_pred * x).sum()
    grad_c = (grad_y_pred * x ** 2).sum()
    grad_d = (grad_y_pred * x ** 3).sum()

    # Update weights using gradient descent
    a -= learning_rate * grad_a
    b -= learning_rate * grad_b
    c -= learning_rate * grad_c
    d -= learning_rate * grad_d


print(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')

自动微分 (Autograd)

PyTorch：张量和自动微分

在上面的示例中，我们必须手动实现神经网络的前向和反向传递。对于小型两层网络，手动实现反向传递并不是什么大问题，但对于大型复杂网络，它很快就会变得非常复杂。

值得庆幸的是，我们可以使用自动微分来自动化神经网络中反向传递的计算。PyTorch 中的 **autograd** 包提供了完全相同的功能。当使用 autograd 时，网络的前向传递将定义一个 **计算图**；图中的节点将是张量，边将是根据输入张量生成输出张量的函数。然后，通过此图反向传播允许您轻松计算梯度。

这听起来很复杂，但在实践中却非常简单。每个张量都表示计算图中的一个节点。如果 x 是一个具有 x.requires_grad=True 的张量，那么 x.grad 是另一个张量，它保存关于某个标量值的 x 的梯度。

在这里，我们使用 PyTorch 张量和 autograd 来实现我们用三次多项式拟合正弦波的示例；现在我们不再需要手动实现网络的反向传递。

# -*- coding: utf-8 -*-
import torch
import math

dtype = torch.float
device = "cuda" if torch.cuda.is_available() else "cpu"
torch.set_default_device(device)

# Create Tensors to hold input and outputs.
# By default, requires_grad=False, which indicates that we do not need to
# compute gradients with respect to these Tensors during the backward pass.
x = torch.linspace(-math.pi, math.pi, 2000, dtype=dtype)
y = torch.sin(x)

# Create random Tensors for weights. For a third order polynomial, we need
# 4 weights: y = a + b x + c x^2 + d x^3
# Setting requires_grad=True indicates that we want to compute gradients with
# respect to these Tensors during the backward pass.
a = torch.randn((), dtype=dtype, requires_grad=True)
b = torch.randn((), dtype=dtype, requires_grad=True)
c = torch.randn((), dtype=dtype, requires_grad=True)
d = torch.randn((), dtype=dtype, requires_grad=True)

learning_rate = 1e-6
for t in range(2000):
    # Forward pass: compute predicted y using operations on Tensors.
    y_pred = a + b * x + c * x ** 2 + d * x ** 3

    # Compute and print loss using operations on Tensors.
    # Now loss is a Tensor of shape (1,)
    # loss.item() gets the scalar value held in the loss.
    loss = (y_pred - y).pow(2).sum()
    if t % 100 == 99:
        print(t, loss.item())

    # Use autograd to compute the backward pass. This call will compute the
    # gradient of loss with respect to all Tensors with requires_grad=True.
    # After this call a.grad, b.grad. c.grad and d.grad will be Tensors holding
    # the gradient of the loss with respect to a, b, c, d respectively.
    loss.backward()

    # Manually update weights using gradient descent. Wrap in torch.no_grad()
    # because weights have requires_grad=True, but we don't need to track this
    # in autograd.
    with torch.no_grad():
        a -= learning_rate * a.grad
        b -= learning_rate * b.grad
        c -= learning_rate * c.grad
        d -= learning_rate * d.grad

        # Manually zero the gradients after updating weights
        a.grad = None
        b.grad = None
        c.grad = None
        d.grad = None

print(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')

PyTorch：定义新的自动微分函数

在幕后，每个原始的 autograd 运算符实际上是两个作用于张量的函数。**前向 (forward)** 函数根据输入张量计算输出张量。**反向 (backward)** 函数接收输出张量关于某个标量值的梯度，并计算输入张量关于该相同标量值的梯度。

在 PyTorch 中，我们可以通过定义 torch.autograd.Function 的子类并实现 forward 和 backward 函数来轻松定义我们自己的 autograd 运算符。然后，我们可以通过构造一个实例并像调用函数一样调用它来使用我们新的 autograd 运算符，并将包含输入数据的张量作为参数传递。

在这个例子中，我们将我们的模型定义为 \(y=a+b P_3(c+dx)\) 而不是 \(y=a+bx+cx^2+dx^3\)，其中 \(P_3(x)=\frac{1}{2}\left(5x^3-3x\right)\) 是勒让德多项式的三次项。我们编写了自己的自定义 autograd 函数来计算 \(P_3\) 的前向和反向，并使用它来实现我们的模型。

# -*- coding: utf-8 -*-
import torch
import math


class LegendrePolynomial3(torch.autograd.Function):
    """
    We can implement our own custom autograd Functions by subclassing
    torch.autograd.Function and implementing the forward and backward passes
    which operate on Tensors.
    """

    @staticmethod
    def forward(ctx, input):
        """
        In the forward pass we receive a Tensor containing the input and return
        a Tensor containing the output. ctx is a context object that can be used
        to stash information for backward computation. You can cache arbitrary
        objects for use in the backward pass using the ctx.save_for_backward method.
        """
        ctx.save_for_backward(input)
        return 0.5 * (5 * input ** 3 - 3 * input)

    @staticmethod
    def backward(ctx, grad_output):
        """
        In the backward pass we receive a Tensor containing the gradient of the loss
        with respect to the output, and we need to compute the gradient of the loss
        with respect to the input.
        """
        input, = ctx.saved_tensors
        return grad_output * 1.5 * (5 * input ** 2 - 1)


dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0")  # Uncomment this to run on GPU

# Create Tensors to hold input and outputs.
# By default, requires_grad=False, which indicates that we do not need to
# compute gradients with respect to these Tensors during the backward pass.
x = torch.linspace(-math.pi, math.pi, 2000, device=device, dtype=dtype)
y = torch.sin(x)

# Create random Tensors for weights. For this example, we need
# 4 weights: y = a + b * P3(c + d * x), these weights need to be initialized
# not too far from the correct result to ensure convergence.
# Setting requires_grad=True indicates that we want to compute gradients with
# respect to these Tensors during the backward pass.
a = torch.full((), 0.0, device=device, dtype=dtype, requires_grad=True)
b = torch.full((), -1.0, device=device, dtype=dtype, requires_grad=True)
c = torch.full((), 0.0, device=device, dtype=dtype, requires_grad=True)
d = torch.full((), 0.3, device=device, dtype=dtype, requires_grad=True)

learning_rate = 5e-6
for t in range(2000):
    # To apply our Function, we use Function.apply method. We alias this as 'P3'.
    P3 = LegendrePolynomial3.apply

    # Forward pass: compute predicted y using operations; we compute
    # P3 using our custom autograd operation.
    y_pred = a + b * P3(c + d * x)

    # Compute and print loss
    loss = (y_pred - y).pow(2).sum()
    if t % 100 == 99:
        print(t, loss.item())

    # Use autograd to compute the backward pass.
    loss.backward()

    # Update weights using gradient descent
    with torch.no_grad():
        a -= learning_rate * a.grad
        b -= learning_rate * b.grad
        c -= learning_rate * c.grad
        d -= learning_rate * d.grad

        # Manually zero the gradients after updating weights
        a.grad = None
        b.grad = None
        c.grad = None
        d.grad = None

print(f'Result: y = {a.item()} + {b.item()} * P3({c.item()} + {d.item()} x)')

nn 模块

PyTorch：nn

计算图和 autograd 是定义复杂运算符并自动求导的非常强大的范式；但是，对于大型神经网络来说，原始的 autograd 有点过于底层了。

在构建神经网络时，我们经常考虑将计算安排成**层**，其中一些层具有**可学习的参数**，这些参数将在学习过程中进行优化。

在 TensorFlow 中，像Keras、TensorFlow-Slim 和TFLearn 这样的包提供了对原始计算图的更高级别的抽象，这些抽象对于构建神经网络很有用。

在 PyTorch 中，nn 包也起到了同样的作用。nn 包定义了一组**模块 (Module)**，它们大致相当于神经网络层。模块接收输入张量并计算输出张量，但也可以保存内部状态，例如包含可学习参数的张量。nn 包还定义了一组在训练神经网络时常用的有用损失函数。

在这个例子中，我们使用 nn 包来实现我们的多项式模型网络。

# -*- coding: utf-8 -*-
import torch
import math


# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)

# For this example, the output y is a linear function of (x, x^2, x^3), so
# we can consider it as a linear layer neural network. Let's prepare the
# tensor (x, x^2, x^3).
p = torch.tensor([1, 2, 3])
xx = x.unsqueeze(-1).pow(p)

# In the above code, x.unsqueeze(-1) has shape (2000, 1), and p has shape
# (3,), for this case, broadcasting semantics will apply to obtain a tensor
# of shape (2000, 3) 

# Use the nn package to define our model as a sequence of layers. nn.Sequential
# is a Module which contains other Modules, and applies them in sequence to
# produce its output. The Linear Module computes output from input using a
# linear function, and holds internal Tensors for its weight and bias.
# The Flatten layer flatens the output of the linear layer to a 1D tensor,
# to match the shape of `y`.
model = torch.nn.Sequential(
    torch.nn.Linear(3, 1),
    torch.nn.Flatten(0, 1)
)

# The nn package also contains definitions of popular loss functions; in this
# case we will use Mean Squared Error (MSE) as our loss function.
loss_fn = torch.nn.MSELoss(reduction='sum')

learning_rate = 1e-6
for t in range(2000):

    # Forward pass: compute predicted y by passing x to the model. Module objects
    # override the __call__ operator so you can call them like functions. When
    # doing so you pass a Tensor of input data to the Module and it produces
    # a Tensor of output data.
    y_pred = model(xx)

    # Compute and print loss. We pass Tensors containing the predicted and true
    # values of y, and the loss function returns a Tensor containing the
    # loss.
    loss = loss_fn(y_pred, y)
    if t % 100 == 99:
        print(t, loss.item())

    # Zero the gradients before running the backward pass.
    model.zero_grad()

    # Backward pass: compute gradient of the loss with respect to all the learnable
    # parameters of the model. Internally, the parameters of each Module are stored
    # in Tensors with requires_grad=True, so this call will compute gradients for
    # all learnable parameters in the model.
    loss.backward()

    # Update the weights using gradient descent. Each parameter is a Tensor, so
    # we can access its gradients like we did before.
    with torch.no_grad():
        for param in model.parameters():
            param -= learning_rate * param.grad

# You can access the first layer of `model` like accessing the first item of a list
linear_layer = model[0]

# For linear layer, its parameters are stored as `weight` and `bias`.
print(f'Result: y = {linear_layer.bias.item()} + {linear_layer.weight[:, 0].item()} x + {linear_layer.weight[:, 1].item()} x^2 + {linear_layer.weight[:, 2].item()} x^3')

PyTorch：optim

到目前为止，我们通过使用 torch.no_grad() 手动修改保存可学习参数的张量来更新模型的权重。对于像随机梯度下降这样的简单优化算法来说，这并不是一个很大的负担，但在实践中，我们通常使用更复杂的优化器来训练神经网络，例如 AdaGrad、RMSProp、Adam 等。

PyTorch 中的 optim 包抽象了优化算法的概念，并提供了常用优化算法的实现。

在这个例子中，我们将像以前一样使用 nn 包来定义我们的模型，但我们将使用 optim 包提供的 RMSprop 算法来优化模型。

# -*- coding: utf-8 -*-
import torch
import math


# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)

# Prepare the input tensor (x, x^2, x^3).
p = torch.tensor([1, 2, 3])
xx = x.unsqueeze(-1).pow(p)

# Use the nn package to define our model and loss function.
model = torch.nn.Sequential(
    torch.nn.Linear(3, 1),
    torch.nn.Flatten(0, 1)
)
loss_fn = torch.nn.MSELoss(reduction='sum')

# Use the optim package to define an Optimizer that will update the weights of
# the model for us. Here we will use RMSprop; the optim package contains many other
# optimization algorithms. The first argument to the RMSprop constructor tells the
# optimizer which Tensors it should update.
learning_rate = 1e-3
optimizer = torch.optim.RMSprop(model.parameters(), lr=learning_rate)
for t in range(2000):
    # Forward pass: compute predicted y by passing x to the model.
    y_pred = model(xx)

    # Compute and print loss.
    loss = loss_fn(y_pred, y)
    if t % 100 == 99:
        print(t, loss.item())

    # Before the backward pass, use the optimizer object to zero all of the
    # gradients for the variables it will update (which are the learnable
    # weights of the model). This is because by default, gradients are
    # accumulated in buffers( i.e, not overwritten) whenever .backward()
    # is called. Checkout docs of torch.autograd.backward for more details.
    optimizer.zero_grad()

    # Backward pass: compute gradient of the loss with respect to model
    # parameters
    loss.backward()

    # Calling the step function on an Optimizer makes an update to its
    # parameters
    optimizer.step()


linear_layer = model[0]
print(f'Result: y = {linear_layer.bias.item()} + {linear_layer.weight[:, 0].item()} x + {linear_layer.weight[:, 1].item()} x^2 + {linear_layer.weight[:, 2].item()} x^3')

PyTorch：自定义 nn 模块

有时您可能希望指定比现有模块序列更复杂的模型；对于这些情况，您可以通过子类化 nn.Module 并定义一个 forward 来定义自己的模块，该 forward 接收输入张量并使用其他模块或张量上的其他 autograd 操作生成输出张量。

在这个例子中，我们将三次多项式实现为自定义模块子类。

# -*- coding: utf-8 -*-
import torch
import math


class Polynomial3(torch.nn.Module):
    def __init__(self):
        """
        In the constructor we instantiate four parameters and assign them as
        member parameters.
        """
        super().__init__()
        self.a = torch.nn.Parameter(torch.randn(()))
        self.b = torch.nn.Parameter(torch.randn(()))
        self.c = torch.nn.Parameter(torch.randn(()))
        self.d = torch.nn.Parameter(torch.randn(()))

    def forward(self, x):
        """
        In the forward function we accept a Tensor of input data and we must return
        a Tensor of output data. We can use Modules defined in the constructor as
        well as arbitrary operators on Tensors.
        """
        return self.a + self.b * x + self.c * x ** 2 + self.d * x ** 3

    def string(self):
        """
        Just like any class in Python, you can also define custom method on PyTorch modules
        """
        return f'y = {self.a.item()} + {self.b.item()} x + {self.c.item()} x^2 + {self.d.item()} x^3'


# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)

# Construct our model by instantiating the class defined above
model = Polynomial3()

# Construct our loss function and an Optimizer. The call to model.parameters()
# in the SGD constructor will contain the learnable parameters (defined 
# with torch.nn.Parameter) which are members of the model.
criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.SGD(model.parameters(), lr=1e-6)
for t in range(2000):
    # Forward pass: Compute predicted y by passing x to the model
    y_pred = model(x)

    # Compute and print loss
    loss = criterion(y_pred, y)
    if t % 100 == 99:
        print(t, loss.item())

    # Zero gradients, perform a backward pass, and update the weights.
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

print(f'Result: {model.string()}')

PyTorch：控制流 + 权重共享

作为动态图和权重共享的示例，我们实现了一个非常奇怪的模型：一个三到五次的多项式，在每次前向传递时，它会在 3 到 5 之间选择一个随机数，并使用该次数的多项式，多次重复使用相同的权重来计算四次和五次项。

对于此模型，我们可以使用普通的 Python 流控制来实现循环，并且可以通过在定义前向传递时简单地重复使用相同的参数来实现权重共享。

我们可以轻松地将此模型实现为模块子类。

# -*- coding: utf-8 -*-
import random
import torch
import math


class DynamicNet(torch.nn.Module):
    def __init__(self):
        """
        In the constructor we instantiate five parameters and assign them as members.
        """
        super().__init__()
        self.a = torch.nn.Parameter(torch.randn(()))
        self.b = torch.nn.Parameter(torch.randn(()))
        self.c = torch.nn.Parameter(torch.randn(()))
        self.d = torch.nn.Parameter(torch.randn(()))
        self.e = torch.nn.Parameter(torch.randn(()))

    def forward(self, x):
        """
        For the forward pass of the model, we randomly choose either 4, 5
        and reuse the e parameter to compute the contribution of these orders.

        Since each forward pass builds a dynamic computation graph, we can use normal
        Python control-flow operators like loops or conditional statements when
        defining the forward pass of the model.

        Here we also see that it is perfectly safe to reuse the same parameter many
        times when defining a computational graph.
        """
        y = self.a + self.b * x + self.c * x ** 2 + self.d * x ** 3
        for exp in range(4, random.randint(4, 6)):
            y = y + self.e * x ** exp
        return y

    def string(self):
        """
        Just like any class in Python, you can also define custom method on PyTorch modules
        """
        return f'y = {self.a.item()} + {self.b.item()} x + {self.c.item()} x^2 + {self.d.item()} x^3 + {self.e.item()} x^4 ? + {self.e.item()} x^5 ?'


# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)

# Construct our model by instantiating the class defined above
model = DynamicNet()

# Construct our loss function and an Optimizer. Training this strange model with
# vanilla stochastic gradient descent is tough, so we use momentum
criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.SGD(model.parameters(), lr=1e-8, momentum=0.9)
for t in range(30000):
    # Forward pass: Compute predicted y by passing x to the model
    y_pred = model(x)

    # Compute and print loss
    loss = criterion(y_pred, y)
    if t % 2000 == 1999:
        print(t, loss.item())

    # Zero gradients, perform a backward pass, and update the weights.
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

print(f'Result: {model.string()}')

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