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通过示例学习PyTorch

Created On: Mar 24, 2017 | Last Updated: Jan 21, 2025 | Last Verified: Nov 05, 2024

作者: Justin Johnson

备注

这是我们较早的PyTorch教程之一。您可以在`学习基础知识 <https://pytorch.org/tutorials/beginner/basics/intro.html>`_中查看最新的初学者内容。

本教程通过独立的示例介绍了`PyTorch <https://github.com/pytorch/pytorch>`__的基本概念。

PyTorch核心提供两大主要功能:

  • 一个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功能

我们将以拟合 \(y=\sin(x)\) 的三阶多项式问题作为实例。网络将有四个参数，并通过梯度下降训练以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。

备注

您可以在:ref:`本页末尾 <examples-download>`浏览各个示例。

张量

热身：numpy

在介绍PyTorch之前，我们将首先使用numpy来实现网络。

Numpy提供了一个n维数组对象，以及许多操作这些数组的函数。Numpy是一个通用的科学计算框架；它不涉及计算图、深度学习或梯度。但我们可以轻松使用numpy通过手动实现网络的前向和后向传播来拟合正弦函数的三阶多项式：

# -*- 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加速其数值计算。对于现代深度神经网络，GPU通常提供`50倍及以上的加速 <https://github.com/jcjohnson/cnn-benchmarks>`__，因此遗憾的是numpy不足以支持现代深度学习。

在这里，我们介绍PyTorch的最基本概念：张量（Tensor）。PyTorch张量在概念上与numpy数组完全相同：张量是一个n维数组，而PyTorch提供了许多操作这些张量的函数。在后台，张量可以跟踪计算图和梯度，但它们也是科学计算的通用工具。

与numpy不同的是，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，只需要指定正确的设备即可。

在这里我们使用PyTorch张量来拟合正弦函数的三阶多项式。与上述numpy示例类似，我们需要手动实现网络的前向和后向传播：

# -*- 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')

自动梯度

PyTorch：张量和自动梯度

在上述示例中，我们不得不手动实现我们神经网络的前向和后向传播。对于一个小型的两层网络来说，手动实现后向传播并不难，但对于大型复杂网络来说可能会变得非常棘手。

幸运的是，我们可以使用`自动微分 <https://en.wikipedia.org/wiki/Automatic_differentiation>`__来自动化计算神经网络中的后向传播。PyTorch中的**autograd**包正是提供了这种功能。当使用autograd时，网络的前向传播将定义一个**计算图**；图中的节点是张量，边是从输入张量生成输出张量的函数。通过这个图进行反向传播可以轻松计算梯度。

这听起来很复杂，但实际上使用起来非常简单。每个张量代表计算图中的一个节点。如果``x``是一个张量，且``x.requires_grad=True``，那么``x.grad``是另一个包含``x``相对于某个标量值的梯度的张量。

在这里我们使用PyTorch张量和autograd来实现我们拟合正弦波的三阶多项式示例；现在我们不再需要手动实现网络的后向传播：

import torch
import math

# We want to be able to train our model on an `accelerator <https://pytorch.org/docs/stable/torch.html#accelerators>`__
# such as CUDA, MPS, MTIA, or XPU. If the current accelerator is available, we will use it. Otherwise, we use the CPU.

dtype = torch.float
device = torch.accelerator.current_accelerator().type if torch.accelerator.is_available() else "cpu"
print(f"Using {device} device")
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autograd函数

在底层，每个原始的autograd操作符实际上有两个处理张量的函数。**前向传播**函数从输入张量计算输出张量。**后向传播**函数接收输出张量相对于某个标量值的梯度，并计算输入张量相对于同一标量值的梯度。

在PyTorch中，我们可以通过定义``torch.autograd.Function``的子类并实现``forward``和``backward``函数来轻松定义自己的autograd操作符。然后我们可以通过创建实例并将输入数据的张量传递给它，如同调用函数一样来使用新的autograd操作符。

在此示例中，我们将模型定义为 \(y=a+b P_3(c+dx)\) 而不是 \(y=a+bx+cx^2+dx^3\)，其中 \(P_3(x)=\frac{1}{2}\left(5x^3-3x\right)\) 是三阶`勒让德多项式`_。我们编写自己的自定义autograd函数来计算 \(P_3\) 的前向和后向传播，并使用它来实现我们的模型：

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 tensors for
        use in the backward pass using the ``ctx.save_for_backward`` method. Other
        objects can be stored directly as attributes on the ctx object, such as
        ``ctx.my_object = my_object``. Check out `Extending torch.autograd <https://docs.pytorch.org/docs/stable/notes/extending.html#extending-torch-autograd>`_
        for further details.
        """
        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是定义复杂操作并自动生成导数的非常强大的范式；然而对于大型神经网络，原始的autograd可能有点过于低级。

在构建神经网络时，我们通常将计算组织为带有一些**可学习参数**的**层**，这些参数将在学习期间进行优化。

在TensorFlow中，像`Keras <https://github.com/fchollet/keras>`__，TensorFlow-Slim，以及`TFLearn <http://tflearn.org/>`__等软件包提供了在原始计算图上的较高级抽象，非常适用于构建神经网络。

在PyTorch中，``nn``包也具有相同的用途。``nn``包定义了一组**模块**，它们大致相当于神经网络层。一个模块接收输入张量并计算输出张量，但也可能包含内部状态，例如包含可学习参数的张量。``nn``包还定义了一组有用的损失函数，这些函数在训练神经网络时常用。

在这个示例中，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：优化器

到目前为止，我们通过使用``torch.no_grad()``手动修改包含可学习参数的张量来更新我们的模型的权重。这对于像随机梯度下降这样的简单优化算法来说并不麻烦，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，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。

在这个示例中，我们将像以前一样使用``nn``包定义我们的模型，但我们将使用``optim``包提供的``RMSprop``算法来优化该模型：

# -*- 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

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

在这个示例中，我们将我们的三阶多项式实现为一个自定义模块子类：

# -*- 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：一个三到五阶多项式，它在每次前向传播时选择一个随机数（范围从3到5），并使用那么多阶数，重复使用相同的权重多次来计算第四和第五阶。

对于这个模型，我们可以使用普通的Python流程控制来实现循环，并通过简单地在定义前向传播时多次使用相同的参数来实现权重共享。

我们可以轻松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()}')

示例

您可以在这里浏览上述示例。

``nn``模块

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