使用示例学习 PyTorch
创建于：2025 年 4 月 1 日 | 最后更新：2025 年 4 月 1 日 | 最后验证：2024 年 11 月 5 日
作者：Justin Johnson
备注
这是我们的旧教程之一。您可以在“学习基础知识”中查看我们最新的入门内容。
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
自动微分，用于构建和训练神经网络
我们将以拟合 \(y=\sin(x)\) 的三次多项式作为我们的运行示例。该网络将有四个参数，将通过梯度下降训练以拟合随机数据，通过最小化网络输出与真实输出之间的欧几里得距离来进行。
备注
您可以在本页末尾浏览个别示例。
目录
张量
热身：numpy ¶
在介绍 PyTorch 之前，我们首先将使用 numpy 实现网络。
Numpy 提供了一个多维数组对象，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；它不知道任何关于计算图、深度学习或梯度的内容。然而，我们可以通过手动使用 numpy 操作实现网络的前向和反向传递，轻松地将三阶多项式拟合到正弦函数：
# -*- 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 是一个非常棒的框架，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，所以不幸的是，numpy 对于现代深度学习来说是不够的。
在这里，我们介绍最基础的 PyTorch 概念：张量。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，但它们也作为科学计算的一般工具非常有用。
与 numpy 不同，PyTorch 张量可以利用 GPU 来加速它们的数值计算。要在 GPU 上运行 PyTorch 张量，您只需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次多项式。就像上面的 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')
自动微分 ¶
PyTorch：张量和自动微分 ¶
在上述示例中，我们必须手动实现神经网络的前向和反向传播。对于一个小型的两层网络，手动实现反向传播并不是什么大问题，但对于大型复杂的网络，这会迅速变得非常复杂。
幸运的是，我们可以使用自动微分来自动化神经网络反向传播的计算。PyTorch 中的 autograd 包正好提供了这一功能。当使用 autograd 时，您网络的正向传播将定义一个计算图；图中的节点将是张量，边将是将输入张量转换为输出张量的函数。通过这个图进行反向传播，然后可以轻松地计算梯度。
这听起来很复杂，但在实际使用中非常简单。每个 Tensor 代表计算图中的一个节点。如果 x 是一个具有 x.requires_grad=True 的 Tensor，那么 x.grad 就是另一个 Tensor，它持有 x 相对于某个标量值的梯度。
在这里，我们使用 PyTorch Tensors 和 autograd 来实现我们的三次多项式拟合正弦波示例；现在我们不再需要手动实现网络的反向传播：
# -*- coding: utf-8 -*-
import torch
import math
# We want to be able to train our model on an `accelerator <https://maskerprc.github.io/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 autograd 运算符实际上是由两个函数组成的，它们在 Tensor 上操作。正向函数从输入 Tensor 计算输出 Tensor。反向函数接收输出 Tensor 相对于某个标量值的梯度，并计算输入 Tensor 相对于该标量值的梯度。
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 运算符。然后，我们可以通过构造一个实例并像函数一样调用它，传递包含输入数据的 Tensors 来使用我们新的 autograd 运算符。
在这个例子中，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
计算图和自动微分是一个非常强大的范式，用于定义复杂算子和自动求导；然而，对于大型神经网络，原始的自动微分可能有点太底层了。
当构建神经网络时，我们通常会考虑将计算组织成层，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，Keras、TensorFlow-Slim 和 TFLearn 等包提供了对原始计算图的更高层次抽象，这对于构建神经网络非常有用。
在 PyTorch 中， nn 包具有相同的作用。 nn 包定义了一系列模块，这些模块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，但也可以持有内部状态，例如包含可学习参数的张量。 nn 包还定义了一系列常用的损失函数，这些函数在训练神经网络时经常使用。
在本例中，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，我们通过手动修改包含可学习参数的张量 torch.no_grad() 来更新模型的权重。这对于像随机梯度下降这样的简单优化算法来说并不是一个巨大的负担，但在实践中，我们通常使用更复杂的优化器 AdaGrad 、 RMSProp 、 Adam 和其他优化器来训练神经网络。
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。
在本例中，我们将使用 nn 包来定义我们的模型，就像之前一样，但我们将使用 RMSprop 算法来优化模型，该算法由 optim 包提供：
# -*- 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
有时候，你可能需要指定比现有模块序列更复杂的模型；对于这些情况，你可以通过继承 nn.Module 并定义一个接收输入张量并使用其他模块或其他张量上的 autograd 操作来生成输出张量的 forward 来定义自己的模块。
在本例中，我们将我们的三阶多项式实现为一个自定义模块的子类：
# -*- 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
例如，为了实现动态图和权重共享，我们实现了一个非常奇怪的模型：一个三阶到五阶的多项式，在每次前向传播时选择一个介于 3 和 5 之间的随机数，并使用那么多阶，多次复用相同的权重来计算四阶和五阶。
对于这个模型，我们可以使用正常的 Python 流程控制来实现循环，并且我们可以在定义前向传播时简单地多次复用相同的参数来实现权重共享。
我们可以轻松地将这个模型实现为一个 Module 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
您可以在此浏览上述示例。
