通过示例学习 PyTorch#
创建于：2017年3月24日 | 最后更新：2025年1月21日 | 最后验证：2024年11月5日
作者： Justin Johnson
注意
这是我们较早的 PyTorch 教程之一。您可以在学习基础中查看我们最新的入门内容。
本教程通过独立的示例介绍 PyTorch 的基本概念。
PyTorch 的核心提供两个主要功能：
一个 n 维张量（Tensor），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
我们将使用一个用三阶多项式拟合 \(y=\sin(x)\) 的问题作为我们的贯穿示例。该网络将有四个参数，并将通过梯度下降进行训练，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
您可以在本页末尾浏览各个示例。
张量#
热身：numpy#
在介绍 PyTorch 之前，我们将首先使用 numpy 实现该网络。
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 是一个用于科学计算的通用框架；它对计算图、深度学习或梯度一无所知。然而，我们可以轻松地使用 numpy，通过手动实现网络的前向和后向传播来拟合三阶多项式到正弦函数
# -*- 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 是一个很棒的框架，但它不能利用 GPU 来加速其数值计算。对于现代深度神经网络，GPU 通常提供 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。
这里我们介绍最基本的 PyTorch 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，但它们作为科学计算的通用工具也很有用。
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，您只需指定正确的设备即可。
这里我们使用 PyTorch 张量来拟合一个三阶多项式到正弦函数。就像上面的 numpy 示例一样，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')
Autograd#
PyTorch: 张量和 autograd#
在上面的示例中，我们必须手动实现神经网络的前向和后向传播。对于一个小的两层网络来说，手动实现后向传播不是什么大问题，但对于大型复杂网络来说，这很快就会变得非常棘手。
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后向传播的计算。PyTorch 中的 autograd 包正是提供了这个功能。当使用 autograd 时，你的网络的前向传播将定义一个计算图；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。通过这个图进行反向传播，就可以轻松计算梯度。
这听起来很复杂，但在实践中却非常简单。每个张量代表计算图中的一个节点。如果 x 是一个设置了 x.requires_grad=True 的张量，那么 x.grad 就是另一个张量，它持有 x 相对于某个标量值的梯度。
这里我们使用 PyTorch 张量和 autograd 来实现我们的用三阶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后向传播
import torch
import math
# We want to be able to train our model on an `accelerator <https://pytorch.ac.cn/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 运算符实际上是两个作用于张量的函数。forward 函数从输入张量计算输出张量。backward 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该相同标量值的梯度。
在 PyTorch 中，我们可以通过定义一个 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函数一样调用它来使用我们新的 autograd 运算符，并传递包含输入数据的张量。
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 \(P_3\) 的前向和后向传播，并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.ac.cn/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 是定义复杂算子并自动求导的非常强大的范式；然而，对于大型神经网络来说，原始的 autograd 可能有点太底层了。
在构建神经网络时，我们经常考虑将计算安排成层，其中一些层具有将在学习过程中优化的可学习参数。
在 TensorFlow 中，像 Keras、TensorFlow-Slim 和 TFLearn 这样的包在原始计算图之上提供了更高级别的抽象，这对于构建神经网络很有用。
在 PyTorch 中，nn 包也起着同样的作用。 nn 包定义了一组模块（Modules），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，但它也可能持有内部状态，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，我们一直通过使用 torch.no_grad() 手动改变持有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，这并不是一个巨大的负担，但在实践中，我们经常使用更复杂的优化器来训练神经网络，比如 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，我们将像之前一样使用 nn 包来定义我们的模型，但是我们将使用 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#
有时您会想要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 方法来定义自己的模块，该方法接收输入张量并使用其他模块或对张量的其他 autograd 操作来产生输出张量。
在这个例子中，我们将我们的三阶多项式实现为一个自定义的模块子类
# -*- 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一个例子，我们实现了一个非常奇怪的模型：一个三到五阶的多项式，在每次前向传播时，它会随机选择一个介于 3 和 5 之间的数字，并使用该阶数，多次重用相同的权重来计算四阶和五阶项。
对于这个模型，我们可以使用普通的 Python 控制流来实现循环，并且我们可以通过在定义前向传播时简单地多次重用相同的参数来实现权重共享。
我们可以很容易地将这个模型实现为一个模块子类
# -*- 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。
