通过示例学习 PyTorch¶

创建时间： 2017 年 3 月 24 日 |上次更新时间：2024 年 1 月 16 日 |上次验证： Nov 05， 2024

作者： Justin Johnson

注意

这是我们较旧的 PyTorch 教程之一。您可以查看我们最新的 Learn the Basics 中的初学者内容。

本教程通过自包含的 PyTorch 介绍了 PyTorch 的基本概念例子。

PyTorch 的核心提供了两个主要功能：

一个 n 维 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

我们将使用一个将 \（y=\sin（x）\）与三阶多项式拟合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，通过最小化欧几里得距离来拟合随机数据在 network output 和 true output 之间。

注意

您可以浏览本页末尾的各个示例。

Tensors ¶

预热：numpy ¶

在介绍 PyTorch 之前，我们首先使用 numpy 的

Numpy 提供了一个 n 维数组对象，以及许多用于操作这些数组。Numpy 是科学计算机科学;它对计算图或深度一无所知学习或梯度。但是，我们可以轻松地使用 numpy 来拟合三阶多项式转正弦函数，通过手动实现 FORWARD 并使用 numPy 操作向后传递网络：

# -*- 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，因此不幸的是，NumPy 对于现代深度学习来说还不够。

下面我们介绍一下 PyTorch 最基本的概念：Tensor。 PyTorch Tensor 在概念上与 numpy 数组相同：Tensor 是一个 n 维数组，PyTorch 为对这些 Tensor 进行操作。在幕后，Tensor 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。

与 numpy 不同的是，PyTorch 张量可以利用 GPU 来加速他们的数值计算。要在 GPU 上运行 PyTorch 张量，您只需需要指定正确的设备。

在这里，我们使用 PyTorch 张量来拟合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 forward 和向后传递网络：

# -*- 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grad ¶

PyTorch：张量和 autograd ¶

在上面的例子中，我们必须手动实现 forward 和神经网络的向后传递。手动实现对于小型两层网络来说，向后传递没什么大不了的，但可以对于大型复杂网络，很快就会变得非常棘手。

值得庆幸的是，我们可以使用 automatic 微分，以自动计算神经网络中的向后传递。PyTorch 中的 autograd 包正是提供此功能的。使用 autograd 时，网络的 forward pass 将定义一个计算图;图中的节点将是 Tensor 和 edges 将是从输入 Tensor 生成输出 Tensor 的函数。然后，通过此图形反向传播，您可以轻松计算梯度。

这听起来很复杂，但在实践中使用起来非常简单。每个 Tensor 表示计算图中的节点。如果是一个 Tensor，则 then 是另一个持有的 gradient 值。xx.requires_grad=Truex.gradx

在这里，我们使用 PyTorch Tensors 和 autograd 来实现我们的拟合正弦波具有三阶多项式示例;现在我们不再需要手动通过网络实现反向传递：

# -*- 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 autograd 函数 ¶

在后台，每个原始 autograd 运算符实际上是两个函数对 Tensor 进行操作。forward 函数计算输出来自输入 Tensor 的 Tensor。backward 函数接收 outputs 相对于某个标量值的 gradient，以及计算输入 Tensor 相对于该 Tensor 的梯度标量值。

在 PyTorch 中，我们可以通过定义子类并实现 AND 函数。然后，我们可以通过以下方式使用新的 autograd 运算符构造一个实例并像函数一样调用它，将包含输入数据的张量。torch.autograd.Functionforwardbackward

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 3 次勒让德多项式。我们编写自己的自定义 autograd 函数来计算 \（P_3\）的正向和反向，并使用它来实现我们的模式：

# -*- 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)')

模块 ¶

PyTorch 的 PyTorch 中： ¶

计算图和 autograd 是一个非常强大的范例定义复数运算符并自动取导数;然而对于大型神经网络，Raw Autograd 可能有点太低级了。

在构建神经网络时，我们经常会考虑将计算到层中，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 提供更高级别的抽象对构建神经有用的原始计算图网络。

在 PyTorch 中，该软件包具有相同的目的。该包定义了一组 Module，它们大致相当于神经网络层。Module 接收输入 Tensor 并进行计算 output Tensors，但也可以保存内部状态，例如 Tensor 包含可学习的参数。该软件包还定义了一个集训练神经时常用的有用损失函数网络。nnnnnn

在此示例中，我们使用 package 来实现我们的多项式模型网络：nn

# -*- 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 ¶

到目前为止，我们已经手动更新了模型的权重使用改变保存可学习参数的 Tensor。对于像 stochastic 这样的简单优化算法来说，这并不是一个巨大的负担梯度下降，但在实践中，我们经常使用更多的复杂的优化器，如、、和其他。torch.no_grad()AdaGradRMSPropAdam

PyTorch 中的包抽象了优化的概念算法，并提供常用优化的实现算法。optim

在此示例中，我们将使用包将模型定义为之前，但我们将使用提供的算法优化模型按包装：nnRMSpropoptim

# -*- 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：自定义模块 ¶

有时，您需要指定比现有模块的顺序;对于这些情况，您可以定义自己的 Modules 通过子类化和定义 which 接收输入 Tensor 并使用其他 modules 或其他 autograd 操作。nn.Moduleforward

在此示例中，我们将三阶多项式实现为自定义模块亚纲：

# -*- 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异模型：每次正向传递的三阶到五阶多项式选择一个介于 3 和 5 之间的随机数并使用该数量的订单，重复使用相同的权重多次计算四阶和五阶。

对于这个模型，我们可以使用普通的 Python 流控制来实现循环，我们可以通过简单地重用相同的参数倍数来实现权重共享定义 forward pass 的 times。

我们可以轻松地将这个模型实现为 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()}')

通过示例学习 PyTorch¶

Tensors ¶

预热：numpy ¶

PyTorch：张量 ¶

自动grad ¶

PyTorch：张量和 autograd ¶

PyTorch：定义新的 autograd 函数 ¶

模块 ¶

PyTorch 的 PyTorch 中： ¶

PyTorch：优化 ¶

PyTorch：自定义模块 ¶

例子 ¶

Tensors ¶

自动grad ¶

模块 ¶

文档

教程

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