学习 PyTorch 以获取示例

创建日期: 2017年3月24日 | 最后更新日期: 2024年1月16日 | 最后验证日期: 2024年11月5日

作者: Justin Johnson

注意

这是我们的其中一个较旧的 PyTorch 教程。您可以查看我们最新的 初学者内容在 学习基础知识。

此教程通过自包含示例介绍了 PyTorch 的基本概念。

在核心层面，PyTorch 提供了两个主要功能：

• 一个n维张量，类似于numpy，但可以在GPU上运行

• 构建和训练神经网络的自动微分

我们将使用拟合\(y=\sin(x)\)与三次多项式的问题作为我们的示例。该网络将有四个参数，并通过最小化网络输出与真实输出之间的欧几里得距离，使用梯度下降进行训练。

注意

您可以浏览本页面末尾的各个示例。

张量

热身：numpy

在介绍PyTorch之前，我们首先将使用numpy实现该网络。

Numpy 提供了一个 n 维数组对象，并且包含了许多操作这些数组的函数。Numpy 是一个通用的科学计算框架；它并不了解计算图、深度学习或梯度的概念。然而，我们可以很容易地使用 numpy 手动实现网络的前向和后向传播过程来拟合正弦函数的三次多项式：

# -*- 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 通常可以提供 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是不够的。

这里我们介绍Pytorch最基础的概念：张量。 一个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。在后台，张量可以跟踪计算图和梯度，但它们也作为科学计算的通用工具非常有用。

与numpy不同，PyTorch张量可以利用GPU来加速数值计算。要在一个PyTorch张量上运行GPU加速，你只需要指定正确的设备即可。

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过程。

# -*- 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')

自动求导

PyTorch：张量与自动求导

在上述示例中，我们不得不手动实现神经网络的前向传播和反向传播。对于一个小的两层网络来说，手动实现反向传播并不是什么大问题，但大型复杂的网络很快就会变得非常复杂。

thankfully，我们可以使用自动微分 来自动化神经网络中反向传播的计算。PyTorch中的autograd包正好提供了这一功能。 当使用autograd时，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让你轻松地计算梯度。

这听起来很复杂，实际上在实践中使用起来非常简单。每个Tensor代表计算图中的一个节点。如果x是一个Tensor，那么它有x.requires_grad=True，则x.grad是另一个Tensor，用于存储x相对于某个标量值的梯度。

在这里，我们使用PyTorch张量和自动求导来实现拟合正弦波的三次多项式示例；现在我们不再需要手动实现网络中的反向传播过程。

# -*- 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：定义新的自动求导函数

在幕后，每个原始自动微分操作符实际上是由两个函数组成的，这两个函数操作Tensor。前向函数从输入Tensor计算输出Tensor。后向函数接收输出Tensor相对于某个标量值的梯度，并计算输入Tensor相对于同一标量值的梯度。

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 函数来轻松定义自己的自动求导操作符。然后，我们可以使用新的自动求导操作符通过构造一个实例并像函数一样调用它，传入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 \(P_3(x)=\frac{1}{2}\left(5x^3-3x\right)\) 是三次 勒让德多项式。我们编写了自己的自定义 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:

# -*- 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

计算图和自动求导是定义复杂运算和自动计算导数的强大范式；然而，对于大型神经网络来说，原始的自动求导可能会略显低级。

当我们构建神经网络时，我们经常将其计算排列成层，其中一些层具有可学习参数，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高级抽象， 这有助于构建神经网络。

在 PyTorch 中，nn 包具有相同的功能。nn 包定义了一组 模块，这些模块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 包还定义了一组常用的损失函数，在训练神经网络时经常使用。

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: optim

到目前为止，我们通过手动修改存储可学习参数的张量来更新模型的权重。torch.no_grad() 这对于简单的优化算法如随机梯度下降来说负担不大，但在实践中，我们经常使用更复杂的优化器如AdaGrad、RMSProp、Adam等。

The optim 包在 PyTorch 中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，我们将使用 nn 包来定义我们的模型，就像之前那样，但我们将使用 RMSprop 包提供的 optim 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

有时您需要指定比现有模块序列更复杂的模型；对于这些情况，您可以定义自己的模块，通过继承 nn.Module 并定义一个 forward 来实现，该 forward 接收输入张量并使用其他模块或其他张量上的自动微分操作生成输出张量。

在本例中，我们将第三阶多项式实现为一个自定义的Module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，在每次前向传播时都会选择一个随机数在3和5之间，并使用该数量的阶数进行计算，多次使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，并且可以通过在定义前向传播时多次复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作为Module子类来实现：

# -*- 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。

张量

自动求导

nn 模块