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根据示例学习 PyTorch

作者Justin Johnson

本教程通过自包含的示例介绍PyTorch的基本概念。

在其核心,PyTorch 提供了两个主要功能:

  • 类似于 numpy 的 n 维张量,但可以在 GPU 上运行

  • 构建和训练神经网络并自动求导

我们将使用一个完全连接的 ReLU 网络作为运行示例。 这个网络只有一个隐藏层并将使用梯度下降训练,通过最小化网络输出与真实输出之间的欧氏距离来拟合随机数据。

注意

你可以在 本页面的末尾 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 实现网络。

Numpy 提供了一个 n 维数组对象,以及用于操作这些数组的许多函数。 Numpy 是科学计算的通用框架;它不知道关于计算图、深度学习或梯度的任何信息。 但是,通过使用 numpy 的各种操作手动实现网络的正向和反向传递,我们可以轻松地使用 numpy 来将两层网络拟合随机数据,:

# -*- coding: utf-8 -*-
import numpy as np

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random input and output data
x = np.random.randn(N, D_in)
y = np.random.randn(N, D_out)

# Randomly initialize weights
w1 = np.random.randn(D_in, H)
w2 = np.random.randn(H, D_out)

learning_rate = 1e-6
for t in range(500):
    # Forward pass: compute predicted y
    h = x.dot(w1)
    h_relu = np.maximum(h, 0)
    y_pred = h_relu.dot(w2)

    # Compute and print loss
    loss = np.square(y_pred - y).sum()
    print(t, loss)

    # Backprop to compute gradients of w1 and w2 with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_w2 = h_relu.T.dot(grad_y_pred)
    grad_h_relu = grad_y_pred.dot(w2.T)
    grad_h = grad_h_relu.copy()
    grad_h[h < 0] = 0
    grad_w1 = x.T.dot(grad_h)

    # Update weights
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2

PyTorch:张量

Numpy 是一个伟大的框架,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倍或更快的加速,因此不幸的是,numpy 对于现代深度学习来说是不够的。

在这里,我们介绍最基本的 PyTorch 概念:张量 PyTorch 张量与 numpy 数组的概念相同:张量是 n 维数组,PyTorch 提供许多函数,用于在这些张量上操作。 在后台,张量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,PyTorch 张量可以使用 GPU 来加速其数值计算。 要在 GPU 上运行 PyTorch 张量,只需将其强制转换为新的数据类型即可。

在这里,我们使用 PyTorch 张量来将两层网络拟合随机数据。 与上面的 numpy 示例一样,我们需要手动实现通过网络的反向和反向传递:

# -*- coding: utf-8 -*-

import torch


dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random input and output data
x = torch.randn(N, D_in, device=device, dtype=dtype)
y = torch.randn(N, D_out, device=device, dtype=dtype)

# Randomly initialize weights
w1 = torch.randn(D_in, H, device=device, dtype=dtype)
w2 = torch.randn(H, D_out, device=device, dtype=dtype)

learning_rate = 1e-6
for t in range(500):
    # Forward pass: compute predicted y
    h = x.mm(w1)
    h_relu = h.clamp(min=0)
    y_pred = h_relu.mm(w2)

    # Compute and print loss
    loss = (y_pred - y).pow(2).sum().item()
    if t % 100 == 99:
        print(t, loss)

    # Backprop to compute gradients of w1 and w2 with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_w2 = h_relu.t().mm(grad_y_pred)
    grad_h_relu = grad_y_pred.mm(w2.t())
    grad_h = grad_h_relu.clone()
    grad_h[h < 0] = 0
    grad_w1 = x.t().mm(grad_h)

    # Update weights using gradient descent
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2

自动求导

PyTorch:张量和自动求导

在上面的示例中,我们必须手动实现神经网络的正向和反向传递。 手动实现向后传递对于小型双层网络来说不是一个大问题,但对于大型复杂网络来说,手动实现这种传递可能很快变得十分复杂。

谢天谢地,我们可以使用自动求导来自动计算神经网络中的反向传递。 PyTorch 中的 autograd 包提供的就是这个功能。 使用 autograd 时,网络的正向传递将定义一个 计算图;图中的节点为张量,边为从输入张量生成输出张量的函数。 然后,通过此图形进行回显,即可轻松计算渐变。

这听起来很复杂,在实践中使用起来非常简单。 每个张量表示计算图中的节点。 如果xx.requires_grad=True的张量,则x.grad是另一个维持x相对于某个标量值的梯度的张量。

在这里,我们使用 PyTorch 张量和自动微分来实现我们的双层网络;现在,我们不再需要手动实现通过网络的反向传递:

# -*- coding: utf-8 -*-
import torch

dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold input and outputs.
# Setting requires_grad=False indicates that we do not need to compute gradients
# with respect to these Tensors during the backward pass.
x = torch.randn(N, D_in, device=device, dtype=dtype)
y = torch.randn(N, D_out, device=device, dtype=dtype)

# Create random Tensors for weights.
# Setting requires_grad=True indicates that we want to compute gradients with
# respect to these Tensors during the backward pass.
w1 = torch.randn(D_in, H, device=device, dtype=dtype, requires_grad=True)
w2 = torch.randn(H, D_out, device=device, dtype=dtype, requires_grad=True)

learning_rate = 1e-6
for t in range(500):
    # Forward pass: compute predicted y using operations on Tensors; these
    # are exactly the same operations we used to compute the forward pass using
    # Tensors, but we do not need to keep references to intermediate values since
    # we are not implementing the backward pass by hand.
    y_pred = x.mm(w1).clamp(min=0).mm(w2)

    # 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 w1.grad and w2.grad will be Tensors holding the gradient
    # of the loss with respect to w1 and w2 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.
    # An alternative way is to operate on weight.data and weight.grad.data.
    # Recall that tensor.data gives a tensor that shares the storage with
    # tensor, but doesn't track history.
    # You can also use torch.optim.SGD to achieve this.
    with torch.no_grad():
        w1 -= learning_rate * w1.grad
        w2 -= learning_rate * w2.grad

        # Manually zero the gradients after updating weights
        w1.grad.zero_()
        w2.grad.zero_()

PyTorch:定义新的自动求导函数

每个原始自动求导运算符的底层机制实际上是在张量上运行的两个函数。 forward 函数计算来自输入张量的输出张力。 backward 函数接收相对于某个标量值的输出张量的梯度,并计算相对于同一标量值的输入张力的梯度。

在 PyTorch 中,我们可以通过定义torch.autograd.Function的子类并实现forwardbackward函数来轻松定义自己的 autograd 操作。 然后,我们可以通过构造实例并像调用函数一样调用新的autograd运算符,并传递包含输入数据的张量。

在下面的示例中,我们定义自己的自定义 autograd 函数来执行非线性的 ReLU,并使用它来实现我们的两层网络:

# -*- coding: utf-8 -*-
import torch


class MyReLU(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 input.clamp(min=0)

    @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
        grad_input = grad_output.clone()
        grad_input[input < 0] = 0
        return grad_input


dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold input and outputs.
x = torch.randn(N, D_in, device=device, dtype=dtype)
y = torch.randn(N, D_out, device=device, dtype=dtype)

# Create random Tensors for weights.
w1 = torch.randn(D_in, H, device=device, dtype=dtype, requires_grad=True)
w2 = torch.randn(H, D_out, device=device, dtype=dtype, requires_grad=True)

learning_rate = 1e-6
for t in range(500):
    # To apply our Function, we use Function.apply method. We alias this as 'relu'.
    relu = MyReLU.apply

    # Forward pass: compute predicted y using operations; we compute
    # ReLU using our custom autograd operation.
    y_pred = relu(x.mm(w1)).mm(w2)

    # 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():
        w1 -= learning_rate * w1.grad
        w2 -= learning_rate * w2.grad

        # Manually zero the gradients after updating weights
        w1.grad.zero_()
        w2.grad.zero_()

nn 模块

PyTorch: nn

计算图和自动梯度是定义复杂运算符和自动获取导数的非常强大的范式;然而,对于大型神经网络,原生自动梯度可能有点太底层。

在构建神经网络时,我们经常考虑将计算安排到中,其中一些具有可学习的参数,这些参数将在学习过程中得到优化。

在 TensorFlow 中,像KerasTensorFlow-SlimTFLearn 这样的包在原始计算图上提供了更高级别的抽象,这些抽象对于构建神经网络非常有用。

在 PyTorch 中nn包也具有相同的用途。 nn包定义了一组 Modules,它们大致相当于神经网络层。 一个 Module 接收输入张量并计算输出张量,而且还可以保留内部状态,如包含可学习参数的张量。 nn包还定义了一组训练神经网络时常用的有用损失函数。

在下面的示例中,我们使用nn包来实现我们的双层网络:

# -*- coding: utf-8 -*-
import torch

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# 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. Each Linear Module computes output from input using a
# linear function, and holds internal Tensors for its weight and bias.
model = torch.nn.Sequential(
    torch.nn.Linear(D_in, H),
    torch.nn.ReLU(),
    torch.nn.Linear(H, D_out),
)

# 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-4
for t in range(500):
    # 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(x)

    # 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

PyTorch:optim

至此,我们通过手动改变维持可学习参数的张量(使用torch.no_grad().data来更新模型的权重,以避免在 autograd 中跟踪历史记录)。 对于随机梯度下降等简单优化算法来说,这不是一个巨大的负担,但在实践中,我们经常使用更精密的优化器(如 AdaGrad、RMSProp、Adam 等)来训练神经网络。

PyTorch 中的optim软件包抽象了优化算法的概念,并提供了常用优化算法的实现。

在下面的示例中,我们将像以前那样使用nn包定义模型,但我们将使用optim包提供的 Adam 算法优化模型:

# -*- coding: utf-8 -*-
import torch

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# Use the nn package to define our model and loss function.
model = torch.nn.Sequential(
    torch.nn.Linear(D_in, H),
    torch.nn.ReLU(),
    torch.nn.Linear(H, D_out),
)
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 Adam; the optim package contains many other
# optimization algoriths. The first argument to the Adam constructor tells the
# optimizer which Tensors it should update.
learning_rate = 1e-4
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)
for t in range(500):
    # Forward pass: compute predicted y by passing x to the model.
    y_pred = model(x)

    # 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()

PyTorch:自定义 nn 模块

有时,你需要编写比现有的一系列 Module 更复杂的模型;对于这些情况,你可以通过继承nn.Module并定义forward来定义自己的 Modules,forward 接收输入张量并使用其它模块或张量上的其它自动求导操作生成输出张量。

在下面的示例中,我们将我们的双层网络实现为自定义 Module 子类:

# -*- coding: utf-8 -*-
import torch


class TwoLayerNet(torch.nn.Module):
    def __init__(self, D_in, H, D_out):
        """
        In the constructor we instantiate two nn.Linear modules and assign them as
        member variables.
        """
        super(TwoLayerNet, self).__init__()
        self.linear1 = torch.nn.Linear(D_in, H)
        self.linear2 = torch.nn.Linear(H, D_out)

    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.
        """
        h_relu = self.linear1(x).clamp(min=0)
        y_pred = self.linear2(h_relu)
        return y_pred


# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# Construct our model by instantiating the class defined above
model = TwoLayerNet(D_in, H, D_out)

# Construct our loss function and an Optimizer. The call to model.parameters()
# in the SGD constructor will contain the learnable parameters of the two
# nn.Linear modules which are members of the model.
criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)
for t in range(500):
    # 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()

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:一个完全连接的 ReLU 网络,该网络在每个前向传递中选择1到4之间的随机数,并使用那么多隐藏层,多次重复使用相同的权重计算最里面的隐藏层。

对于此模型,我们可以使用正常的 Python 流控制来实现循环,并且我们可以在定义正向传递时多次重用同一模块,从而在最内层之间实现权重共享。

我们可以轻松地实现此模型作为一个模块子类:

# -*- coding: utf-8 -*-
import random
import torch


class DynamicNet(torch.nn.Module):
    def __init__(self, D_in, H, D_out):
        """
        In the constructor we construct three nn.Linear instances that we will use
        in the forward pass.
        """
        super(DynamicNet, self).__init__()
        self.input_linear = torch.nn.Linear(D_in, H)
        self.middle_linear = torch.nn.Linear(H, H)
        self.output_linear = torch.nn.Linear(H, D_out)

    def forward(self, x):
        """
        For the forward pass of the model, we randomly choose either 0, 1, 2, or 3
        and reuse the middle_linear Module that many times to compute hidden layer
        representations.

        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 Module many
        times when defining a computational graph. This is a big improvement from Lua
        Torch, where each Module could be used only once.
        """
        h_relu = self.input_linear(x).clamp(min=0)
        for _ in range(random.randint(0, 3)):
            h_relu = self.middle_linear(h_relu).clamp(min=0)
        y_pred = self.output_linear(h_relu)
        return y_pred


# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# Construct our model by instantiating the class defined above
model = DynamicNet(D_in, H, D_out)

# 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-4, momentum=0.9)
for t in range(500):
    # 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()