本教程通过自包含的示例介绍PyTorch的基本概念。
在其核心，PyTorch提供了两个主要特性：
- 一个n维张量，类似于numpy，但可以在gpu上运行
- 自动区分建立和训练神经网络
我们将使用一个全连接的ReLU网络作为运行示例。网络将有一个单独的隐藏层，并通过梯度下降训练来匹配随机数据，使网络输出与真实输出之间的欧氏距离最小化。
Tensors
Warm-up: numpy
在介绍PyTorch之前，我们将首先使用numpy实现网络。
Numpy提供一个n维数组对象，以及许多用于操作这些数组的函数。Numpy是科学计算的通用框架;它对计算图形、深度学习或梯度一无所知。但是，通过使用numpy操作手动实现正向和反向遍历网络，我们可以很容易地使用numpy将双层网络匹配到随机数据。
# -*- 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_w2PyTorch: Tensors
Numpy是一个很好的框架，但是它不能利用gpu加速其数值计算。对于现代深度神经网络，gpu通常提供50倍或更大的速度，因此不幸的是，numpy不足以支持现代深度学习。
这里我们引入最基本的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提供了许多作用于这些张量的函数。在幕后，张量可以跟踪计算图形和梯度，但它们作为科学计算的通用工具也很有用。
与numpy不同的是，PyTorch张量可以利用gpu加速数值计算。要在GPU上运行PyTorch张量，只需将其转换为新的数据类型。
在这里，我们使用PyTorch张量来拟合一个两层网络到随机数据。像上面的numpy示例一样，我们需要手动实现通过网络的向前和向后传递
# -*- 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()
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_w2Autograd
PyTorch: Tensors and autograd
在上面的例子中，我们必须手动实现神经网络的正向和反向传递。手工实现后向传递对于小型两层网络来说不是什么大问题，但是对于大型复杂网络来说很快就会变得非常复杂。
幸运的是，我们可以使用自动微分来自动计算神经网络中的向后传递。PyTorch中的autograd包提供了这种功能。当使用autograd时，网络的正向传递将定义一个计算图形；图中的节点是张量，边是由输入张量生成输出张量的函数。通过这个图的反向传播，您可以轻松地计算梯度。
这听起来很复杂，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x是具有x.requires_grad = True的Tensor，则x.grad是另一个Tensor，相对于某个标量值保持x的渐变。
在这里，我们使用PyTorch张量和autograd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向后传递：
# -*- 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. #设置requires_grad = False表示我们不需要在向后传递期间计算关于这些张量的梯度。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 a scalar value held in the loss. loss = (y_pred - y).pow(2).sum() 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: Defining new autograd functions
实际上，每个原始的autograd运算符实际上是两个作用于张量的函数。前向函数从输入张量计算输出张量。后向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函数来轻松定义我们自己的autograd运算符。 然后，我们可以通过构造一个实例并将其称为函数来使用我们的新autograd运算符，并传递包含输入数据的Tensors。
在本例中，我们定义了自己的自定义autograd函数来执行ReLU非线性，并使用它来实现我们的两层网络
# -*- coding: utf-8 -*-
import torch
class MyReLU(torch.autograd.Function):
"""
我们可以通过继承torch.autograd.Function并实现在Tensors上运行的前向和后向传递来实现我们自己的自定义autograd函数。
"""
@staticmethod
def forward(ctx, input):
"""
在前向传递中，我们接收包含输入的Tensor并返回包含输出的Tensor。 ctx是一个上下文对象，可用于存储信息以进行反向计算。
您可以使用ctx.save_for_backward方法缓存任意对象以在后向传递中使用。
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):
"""
在向后传递中，我们接收包含相对于输出的损失梯度的Tensor，并且我们需要计算相对于输入的损失的梯度。
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()
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_()TensorFlow: Static Graphs
PyTorch autograd看起来很像TensorFlow：在两个框架中我们定义了一个计算图，并使用自动微分来计算梯度。 两者之间最大的区别是TensorFlow的计算图是静态的，PyTorch使用动态计算图。
在TensorFlow中，我们定义计算图一次，然后一遍又一遍地执行相同的图，可能将不同的输入数据提供给图。 在PyTorch中，每个前向传递定义了一个新的计算图。
静态图很好，因为你可以预先优化图形; 例如，框架可能决定融合某些图形操作以提高效率，或者提出一种策略，用于在多个GPU或许多机器上分布图形。如果您反复使用相同的图表，那么这个可能代价高昂的前期优化可以分摊，因为相同的图表会反复重新运行。
静态和动态图表不同的一个方面是控制流程。 对于某些模型，我们可能希望对每个数据点执行不同的计算; 例如，对于每个数据点，可以针对不同数量的时间步长展开循环网络; 这种展开可以作为循环实现。使用静态图形，循环结构需要是图形的一部分; 因此，TensorFlow提供了诸如tf.scan之类的运算符，用于将循环嵌入到图中。 使用动态图形情况更简单：由于我们为每个示例动态构建图形，我们可以使用常规命令流程控制来执行每个输入不同的计算。
与上面的PyTorch autograd示例相比，这里我们使用TensorFlow来拟合一个简单的双层网：
# -*- coding: utf-8 -*-
import tensorflow as tf
import numpy as np
# First we set up the computational graph:
# 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 placeholders for the input and target data; these will be filled
# with real data when we execute the graph.
x = tf.placeholder(tf.float32, shape=(None, D_in))
y = tf.placeholder(tf.float32, shape=(None, D_out))
# Create Variables for the weights and initialize them with random data.
# A TensorFlow Variable persists its value across executions of the graph.
w1 = tf.Variable(tf.random_normal((D_in, H)))
w2 = tf.Variable(tf.random_normal((H, D_out)))
# Forward pass: Compute the predicted y using operations on TensorFlow Tensors.
# Note that this code does not actually perform any numeric operations; it
# merely sets up the computational graph that we will later execute.
h = tf.matmul(x, w1)
h_relu = tf.maximum(h, tf.zeros(1))
y_pred = tf.matmul(h_relu, w2)
# Compute loss using operations on TensorFlow Tensors
loss = tf.reduce_sum((y - y_pred) ** 2.0)
# Compute gradient of the loss with respect to w1 and w2.
grad_w1, grad_w2 = tf.gradients(loss, [w1, w2])
# Update the weights using gradient descent. To actually update the weights
# we need to evaluate new_w1 and new_w2 when executing the graph. Note that
# in TensorFlow the the act of updating the value of the weights is part of
# the computational graph; in PyTorch this happens outside the computational
# graph.
learning_rate = 1e-6
new_w1 = w1.assign(w1 - learning_rate * grad_w1)
new_w2 = w2.assign(w2 - learning_rate * grad_w2)
# Now we have built our computational graph, so we enter a TensorFlow session to
# actually execute the graph.
with tf.Session() as sess:
# Run the graph once to initialize the Variables w1 and w2.
sess.run(tf.global_variables_initializer())
# Create numpy arrays holding the actual data for the inputs x and targets
# y
x_value = np.random.randn(N, D_in)
y_value = np.random.randn(N, D_out)
for _ in range(500):
# Execute the graph many times. Each time it executes we want to bind
# x_value to x and y_value to y, specified with the feed_dict argument.
# Each time we execute the graph we want to compute the values for loss,
# new_w1, and new_w2; the values of these Tensors are returned as numpy
# arrays.
loss_value, _, _ = sess.run([loss, new_w1, new_w2],
feed_dict={x: x_value, y: y_value})
print(loss_value)nn module
PyTorch: nn
计算图和autograd是定义复杂运算符和自动获取导数的非常强大的范例; 然而，对于大型神经网络，原始autograd可能有点太低级别。
在构建神经网络时，我们经常考虑将计算安排到层中，其中一些层具有可学习的参数，这些参数将在学习期间进行优化。
在TensorFlow中，像Keras，TensorFlow-Slim和TFLearn这样的软件包提供了对构建神经网络有用的原始计算图形的更高级别的抽象。
在PyTorch中，nn包服务于同样的目的。 nn包定义了一组模块，它们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，但也可以保持内部状态，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)
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.gradPyTorch: optim
到目前为止，我们通过手动改变持有可学习参数的Tensors来更新模型的权重（使用torch.no_grad（）或.data以避免在autograd中跟踪历史记录）。对于像随机梯度下降这样的简单优化算法来说，这不是一个巨大的负担，但在实践中，我们经常使用更复杂的优化器如AdaGrad，RMSProp，Adam等来训练神经网络。
PyTorch中的optim包提取了优化算法的思想，并提供了常用优化算法的实现。
在这个例子中，我们将使用nn包像以前一样定义我们的模型，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)
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: Custom nn Modules
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，您可以通过继承nn.Module并定义一个接收输入Tensors并使用其他模块或Tensors上的其他autograd操作生成输出Tensors的forward来定义您自己的模块。
在这个例子中，我们将我们的双层网络实现为自定义模块子类：
# -*- 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)
print(t, loss.item())
# Zero gradients, perform a backward pass, and update the weights.
optimizer.zero_grad()
loss.backward()
optimizer.step()PyTorch: Control Flow + Weight Sharing
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：一个完全连接的ReLU网络，在每个正向通道上选择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来计算最里面的隐藏层。
对于这个模型，我们可以使用普通的Python流控制来实现循环，并且我们可以通过在定义正向传递时多次重用同一个模块来实现最内层之间的权重共享。
我们可以很容易地将这个模型实现为模块子类：
# -*- 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)
print(t, loss.item())
# Zero gradients, perform a backward pass, and update the weights.
optimizer.zero_grad()
loss.backward()
optimizer.step()