前提
第一个关于专业方向的博客，虽然翻译官网为重，但里面的程序自己都有敲，路漫漫其修远兮，清楚连门都没有摸进去，但是以此纪念自己的代码成长之路，慢慢来。
本文来源：【https://pytorch.org/tutorials/beginner/pytorch_with_examples.html#】
Abstract
通过例子介绍pytorch的基本概念~
PyTorch有两个主要的特点：
1.作为一维Tensor，和Numpy数组相似，但是能使用GPU
2.用于创建和训练神经网络的自动微分
一 Tensor
1.1Warm-up: numpy
先用numpy热热身啊。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，我们可以通过使用numpy操作手动实现网络的前向和后向传递以及使用numpy操作用随机数据拟合两层网络。
# -*- 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
note
- .dot():两个数组的点积
- .np.maximum(X,Y,out=None):X和Y逐位比较，取大值。
- .T.dot()：先求转置再求点积
1.2PyTorch：Tensors
PyTorch张量与numpy数组在概念上是相同的:张量是n维数组，PyTorch为这些张量提供了很多函数。在幕后，张量可以跟踪计算图和梯度，但它们也可以作为科学计算的通用工具。
与numpy不同的是，PyTorch张量可以利用gpu加速它们的数值计算。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的随机数据。
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：
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)#矩阵相乘
h_relu = h.clamp(min=0)#torch.clamp(input，min,max) 将超过min，max的值全部变为min和max
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_w2
Autograd
2.1 Tensors and autograd
前面介绍的Numpy和PyTorch的Tensors都是手动计算forward和backward，对于小型NN而言可以，但是复杂的网络就不行了。所以，在神经网络中，我们可以使用[automatic differentiation]（自动微分）来自动计算backward。
当使用autograd时，网络的forward将定义一个计算图;图中的节点将是张量，边将是从输入张量产生输出张量的函数。通过这个图进行反向传播，这样就可以轻松地计算梯度。
如果x是一个标记着requires_grad = True的张量。然后x.grad是根据标量值求出的梯度。
使用PyTorch张量和autograd来实现我们的双层网络：
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 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_()
Q：为什么只求w1、w2的梯度呢：因为要根据他们的梯度更新权重啊
BUG：在打印loss的时候我把item（）放在了loss的计算公式中，可是出现'float'不能用backward的错误，所以只能通过loss值来调用item
2.2Defining New Autograd Function
每个原始的autograd操作实际上是两个对张量进行操作的函数。
- Forward：从输入张量计算出输出张量。
- Backward：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，通过定义torch.autograd.Function子类，定义Autograd的操作，并且实现Forward和Backward。然后，我们可以使用新的autograd运算符，构造一个实例并将其调用为函数，传递包含输入数据的张量。
在这个例子中，我们定义了我们自己的自定义autograd函数来执行ReLU非线性，并使用它来实现我们的双层网络：
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()
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_()
BUG：
在写这个例子时，没有在定义函数上引用@staticmethod，导致只能执行一条语句。这是一个定义返回静态函数的方法，可以不用实例化，因为例子中没有对类进行实例化就调用了。
2.3Tensorflow：staticGraphs
时间问题没有做这个例子，感兴趣可以去官网查看啊。
三：NN Module
3.1PyTorch：NN
计算图和Autograd是定义复杂运算符和自动求导的强大范例;
在构建神经网络时，我们经常考虑将计算安排到各个层，其中一些层具有可学习的参数，这些参数将在学习过程中得到优化。
NN包定义了一组Module，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，但也可能保持内部状态，例如包含可学习参数的张量。nn包还定义了一组有用的损失函数，这些函数通常用于训练神经网络。
在本例中，我们使用nn包来实现我们的两层网络：
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.grad
Note：
主要就是nn.Sequential这个函数，将Model定义为一个层序列。在forward时，直接调用model求出output。在backward之前要清零。
3.2PyTorch：optim
optim包抽象了优化算法的思想，并且提供了算法实现。
在本例中，我们将使用nn包来定义我们的模型，但我们将使用optim包提供的Adam算法来优化模型：
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()
求完loss之后，在定义优化器更新模型权重。Adam优化器的第一个参数是告诉优化器应该更新哪些张量。
3.3PyTorch：Custom NNModules
定义自己的Model：
通过torch.nn.Module,定义网络类，在里面重写init和forward函数，实现module：
定义一个forward，它接收输入张量并使用其他模块或张量上的其他autograd运算产生输出张量。
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()
3.4PyTorch：Control Flow+WeightSharing
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，在每一次转发中选择一个1到4之间的随机数，并使用多个隐藏层，多次重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，我们可以通过在定义前向传递时多次重用同一个模块来实现最内部层之间的权重共享。
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()
总结
主要通过9个例子学习pytorch的tensor概念和autograd的使用，我们可以自定义Autograd函数和Module方法。
在forward时，我们主要是计算得出输出值
之后将梯度清零，.zero_grad()
loss.backward
更新权重：.step()
