pytorch学习笔记（四）
1.前言
前面我们已经简单建立一个分类器的神经网络，虽然训练的效果比较一般，不过这就是一个神经网络大体应该具备的特征，后面的优化也就是基于这个不断进行尝试对某些部分进行优化以提高学习效率，我们接下来跳过Pytorch for former torch users，直接来看learning pytorch with examples
2.正文
我们将用一个全连接的relu神经网络作为我们的实例，这个网络将有一个隐藏层并且会通过最小化网络输出和真实输出之间的欧几里得距离来训练梯度下降以适合随机数据，而我们通过这个例子来进一步加深我们对于pytorch基本知识的理解和掌握
2.1 Tensor
2.1.1 热身：numpy
相信大家对numpy都不会陌生，我们直接来看代码吧
import numpy as np
#N is batch size;D_in isinput 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()
if t%100 == 99:
print(t,loss)
#backprop to compute gradients of w1 and w2 tith 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这里我们用numpy建立一个两层的网络并用产生的随机数组进行训练，初始化的权重w1，w2也是随机的，我们通过之后的不断的更新来逼近真实情况
两层神经网络
在单层线性网络的时候我们用的是类似f=wx+b的形式来训练网络，这样一个问题就是线性拟合不能很好解决问题，于是我们通过加网络层，或者理解为网络嵌套来把线性转为非线性，而我们这里用到的非线性函数就是relu函数
类似的，我们还可以加为三层四层等等，这就是所谓的全连接层网络，层数可以任意添加，
而理解了这个，代码中类似h = x.dot(w1)就好理解了
隐藏层
顾名思义，隐藏在输入和输出之间的网络层，例如这个里面的h就是一个隐藏层，也相当于中间处理，能够使结果更加准确
其他部分就和我们之前三个学习笔记里面提到的一样，步骤形式也大同小异
输出：
99 611.8403334325828
199 5.780260334791743
299 0.09678974435224459
399 0.0019321130866979581
499 4.126089452091746e-05可以看到到后面loss已经非常小了
2.1.2Pytorch：Tensor
我们之前也介绍过什么是tensor，其实也就和numpy array一样，但不同的是pytorch tensor可以在gpu上跑，速度更快，同样，我们用pytorch tensor来写一个两层的神经网络
import torch
dtype = torch.float
device = torch.device("cpu")
#device = torch.device("cuda:0")#Uncommrnt this to run on GPU
#N is batch size;D_in isinput 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
w1 -= learning_rate * grad_w1
w2 -= learning_rate * grad_w2输出：
99 688.8875122070312
199 4.103602886199951
299 0.04172804579138756
399 0.0007906379760242999
499 8.704190258868039e-05就不再多说什么了，没什么区别
2.2Autograd
2.2.1 pytorch：tensor and autograd
在前面我们手动码了forward和backward，但是在大的复杂的网络中这些全都要手码就崩了，因此我们有了autograd这个工具，前面有介绍过，接下来我们就看看结合autograd我们的两层网络该怎么写
import torch
dtype = torch.float
device = torch.device("cpu")
#device = torch.device("cuda:0")#Uncommrnt this to run on GPU
#N is batch size;D_in isinput 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, 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
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()
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 weight have requires_grad = True,but we don't need to track this
#in autograde
#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_()里面涉及的前面也都讲过
输出：
99 468.9629821777344
199 2.9594504833221436
299 0.023482277989387512
399 0.0004086267144884914
499 5.1561615691753104e-052.2.2Define new autograd functions
在pytorch我们可以通过定义一个子类torch.autograd.Function并完成forward和backward函数来很简单的定义我们自己的autograd操作，接下来我们定一个我们自己的relu函数并把它用在我们的two-layer网络：
import torch
class MyReLU(torch.autograd.Function):
@staticmethod
def forward(ctx, input):
ctx.save_for_backward(input)
return input.clamp(min=0)
@staticmethod
def backward(ctx, grad_output):
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")#Uncommrnt this to run on GPU
#N is batch size;D_in isinput 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, 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
relu = MyReLU.apply
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()
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 weight have requires_grad = True,but we don't need to track this
#in autograde
#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_()其中一般来说，要使用某个类的方法，需要先实例化一个对象再调用方法。而使用@staticmethod或@classmethod，就可以不需要实例化，直接类名.方法名()来调用。
输出：
99 664.2792358398438
199 3.2187328338623047
299 0.023685619235038757
399 0.00038831226993352175
499 4.969811925548129e-05这里后面讲的TensorFlow我就不写了，学完pytorch之后我还会去专门学习TensorFlow
2.3 nn.module
2.3.1 nn
nn中定义了一系列可以近似等同于神经网络层的modules，我们来看看用nn来完成tow-layer network：
import torch
#N is batch size;D_in isinput 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)
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 lossfunction.
loss_fn = torch.nn.MSELoss(reduction='sum')
learning_rate = 1e-4
for t in range(500):
#Forward pass:compute predicted y
y_pred = model(x)
#compute and print loss using operations on Tensors
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()
#this call will compute gradients for all learnable parameters in the model.
loss.backward()
with torch.no_grad():
for param in model.parameters():
param -= learning_rate*param.grad代码的注释比较详细，不多赘述
输出：
99 2.496163845062256
199 0.06094813346862793
299 0.003522129962220788
399 0.0002878477971535176
499 2.720016345847398e-052.3.2 optim
现在我们用optim中的Adam算法来优化模型
import torch
#N is batch size;D_in isinput 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)
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 lossfunction.
loss_fn = torch.nn.MSELoss(reduction='sum')
learning_rate = 1e-4
optimizer = torch.optim.Adam(model.parameters(),lr=learning_rate)
for t in range(500):
#Forward pass:compute predicted y
y_pred = model(x)
#compute and print loss using operations on Tensors
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 all the variables it will update.This is because by fault,gradients are
#accumulated in buffers whenever .backward() is called.
optimizer.zero_grad()
#this call will compute gradients for all learnable parameters in the model.
loss.backward()
#calling the step function on an Optimizer makes an updata to its parameters
optimizer.step()输出：
99 51.58766174316406
199 0.7978752851486206
299 0.0029272770043462515
399 9.20035017770715e-06
499 1.124239989991338e-08
别的不多说了，我们讲讲Adam吧，算法如下：
从while循环往下看，第一行是更新step， 第二行是计算梯度， 第三行计算一阶矩的估计，即mean均值 第四行计算二阶距的估计，即variance，和方差类似，都是二阶距的一种。 第五、六行则是对mean和var进行校正，因为mean和var的初始值为0，所以它们会向0偏置，这样处理后会减少这种偏置影响。 第七行是梯度下降。注意alpha后的梯度是用一阶距和二阶距估计的。
2.3.3 Custom nn Modules
其实就是把我们前面写的封装起来成为一个类
import torch
class TwoLayerNet(torch.nn.Module):
def __init__(self,D_in,H,D_out):
super(TwoLayerNet, self).__init__()
self.linear1 = torch.nn.Linear(D_in,H)
self.linear2 = torch.nn.Linear(H,D_out)
def forward(self, x):
h_relu = self.linear1(x).clamp(min=0)
y_pred = self.linear2(h_relu)
return y_pred
#N is batch size;D_in isinput 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)
y = torch.randn(N, D_out)
model = TwoLayerNet(D_in,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 lossfunction.
criterion = torch.nn.MSELoss(reduction='sum')
learning_rate = 1e-4
optimizer = torch.optim.SGD(model.parameters(),lr=learning_rate)
for t in range(500):
#Forward pass:compute predicted y
y_pred = model(x)
#compute and print loss using operations on Tensors
loss = criterion(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 all the variables it will update.This is because by fault,gradients are
#accumulated in buffers whenever .backward() is called.
optimizer.zero_grad()
#this call will compute gradients for all learnable parameters in the model.
loss.backward()
#calling the step function on an Optimizer makes an updata to its parameters
optimizer.step()2.3.4 Control Flow + Weight Sharing
在这里我们会在网络每个前向传递中选择1-4之间的随机数重复计算隐藏层中的参数，这里我们会发现在定义一个计算图时重复多次使用一个模型是非常安全的，这是相比于只能使用一次module的LuTorch是非常大的一个提升
import torch
import random
class TwoLayerNet(torch.nn.Module):
def __init__(self,D_in,H,D_out):
super(TwoLayerNet, 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):
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 isinput 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)
y = torch.randn(N, D_out)
model = TwoLayerNet(D_in,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 lossfunction.
criterion = torch.nn.MSELoss(reduction='sum')
learning_rate = 1e-4
optimizer = torch.optim.SGD(model.parameters(),lr=learning_rate)
for t in range(500):
#Forward pass:compute predicted y
y_pred = model(x)
#compute and print loss using operations on Tensors
loss = criterion(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 all the variables it will update.This is because by fault,gradients are
#accumulated in buffers whenever .backward() is called.
optimizer.zero_grad()
#this call will compute gradients for all learnable parameters in the model.
loss.backward()
#calling the step function on an Optimizer makes an updata to its parameters
optimizer.step()3.小结
这次的学习其实是对之前快速学习一个卷积网络的巩固，并且在细节方面有所加深，更加充分理解其中函数的作用以及层层递进从一个简单的网络到优化再到封装，进一步加强对于pytorch函数的理解和对框架的认知吧