8. 损失函数与反向传播

8.1 损失函数

① Loss损失函数一方面计算实际输出和目标之间的差距。

② Loss损失函数另一方面为我们更新输出提供一定的依据。

8.2 L1loss损失函数 

 ① L1loss数学公式如下图所示，例子如下下图所示。

import torch
from torch.nn import L1Loss
inputs = torch.tensor([1,2,3],dtype=torch.float32)
targets = torch.tensor([1,2,5],dtype=torch.float32)
inputs = torch.reshape(inputs,(1,1,1,3))
targets = torch.reshape(targets,(1,1,1,3))
loss = L1Loss()  # 默认为 maen
result = loss(inputs,targets)
print(result)

结果：

tensor(0.6667)

import torch
from torch.nn import L1Loss
inputs = torch.tensor([1,2,3],dtype=torch.float32)
targets = torch.tensor([1,2,5],dtype=torch.float32)
inputs = torch.reshape(inputs,(1,1,1,3))
targets = torch.reshape(targets,(1,1,1,3))
loss = L1Loss(reduction='sum') # 修改为sum，三个值的差值，然后取和
result = loss(inputs,targets)
print(result)

结果：

tensor(2.)

8.3  MSE损失函数

 ① MSE损失函数数学公式如下图所示。

 

import torch
from torch.nn import L1Loss
from torch import nn
inputs = torch.tensor([1,2,3],dtype=torch.float32)
targets = torch.tensor([1,2,5],dtype=torch.float32)
inputs = torch.reshape(inputs,(1,1,1,3))
targets = torch.reshape(targets,(1,1,1,3))
loss_mse = nn.MSELoss()
result_mse = loss_mse(inputs,targets)
print(result_mse)

结果：

tensor(1.3333)

 8.4 交叉熵损失函数

① 交叉熵损失函数数学公式如下图所示。

 

 

import torch
from torch.nn import L1Loss
from torch import nn

x = torch.tensor([0.1,0.2,0.3])
y = torch.tensor([1])
x = torch.reshape(x,(1,3)) # 1的 batch_size，有三类
loss_cross = nn.CrossEntropyLoss()
result_cross = loss_cross(x,y)
print(result_cross)

结果：

tensor(1.1019)

 8.5 搭建神经网络

import torch
import torchvision
from torch import nn 
from torch.nn import Conv2d, MaxPool2d, Flatten, Linear, Sequential
from torch.utils.data import DataLoader
from torch.utils.tensorboard import SummaryWriter

dataset = torchvision.datasets.CIFAR10("./dataset",train=False,transform=torchvision.transforms.ToTensor(),download=True)       
dataloader = DataLoader(dataset, batch_size=1,drop_last=True)

class Tudui(nn.Module):
    def __init__(self):
        super(Tudui, self).__init__()        
        self.model1 = Sequential(
            Conv2d(3,32,5,padding=2),
            MaxPool2d(2),
            Conv2d(32,32,5,padding=2),
            MaxPool2d(2),
            Conv2d(32,64,5,padding=2),
            MaxPool2d(2),
            Flatten(),
            Linear(1024,64),
            Linear(64,10)
        )
        
    def forward(self, x):
        x = self.model1(x)
        return x
    
tudui = Tudui()
for data in dataloader:
    imgs, targets = data
    outputs = tudui(imgs)
    print(outputs)
    print(targets)

结果：

 8.6 数据集计算损失函数

 

import torch
import torchvision
from torch import nn 
from torch.nn import Conv2d, MaxPool2d, Flatten, Linear, Sequential
from torch.utils.data import DataLoader
from torch.utils.tensorboard import SummaryWriter

dataset = torchvision.datasets.CIFAR10("./dataset",train=False,transform=torchvision.transforms.ToTensor(),download=True)       
dataloader = DataLoader(dataset, batch_size=64,drop_last=True)

class Tudui(nn.Module):
    def __init__(self):
        super(Tudui, self).__init__()        
        self.model1 = Sequential(
            Conv2d(3,32,5,padding=2),
            MaxPool2d(2),
            Conv2d(32,32,5,padding=2),
            MaxPool2d(2),
            Conv2d(32,64,5,padding=2),
            MaxPool2d(2),
            Flatten(),
            Linear(1024,64),
            Linear(64,10)
        )
        
    def forward(self, x):
        x = self.model1(x)
        return x
    
loss = nn.CrossEntropyLoss() # 交叉熵    
tudui = Tudui()
for data in dataloader:
    imgs, targets = data
    outputs = tudui(imgs)
    result_loss = loss(outputs, targets) # 计算实际输出与目标输出的差距
    print(result_loss)

结果：

 8.7 损失函数反向传播

① 反向传播通过梯度来更新参数，使得loss损失最小，如下图所示。

 

import torch
import torchvision
from torch import nn 
from torch.nn import Conv2d, MaxPool2d, Flatten, Linear, Sequential
from torch.utils.data import DataLoader
from torch.utils.tensorboard import SummaryWriter

dataset = torchvision.datasets.CIFAR10("./dataset",train=False,transform=torchvision.transforms.ToTensor(),download=True)       
dataloader = DataLoader(dataset, batch_size=64,drop_last=True)

class Tudui(nn.Module):
    def __init__(self):
        super(Tudui, self).__init__()        
        self.model1 = Sequential(
            Conv2d(3,32,5,padding=2),
            MaxPool2d(2),
            Conv2d(32,32,5,padding=2),
            MaxPool2d(2),
            Conv2d(32,64,5,padding=2),
            MaxPool2d(2),
            Flatten(),
            Linear(1024,64),
            Linear(64,10)
        )
        
    def forward(self, x):
        x = self.model1(x)
        return x
    
loss = nn.CrossEntropyLoss() # 交叉熵    
tudui = Tudui()
for data in dataloader:
    imgs, targets = data
    outputs = tudui(imgs)
    result_loss = loss(outputs, targets) # 计算实际输出与目标输出的差距
    result_loss.backward()  # 计算出来的 loss 值有 backward 方法属性，反向传播来计算每个节点的更新的参数。这里查看网络的属性 grad 梯度属性刚开始没有，反向传播计算出来后才有，后面优化器会利用梯度优化网络参数。      
    print("ok")