使用Pytorch框架进行深度学习任务，特别是分类任务时，经常会用到如下：

import torch.nn as nn
criterion = nn.CrossEntropyLoss().cuda()
loss = criterion(output, target)

即使用torch.nn.CrossEntropyLoss()作为损失函数。

那nn.CrossEntropyLoss()内部到底是啥？？

nn.CrossEntropyLoss()是torch.nn中包装好的一个类，对应torch.nn.functional中的cross_entropy。
此外，nn.CrossEntropyLoss()是nn.logSoftmax()和nn.NLLLoss()的整合(将两者结合到一个类中)。

nn.logSoftmax()

定义如下：

从公式看，其实就是先softmax在log。

nn.NLLLoss()

定义如下：

此loss期望的target是类别的索引 (0 to N-1, where N = number of classes)。

例子1：

import torch.nn as nn
 m = nn.LogSoftmax()
 loss = nn.NLLLoss()
 # input is of size nBatch x nClasses = 3 x 5
 input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
 # each element in target has to have 0 <= value < nclasses
 target = autograd.Variable(torch.LongTensor([1, 0, 4]))
 output = loss(m(input), target)

可以看到，nn.NLLLoss的输入target是类别值，并不是one-hot编码格式，这个要注意！！

nn.CrossEntropyLoss()

定义如下：

仔细看看公式，发现其实它就是nn.LogSoftmax() + nn.NLLLoss()
调用时输入参数如下：

• input : 模型输出，包含每个类的得分，2-D tensor,shape为 batch * n类
• target: 大小为 n 的 1—D tensor，包含类别的索引(0到 n-1)。
  注意CrossEntropyLoss()的target输入也是类别值，不是one-hot编码格式

例子2：

import torch.nn as nn
 loss = nn.CrossEntropyLoss()
 # input is of size nBatch x nClasses = 3 x 5
 input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
 # each element in target has to have 0 <= value < nclasses
 target = autograd.Variable(torch.LongTensor([1, 0, 4]))
 output = loss(input, target)

例子1和例子2结果等价

如果是one-hot编码该怎么计算loss？

for images, target in train_loader:
    images, target = images.cuda(), target .cuda()
    N = target .size(0)
    # N 是batch-size大小
    # C is the number of classes.
    labels = torch.full(size=(N, C), fill_value=0).cuda()
    labels.scatter_(dim=1, index=torch.unsqueeze(target, dim=1), value=1)

    score = model(images)
    log_prob = torch.nn.functional.log_softmax(score, dim=1)
    loss = -torch.sum(log_prob * labels) / N
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

其中C是类别数目，labels是one-hot编码格式的二维向量（2-D tensor）。
需要先将例子1,2的target转为one-hot形式labels。
该loss计算可以替代例子1和例子2的loss计算方式

上述计算案例如下：

import torch.nn as nn
import torch
from torch import autograd
import torch.nn.functional as F
# logsoft-max + NLLLoss
m = nn.LogSoftmax()
loss = nn.NLLLoss()
input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
target = autograd.Variable(torch.LongTensor([1, 0, 4]))
output = loss(m(input), target)
print('logsoftmax + nllloss output is {}'.format(output))

# crossentripyloss
loss = nn.CrossEntropyLoss()
# input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
target = autograd.Variable(torch.LongTensor([1, 0, 4]))
output = loss(input, target)
print('crossentropy output is {}'.format(output))


# one hot label loss
C = 5
target = autograd.Variable(torch.LongTensor([1, 0, 4]))
print('target is {}'.format(target))
N = target .size(0)
# N 是batch-size大小
# C is the number of classes.
labels = torch.full(size=(N, C), fill_value=0)
print('labels shape is {}'.format(labels.shape))
labels.scatter_(dim=1, index=torch.unsqueeze(target, dim=1), value=1)
print('labels is {}'.format(labels))

log_prob = torch.nn.functional.log_softmax(input, dim=1)
loss = -torch.sum(log_prob * labels) / N
print('N is {}'.format(N))
print('one-hot loss is {}'.format(loss))

结果如下：

logsoftmax + nllloss output is 3.005390167236328
crossentropy output is 3.005390167236328
target is tensor([1, 0, 4])
labels shape is torch.Size([3, 5])
labels is tensor([[0., 1., 0., 0., 0.],
        [1., 0., 0., 0., 0.],
        [0., 0., 0., 0., 1.]])
N is 3
one-hot loss is 3.005390167236328

可知相同的输入下全部等价。

补充：

以及关于cross entropy有关的函数及在torch.nn和torch.nn.functional中对应关系如下：

torch.nn和torch.nn.functional的区别在于torch.nn中对应的函数其实就是对F里的函数进行包装的类。

参考

https://www.jianshu.com/p/6049dbc1b73f
https://www.cnblogs.com/marsggbo/p/10401215.html
https://pytorch-cn.readthedocs.io/zh/latest/package_references/torch-nn/#loss-functions
https://blog.csdn.net/dss_dssssd/article/details/84036913