in mathematics

• softmax function (normalized exponential function)
  

• cross entropy
  

in pytorch

• NLLLoss
  

• cross entropy loss
  
  doc : This criterion combines nn.LogSoftmax() and nn.NLLLoss() in one single class.

import torch
import torch.nn.functional as F

output = torch.randn(3, 5, requires_grad=True)
target = torch.tensor([1, 0, 4])


y1 = F.cross_entropy(output,target)
y2 = F.nll_loss(F.log_softmax(output,dim=1), target)

# y1 == y2
print(y1)
print(y2)