nll_loss

'''
    torch.nn         torch.nn.functional (F)
CrossEntropyLoss         cross_entropy
   LogSoftmax             log_softmax
   NLLLoss                 nll_loss

'''

import torch
import torch.nn.functional as F

input=torch.randn(3,4)
label=torch.tensor([0,2,1])
print("input",input)

softmax=F.softmax(input,dim=1)
print("softmax",softmax)

log_softmax=F.log_softmax(input,dim=1)
print("log_softmax",log_softmax)

loss_nll=F.nll_loss(log_softmax,label)
print("loss_nll",loss_nll)

loss_cross=F.cross_entropy(input,label)
print("loss_cross",loss_cross)

'''
input tensor([[ 0.0363,  0.1419,  2.1639,  1.5429],
        [-0.6606, -0.0991, -0.6160, -2.4418],
        [-1.1279, -1.5333, -0.2142,  0.8669]])
softmax tensor([[0.0666, 0.0740, 0.5590, 0.3004],
        [0.2521, 0.4419, 0.2636, 0.0425],
        [0.0869, 0.0579, 0.2166, 0.6386]])
log_softmax tensor([[-2.7092, -2.6036, -0.5816, -1.2026],
        [-1.3781, -0.8166, -1.3335, -3.1592],
        [-2.4433, -2.8488, -1.5296, -0.4485]])
loss_nll tensor(1.4971)
loss_cross tensor(1.4971)

0.0363 0.1419 2.1639 1.5429
-0.6606    -0.0991    -0.616 -2.4418
-1.1279    -1.5333    -0.2142    0.8669

dim=0
exp                                 sum
1.0370     1.1525     8.7050     4.6781     15.57258663
0.5165     0.9057     0.5401     0.0870     2.049298083
0.3237     0.2158     0.8072     2.3795     3.726244435

softmax
0.0666     0.0740     0.5590     0.3004
0.2521     0.4419     0.2636     0.0425
0.0869     0.0579     0.2166     0.6386 

log_softmax
-2.7092    -2.6036    -0.5816    -1.2026
-1.3781    -0.8166    -1.3335    -3.1593
-2.4433    -2.8487    -1.5296    -0.4485 

1.0370=exp(0.0363)
0.0666=1.0370/15.57258663
-2.7092=ln(0.0666)
1.497070103=abs(-2.7092-1.3335-0.44850/3

'''