# How to understand a large result of torch.nn.NLLLoss() with correct predicts?

I'm learning the usage of torch.nn.NLLLoss() and torch.nn.LogSoftmax(), and I'm confused about the results of them.

For example:

lsm = torch.nn.LogSoftmax(dim=-1)
nll = nn.NLLLoss()

grnd_truth = torch.tensor()
# let's say it predicted correctly!!!
raw_logits = torch.tensor([[0.3665, 0.5542, -1.0306]])

logsoftmax = lsm(raw_logits)
final_loss = nll(logsoftmax, grnd_truth)

logsoftmax:
>>> tensor([[-0.8976, -0.7099, -2.2947]])
final_loss:
>>> tensor(0.7099)    # Is it normal getting so large loss when predicted correctly?

# let's try a incorrect prediction
grnd_truth = torch.tensor()
nll(lsm(raw_logits), grnd_truth)
>>> tensor(0.8976)    # Is this not enough large?


Obviously, we can see that the mis-classified loss is not large enough, comparing to the loss of a correctly classifing that is near to former.

I read the docs of NLLLoss, and I know its formula. I guessed that the designers must have their reasons to use the formula, but I didn't have gotten it.

In the fact, the reason of I posting this question, is that I encountered a difficulty to train a triple-classification module with NLLLoss() andLogSoftmax().

Is the goal of a lossing func that make the loss as small as possible when the prediction is right, and vice versa?

The equivalent formula in TensorFlow is the Categorical Cross Entropy or Sparse Categorical Cross Entropy.

https://www.tensorflow.org/api_docs/python/tf/keras/losses/CategoricalCrossentropy

https://www.tensorflow.org/api_docs/python/tf/keras/losses/SparseCategoricalCrossentropy

Maybe it could describe better the aim of the formula.

As far as I know, it is mainly used to apply multi-class classification on large datasets automatically with labels or integer targets.

https://github.com/christianversloot/machine-learning-articles/blob/main/how-to-use-sparse-categorical-crossentropy-in-keras.md

Note: Pytorch just uses Log probabilities, whereas TensorFlow doesn't.