Softmax isn't a loss function. It is used to transform model outputs into positive numbers that sum to 1, so that they can be interpreted as probabilities, and then those numbers are passed into (typically) the cross entropy loss function. I think you mean, which models are trained using some function other than softmax to transform the model outputs. There are a number of alternatives to softmax, such as the ones described here https://www.emergentmind.com/topics/sparsemax
replyThe cross entropy loss function is softmax. They are one and the same.
replyThey’re not. Cross entropy loss is E[-log q] where q is a probability. You could convert the model outputs x into probabilities using some other function like q = 1/Z x^2, and compute cross entropy loss just fine.
replyBehold the softmax: https://docs.pytorch.org/docs/2.11/generated/torch.nn.CrossE...
replyBehold the actual definition of cross entropy: https://en.wikipedia.org/wiki/Cross-entropy
replyIt's true that the PyTorch API conflates cross entropy and softmax, but they are separate concepts.