CrossEntropy but for values lower than 1

1

I want to train a network that predicts the typical single-class classification, normally optimized using CrossEntropyLoss, but for which the ouput of the predicted class should try to be specific values <= 1.

An example: for a given training sample X of class 1, the intended predicted ouput might not be [1 0 0], but specifically [0.8 0 0]. X2 of class 3 might have an intended predicted ouput of [0.6 0 0].

I’m thinking of making a custom modified version of crossentropy loss to fit these needs. Before I try to, does anything jump to mind that could be appropriate?

2

This sounds like label smoothing and you could maybe use the implementation from this topic.
Let me know, if that would work for you.