CrossEntropy but for values lower than 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?

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