Bayes-Sufficient Representations in Supervised Learning 文章

arXiv:2606.04045v1 Announce Type: cross Abstract: Representation learning is often described as preserving the information in an input that is relevant for prediction. This work asks what relevance means for a fixed supervised decision problem. A representation is defined to be Bayes-sufficient for a joint distribution and loss if some prediction head can use it to implement a Bayes-optimal action rule. This makes the target information loss-dependent. In the almost-surely unique Bayes-action case, the relevant object is a Bayes quotient, which identifies inputs that require the same Bayes-optimal action. A representation is sufficient when it refines this quotient, and Bayes-minimal when it is informationally equivalent to it.