Learning Transfers: Kan Extensions for Neural Invariants

תקציר מקורי באנגליתarXiv:2606.07627v2 Announce Type: replace Abstract: Transfer learning presumes that a representation learned on a source task carries structure that remains usable on a related target task. Standard evaluations probe this through target accuracy or a distributional discrepancy, without stating which structural invariant should survive the change of task. We make that invariant explicit and computable. We model a task as a small category: its objects are the task's components, such as data domains or class labels, and its morphisms are the admissible relations between them, such as the comparison of a coarse class with a fine class refining it. A change of task is a functor $J:\mathcal A\to\mathcal B$ from the source task category to the target task category, recording where each component