3 Learning Sketches and Factorization Obstructions

A loss tells us that a model is wrong by some amount. A learning sketch first tells us what kind of agreement the model promised. It records the objects and operations of the problem, the paths intended to agree, and any limit or colimit properties the candidate model must realize. This declaration turns non-compositionality into a typed factorization failure before a norm, likelihood, or empirical statistic is chosen.

¹1. Sketches originate in categorical logic and model theory. Here they serve as compact, machine-readable declarations of learning structure [ Ehresmann , 1968 , Barr and Wells , 1999 ] . ↩