2 Learning by Repair

Machine learning usually begins with a scalar objective. A model makes a prediction, the objective reports an error, and optimization changes the parameters. This pattern is powerful, but it suppresses a prior question: what structural promise did the model fail to keep?

¹1. The LINCS viewpoint does not discard task loss. It asks which typed failure the loss is observing, and whether that failure licenses the proposed update. ↩

In many systems the important promise is compositional. Two routes through a model should agree; local sections should glue; an update should preserve a decision; a preference field should integrate; a skill should remain executable after composition. A scalar loss may witness these failures, but it does not by itself preserve their type or location.

LINCS keeps the failed diagram visible. A problem is declared as a learning sketch. Its candidate model is tested for a factorization, limit, colimit, descent, closure, or realization property. Failure produces an obstruction. The obstruction is then differentiated, quotiented by irrelevant variation, localized over a computational cover, and connected to a guarded repair.