3.8 A sketch as a model of learning

The declaration is not merely a convenient notation for a loss. It is the model that makes the learning process actionable. Its objects can represent data, representations, policies, modules, agents, arguments, or evidence states; its arrows represent the transformations through which learning is organized; and its equations and universal properties state which parts of that organization must remain coherent.

This shifts the role of modeling. In conventional causal inference, an SCM or SEM models mechanisms in an external domain and supports surgery on a designated mechanism. A learning sketch can include such a domain model, but it can also model the learner that constructs, compares, and repairs domain models. The resulting intervention target may be a parameter, a component morphism, an architectural route, an observation map, or the declaration itself.

The distinction matters because a repair cannot be licensed by location alone. A failed path identifies where the current declaration is not realized; it does not determine whether one should change a parameter, replace a mechanism, redraw the architecture, or revise the theory. Those choices belong to the repair language and admission contract attached to the sketch.