lin-0067
4.6 Probe semantics
An automatic-differentiation system can produce many directional derivatives. LINCS requires the tangent site to say what those directions mean.
A tangent site for a realized learning sketch specifies:
the admissible base points or regimes;
the admissible tangent directions at each object;
how directions are transported along sketch arrows;
the cover over which tangent obstructions are observed; and
the null, gauge, or decision-invariant directions to be quotiented.
Examples include perturbations of tokens versus parameters, interventions versus domain shifts, policy directions versus advantage baselines, and semantic paraphrases versus warrant-changing argument edits. The derivative operator alone does not distinguish them.
A parameter gradient is not automatically a semantic tangent direction. A map from parameter perturbations to deformations of the declared diagram must be specified and, when repair is claimed, shown to be sufficiently identified.