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.

Definition 4.6 Tangent site

A tangent site for a realized learning sketch specifies:

  1. the admissible base points or regimes;

  2. the admissible tangent directions at each object;

  3. how directions are transported along sketch arrows;

  4. the cover over which tangent obstructions are observed; and

  5. 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.

Boundary

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.