lin-0122

9.5 Repair as structural surgery

The repair language makes a learning sketch actionable in the same broad sense that a causal model is actionable. A causal intervention replaces a target mechanism while invoking a modularity assumption for the mechanisms not targeted. A LINCS repair similarly specifies an edit together with the obligations it promises to preserve.

Definition 9.9 Structural intervention

A structural intervention on an actionable learning model \(\mathfrak L=(\mathbb S,D,\Lambda ,\mathcal R,\mathcal A)\) is an edit

\[ e:(\mathbb S,D)\longrightarrow (\mathbb S_e,D_e) \]

equipped with:

  1. a typed target in the realization or declaration;

  2. an explicit class of non-target objects, arrows, equations, observers, and admission blocks to be preserved;

  3. a propagation rule producing the candidate repaired behavior; and

  4. a registered validation protocol, using evidence independent of the proposal signal, that must be evaluated before admission.

Four common cases form a hierarchy:

\[ \begin{array}{rcl} \text{parameter} & :& D\mapsto D’ \text{ inside a fixed realization class},\\ \text{component} & :& f\mapsto f’ \text{ for a selected module or morphism},\\ \text{architecture} & :& \mathbb S\mapsto \mathbb S’ \text{ with changed routes or covers},\\ \text{declaration} & :& \mathbb S\hookrightarrow \mathbb S^+ \text{ with new generators or axioms}. \end{array} \]

Each higher level enlarges what can be repaired and also what must be revalidated. Parameter repair can often be tested inside a fixed sketch. Declaration repair must transport prior evidence, preserve the successful fragment of the old theory, and face observations capable of distinguishing the augmented declaration from its predecessor.

The phrase structural surgery marks the methodological inheritance from causal inference, not an automatic causal interpretation. When the edited morphism denotes a causally grounded mechanism, the repair may realize an intervention in Pearl’s sense. When it denotes an adapter, reward representation, warrant, or cover, it is an intervention on the learning system. The categorical typing is shared; the causal semantics is not.

Boundary

A typed edit becomes a causal intervention only through an explicit mechanism model and realizable intervention protocol. LINCS supplies an actionable structural model and invariant-preservation obligations; it does not supply causal meaning merely by naming an edit “surgery.”