8.11 Scaling and implementation choices

A naive all-path, all-direction audit is unnecessary. Practical Deep LINCS uses the locality already present in the sketch:

• generate a relation basis rather than enumerate every equivalent path;

• localize obstructions to the smallest subdiagrams that witness them;

• use Jacobian–vector and vector–Jacobian products instead of materialized Jacobians;

• sample sparse interaction probes from the declared signature;

• cache shared prefixes and suffixes of compared paths; and

• separate training-time observers from slower admission-time audits.

If there are \(R\) local relation generators and \(K\) admitted probes, the audit should scale with the evaluated local modules and approximately with \(RK\), not with the number of all global path pairs. Chapter 9 develops the localization and admission mechanisms that make this possible.