RSD: A Local Triangulation Audit Primitive for Learned Vector Blocks

Abstract

Local XAI audits compare a finite block of learned vectors with a weak side signal. Baselines such as nearest-neighbor lookup, low-rank coordinate models, and relation factorization expose different parts of this audit. We introduce Relational Semantic Decomposition, abbreviated as RSD, as a local triangulation audit for learned vector blocks. Given coordinates X and a declared bounded weak affinity proxy A, RSD fits simplex memberships S and coordinate poles C. It reuses S in a relation decoder for A and reports the coordinate residual R=X-SC. This yields a scoped audit unit: compatibility for the chosen block, proxy, decoder class, and loss budget, plus component mass and residual readouts. Synthetic controls check simplex reconstruction, proxy decoding, and fixed-S residual decomposition. The theorem-statement, month, and dog/wolf blocks illustrate why low proxy loss should be read with component mass, residual readouts, and block size.