evaluation-geometry-predicts-editability

OUT derived (depth 4)

Created 2026-08-25T03:10:25+00:00 · Reviewed 2026-08-25T04:02:18+00:00

The convergence of evaluation geometry (cosine/Spearman in SBERT/MTEB) and editing geometry (covariance whitening in ROME) on the same second-moment structure means that improving evaluation alignment and enabling reliable editing are two operational views of the same geometric optimization over the residual-stream covariance.

Justifications

SL — The evaluation side (cosine→Spearman as geometry probe) and the editing side (rank-one updates bounded by covariance) must both be present to recognize they are the same object; this bridges the SBERT/MTEB and ROME research communities.

Antecedents (all must be IN):

IN evaluation-geometry-convergence — The convergence of embedding evaluation (cosine → Spearman correlation in SBERT/MTEB) and internal geometry analysis (covariance whitening in ROME, polytope geometry in Park) on the same second-moment structure reveals that standard benchmark evaluation is measuring the same geometric quantity that governs internal feature organization—evaluation and analysis are two readouts of one space.
OUT geometric-editing-addressability-bound — The covariance-geometry framework defines a precise and minimal addressable space for knowledge editing (rank-one updates to a single MLP value projection), but the combination of superposition and distributed corpus acquisition structurally bounds this to single-fact local corrections—edits cannot create novel multi-hop associations because the target knowledge was never locally consolidated in the first place.

Dependents

These beliefs depend on this one:

OUT evaluation-geometry-is-editing-coordinate-system — The optimal evaluation metric for an embedding model (cosine/Spearman pipeline) is simultaneously the optimal coordinate system for specifying knowledge edits, because both are readouts of the same universal covariance geometry
OUT geometry-as-universal-semantic-currency — The covariance geometry is the single operational definition of "meaning" in LLMs, simultaneously determining what can be measured (evaluation via cosine/Spearman), what can be modified (rank-one editing via C⁻¹k*), what converges across architectures (SAE/Park universality), and what is hierarchically structured (feature neighborhoods as theorem instantiations)—making it a model-independent semantic currency rather than an architecture-specific artifact.
OUT mteb-no-dominant-model-as-geometric-signature — MTEB's observation that no single embedding model dominates all eight tasks is the expected geometric signature of a shared canonical semantic space probed by task-specific linear readouts, and the same second-moment structure that generates this task-specificity pattern is precisely what makes rank-one knowledge editing possible.