K-FAC Laplace Evidence Is Boundary-Fragile: Detecting Fragile Model-Selection Boundaries from Approximate Curvature

The central finding is that K-FAC Laplace evidence can appear stable on broad model rankings while becoming fragile near evidence decision boundaries. In near-boundary comparisons, residual-induced evidence errors can reverse close decisions, and this fragility is governed by margin-relative error rather than by absolute approximation error alone.

The paper introduces a K-FAC-side Boundary Fragility Score for audit-oriented screening of close evidence comparisons. Using approximate-side margin and effective-dimension features, the score predicts fragile near-boundary comparisons under pair-grouped validation, with effective-dimension features adding signal beyond raw approximate margin. The score is intended as a benchmark-local warning rule for deciding when a K-FAC evidence comparison should be audited, refined, or treated cautiously, not as a universally calibrated deployment classifier.

Empirically, the study combines exact-block residual analysis, low-Kronecker-rank residual compression, broad-grid and near-boundary Laplace evidence tests, pair-clustered proxy validation, directionality robustness checks, and repair diagnostics. The results suggest that approximate curvature methods should be evaluated not only by global approximation quality, but also by whether their induced evidence errors can move close decision boundaries.

This version updates the manuscript for final polishing, clearer exposition, and consistency. The core results and conclusions remain unchanged. Code can be made available upon reasonable request.