arXiv:2610.02894v1 Announce Type: cross
Abstract: Match only geometry you can identify; otherwise spread the penalty. We quantify that decision by the trust ratio tau = epsilon / gamma (estimation uncertainty over spectral separation). Under the linear-quadratic Matching response, oracle-relative drift between estimated and oracle projector matching scales as tau^2 for probes in the chosen top-r deployment subspace — O(tau^2) in the Davis-Kahan separation region tau < 1/2, with practical usefulness depending on constants. Confidence-Calibrated Matching (CCM) turns tau into a policy — directional when tau is small, progressively isotropic when not — with thresholds from calibration, not from the theorem (match sits in the separation region; soft is mostly heuristic). Experiments show both regimes, including UCI HAR embeddings where always-match is worse than abstain on every cell.
Abstract: Match only geometry you can identify; otherwise spread the penalty. We quantify that decision by the trust ratio tau = epsilon / gamma (estimation uncertainty over spectral separation). Under the linear-quadratic Matching response, oracle-relative drift between estimated and oracle projector matching scales as tau^2 for probes in the chosen top-r deployment subspace — O(tau^2) in the Davis-Kahan separation region tau < 1/2, with practical usefulness depending on constants. Confidence-Calibrated Matching (CCM) turns tau into a policy — directional when tau is small, progressively isotropic when not — with thresholds from calibration, not from the theorem (match sits in the separation region; soft is mostly heuristic). Experiments show both regimes, including UCI HAR embeddings where always-match is worse than abstain on every cell.
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