Recover exact-score topology using covariance-based pilot selection

Determine whether a pilot selector that chooses rotation, bit width, and verification cutoff using covariance statistics alone can recover exact-score topology.

Background

The paper shows that global fidelity metrics do not reliably predict decision-level risk, while residual covariance and margin information are informative for ranking and pruning decisions. It therefore leaves unresolved whether covariance statistics alone are sufficient to select the rotation, bit width, and verification cutoff needed to preserve the topology induced by exact scores.

References

Whether the trace-length saturation boundary can be characterized from representation geometry alone; whether adaptive candidate sets (beam search) admit a martingale extension of the coupling argument; and whether a pilot selector choosing rotation, bit width, and verification cutoff from covariance statistics alone recovers exact-score topology.

— When Does Low-Bit Quantization Preserve the Decisions of Vector Search?  (2609.09854 - Xiao et al., 9 Sep 2026) in Section 8, Discussion: Practical Guidance, paragraph “Open directions”