[Submitted on 9 Sep 2026 (v1), last revised 11 Nov 2026 (this version, v2)]
Abstract:An orthogonal rotation improves the distance rank correlation of two-bit Cohere codes from 0.75 to 0.91, yet increases nearest-neighbour comparison flips by 51%. We analyse quantization through the comparisons made by graph search. A comparison changes only when its quantization error exceeds its exact margin, giving a flip bound that separates close calls from large errors. Shared endpoints induce correlated distance errors that partly cancel within a comparison. An exact replay identity connects candidate-level actions to the output of neighbour selection. A Gaussian model gives coordinate-code errors in closed form, and a rare-spike construction exposes heavy tails in the population-radius error. Held-out blocks give model-free certificates for acceptance rules based on exact or quantized margins. Across 24 dataset-code configurations, calibration-estimated risk correlates with held-out ranking and pruning flips at 0.97 and 0.99, compared with 0.91 and 0.99 for a margin-to-noise summary and 0.74 and 0.05 for distance rank correlation. Paired builds of 200,000-vector graphs connect rotation, query scoring, and topology to end-to-end recall and search work.
Submission history
From: Wenxuan Xiao [view email]
[v1] Wed, 9 Sep 2026 08:06:50 UTC (50 KB)
[v2] Wed, 11 Nov 2026 14:23:38 UTC (1,141 KB)
