发表机构
Astrmira Tech.（阿斯特米拉科技公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究低比特量化对向量搜索决策的影响，提出分布无关分解和协方差感知尾部界，证明Vamana邻居选择的确定性耦合定理，并发现标准化精确边距能更好预测翻转率，适用于多种量化方法。
AI 中文摘要
低比特量化在某些向量表示上能实现高召回率，但在其他表示上则可能严重失效，而平均失真和全局秩相关无法解释这种差异。我们从排序和图剪枝算法所消耗的比较层面研究量化向量搜索。我们的第一个结果是分布无关的分解：比较翻转的概率受近零精确边距的概率质量加上校准残差的尾部概率的约束。然后，我们考虑共享查询或图节点的残差之间的依赖性，并在联合矩生成函数代理下推导出协方差感知的二阶矩恒等式和尾部界。对于冻结的候选排列，我们证明了Vamana邻居选择的确定性耦合定理：当所有候选级剪枝动作在冻结的精确状态上一致时，近似重放恰好返回精确邻居列表。我们通过精确高斯预言机将这些结果与表示几何联系起来，在对齐双线性模型中建立了确定性幅度比特的严格相关性增益，并给出一个罕见污染构造，说明为什么边际高斯诊断不意味着所需的残差尾部。当解析假设不可用时，保留块证书限制了冻结量化规则的选择性失败风险。在学习、经典和合成嵌入中，标准化精确边距预测保留的排序和剪枝翻转率明显优于全局秩相关。该框架通过通用决策接口适用于坐标二进制码、RaBitQ、Lucene BBQ和乘积量化器。
英文摘要
Low-bit quantization can achieve high recall on some vector representations and fail sharply on others, while average distortion and global rank correlation do not explain the difference. We study quantized vector search at the level of the comparisons consumed by ranking and graph-pruning algorithms. Our first result is a distribution-free decomposition: the probability that a comparison flips is bounded by the probability mass of exact margins near zero plus the tail probability of the calibrated residual. We then account for dependence between residuals that share a query or graph node, and derive covariance-aware second-moment identities and tail bounds under a joint MGF proxy. For a frozen candidate permutation, we prove a deterministic coupling theorem for Vamana neighbour selection: the approximate replay returns the exact neighbour list exactly when all candidate-level pruning actions agree on the frozen exact states. We connect these results to representation geometry through an exact Gaussian oracle, establish a strict correlation gain from a deterministic magnitude bit in an aligned bilinear model, and give a rare-contamination construction showing why marginal Gaussian diagnostics do not imply the required residual tails. When analytical assumptions are unavailable, a held-out block certificate bounds the selective failure risk of a frozen quantized rule. Across learned, classical, and synthetic embeddings, standardized exact margins predict held-out ranking and pruning flip rates substantially better than global rank correlation. The framework applies to coordinate binary codes, RaBitQ, Lucene BBQ, and product quantizers through a common decision interface.
CommentsJMLR-style preprint with theoretical and experimental appendices
