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Life sciences · Preprint
arXiv · September 9, 2026
Raises a question worth testing. It does not answer one.
This preprint develops a distribution-free theoretical framework to predict when low-bit quantization preserves vector search ranking and graph-pruning decisions, grounded in exact margin distributions and calibrated residual tails. The authors show that standardized exact margins outperform global rank correlation as a predictor of quantization-induced decision flips and introduce a held-out block certificate for bounding selective failure risk. The work is foundational but lacks peer review and does not address real-world retrieval accuracy or user outcomes.
Theoretical analysis with empirical validation across multiple embedding types and quantization methods. Learned, classical, and synthetic vector embeddings; multiple quantization schemes including coordinate binary codes, RaBitQ, Lucene BBQ, and product quantizers.. Intervention: Low-bit quantization applied to vector representations. Compared with: Exact (unquantized) vector search decisions; global rank correlation as diagnostic.
Probability that a comparison flips is bounded by probability mass of exact margins near zero plus tail probability of calibrated residual Standardized exact margins predict held-out ranking and pruning flip rates substantially better than global rank correlation Deterministic coupling theorem for Vamana neighbour selection: approximate replay returns exact neighbour list when all candidate-level pruning actions agree on frozen exact states
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A theoretical and empirical study of quantization effects on vector search decisions, developing mathematical bounds and diagnostic tools but lacking clinical or practice-outcome validation.
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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.
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