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Block Sphere Vector Quantization

NeurIPS 2026 · Architectures and efficiency › Quantization · approach: Post-training weight quantization · 0 citations (OpenAlex)

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Compares rotation-based quantizers (EDEN, RaBitQ, TurboQuant) under MSE, expected inner-product, and high-probability criteria, then proposes Block-Sphere Quantization, which quantizes p-dimensional blocks of randomly rotated vectors with the exact block marginal, improving MSE and inner-product constants.

Problem

Rotation-based vector quantizers (EDEN, RaBitQ, TurboQuant) are guaranteed under different distortion criteria and assumptions, making their comparison hard; existing coordinate-wise codebooks ignore the spherical geometry of rotated unit vectors.

Approach

Group coordinates of randomly rotated unit vectors into small blocks and build a block codebook from the exact Euclidean-ball marginal induced by the sphere (no data-learned codebook), with ratio-style rescaling for MSE or unbiased inner-product estimation.

Key results

• BQ (p=3) unbiased inner-product constant at 1-bit 0.553/(d-1) vs EDEN 0.571/(d-1) and TurboQuant-prod ~1.57/d (approximate, theory).
• On LongBench-E with Llama-3.1-8B-Instruct at ~3.5-bit key cache, BQ averages 44.03 vs EDEN 43.87, RaBitQ 43.52, TurboQuant 43.20 (full cache 44.15).
• On Needle-In-A-Haystack, BQ scores 0.962 vs EDEN 0.953, RaBitQ 0.944, TurboQuant 0.933 (full cache 0.965).

Surprising findings

• Authors claim a corrected Shannon lower bound with exponent bd/(d-1) rather than b, since the unit sphere has intrinsic dimension d-1.
• The gain of BQ over EDEN in KV-cache experiments is small (about 0.16 average points on LongBench-E).

Limitations

• Exact nearest-centroid assignment cost grows as 2^(bp); experiments use a lookup-table approximation of the codebook search.
• Improvements over baselines are small in constants (e.g., p=2 MSE 0.108 vs 0.117 at 2 bits), and KV-cache gains are within a few tenths of a point.

Experimental setup

Datasets: DBpedia Entities GloVe OpenAI3 DBpedia Needle-In-A-Haystack LongBench-E

Benchmarks: DBpedia Entities reconstruction MSE GloVe OpenAI3 DBpedia Needle-In-A-Haystack LongBench-E

Metrics: reconstruction MSE inner-product error Recall@1@k NIAH score LongBench-E average score

Baselines: EDEN RaBitQ TurboQuant

Builds on: EDEN RaBitQ TurboQuant product quantization QJL

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