VQ-bench: A Composable Vector Quantization Framework

Vector quantization is a fundamental tool for compressing high-dimensional embeddings, yet existing multi-codebook methods rely on static codebooks that limit expressiveness under heterogeneous data geometry. While recent dynamic quantizers like QINCo adapt codebooks to individual inputs and improve expressiveness, their strict sequential dependencies create decoding bottlenecks. We propose Residual Quantization via Mixture of Experts (RQ-MoE), a framework combining a two-level MoE with dual-stream quantization to enable input-dependent codebook adaptation for efficient vector quantization. RQ-MoE enables dynamic codebook construction and decouples instruction from quantization, facilitating parallel decoding. Theoretically, we show that standard Residual Quantization and QINCo can be recovered as constrained special cases of RQ-MoE, and derive a guideline for setting expert dimensionality in RQ-MoE. Extensive experiments show that RQ-MoE achieves state-of-the-art or on-par performance in reconstruction and retrieval, while providing 6x-14x faster decoding than prior vector quantization methods. The implementation is available at https://github.com/KDEGroup/RQ-MoE.

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: EDEN and TurboQuant are favorable for MSE distortion, EDEN is also effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison further clarifies that EDEN provides particularly strong guarantees for expected distortion measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.

In this work, we developed and tested 3 techniques for vector quantization (VQ) based model weight compression. To mitigate codebook collapse and enable end-to-end training, we adopted cosine similarity-based assignment. Building on ideas from attention-based formulations in Differentiable K-Means (DKM), we further improved this approach by using cosine similarity for assignment combined with top-1 sampling and a straight-through estimator, thereby eliminating the need for weighted-average reconstruction. Finally, we investigated the use of differentiable neural architecture search (NAS) to adaptively select layer-wise quantization configurations, further optimizing the compression process. Although our method does not consistently outperform existing approaches across all quantization levels, it provides useful insights into the design trade-offs and behaviors of VQ-based model compression methods.