Generalized Radius and Integrated Codebook Transforms for Differentiable Vector Quantization

TL;DR

GRIT-VQ introduces a differentiable vector quantization framework that improves codebook utilization and stability in training generative models by replacing heuristic estimators with a geometry-aware, data-agnostic approach.

Contribution

It proposes a unified surrogate framework for VQ that maintains hard assignments while enabling stable, fully differentiable training through a radius-based update and integrated codebook transform.

Findings

Improves reconstruction error in image tasks

Enhances generative quality and recommendation accuracy

Increases codebook utilization significantly

Abstract

Vector quantization (VQ) underpins modern generative and representation models by turning continuous latents into discrete tokens. Yet hard nearest-neighbor assignments are non-differentiable and are typically optimized with heuristic straight-through estimators, which couple the update step size to the quantization gap and train each code in isolation, leading to unstable gradients and severe codebook under-utilization at scale. In this paper, we introduce GRIT-VQ (Generalized Radius and Integrated Transform-Vector Quantization), a unified surrogate framework that keeps hard assignments in the forward pass while making VQ fully differentiable. GRIT-VQ replaces the straight-through estimator with a radius-based update that moves latents along the quantization direction with a controllable, geometry-aware step, and applies a data-agnostic integrated transform to the codebook so that all codes are updated through shared parameters instead of independently. Our theoretical analysis clarifies the fundamental optimization dynamics introduced by GRIT-VQ, establishing conditions for stable gradient flow, coordinated codebook evolution, and reliable avoidance of collapse across a broad family of quantizers. Across image reconstruction, image generation, and recommendation tokenization benchmarks, GRIT-VQ consistently improves reconstruction error, generative quality, and recommendation accuracy while substantially increasing codebook utilization compared to existing VQ variants.