Generalized Radius and Integrated Codebook Transforms for Differentiable Vector Quantization

Haochen You, Heng Zhang, Hongyang He, Yuqi Li, Baojing Liu
Conference on Parsimony and Learning, PMLR 328:1125-1160, 2026.

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 & 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 rather than 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v328-you26a, title = {Generalized Radius and Integrated Codebook Transforms for Differentiable Vector Quantization}, author = {You, Haochen and Zhang, Heng and He, Hongyang and Li, Yuqi and Liu, Baojing}, booktitle = {Conference on Parsimony and Learning}, pages = {1125--1160}, year = {2026}, editor = {Burkholz, Rebekka and Liu, Shiwei and Ravishankar, Saiprasad and Redman, William and Huang, Wei and Su, Weijie and Zhu, Zhihui}, volume = {328}, series = {Proceedings of Machine Learning Research}, month = {23--26 Mar}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v328/main/assets/you26a/you26a.pdf}, url = {https://proceedings.mlr.press/v328/you26a.html}, 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 & 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 rather than 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.} }
Endnote
%0 Conference Paper %T Generalized Radius and Integrated Codebook Transforms for Differentiable Vector Quantization %A Haochen You %A Heng Zhang %A Hongyang He %A Yuqi Li %A Baojing Liu %B Conference on Parsimony and Learning %C Proceedings of Machine Learning Research %D 2026 %E Rebekka Burkholz %E Shiwei Liu %E Saiprasad Ravishankar %E William Redman %E Wei Huang %E Weijie Su %E Zhihui Zhu %F pmlr-v328-you26a %I PMLR %P 1125--1160 %U https://proceedings.mlr.press/v328/you26a.html %V 328 %X 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 & 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 rather than 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.
APA
You, H., Zhang, H., He, H., Li, Y. & Liu, B.. (2026). Generalized Radius and Integrated Codebook Transforms for Differentiable Vector Quantization. Conference on Parsimony and Learning, in Proceedings of Machine Learning Research 328:1125-1160 Available from https://proceedings.mlr.press/v328/you26a.html.

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