Lattice-Based Vector Quantization for Low-Bit Quantization-Aware Training

Rishika Kohli, Soma S Dhavala, Shaifu Gupta, Manoj Singh Gaur
Conference on Parsimony and Learning, PMLR 328:218-241, 2026.

Abstract

Quantization is an effective approach for deploying deep learning models on resource-constrained hardware, but maintaining accuracy and training stability at extreme low precision remains a major challenge. In this work, we study lattice-based vector quantization (VQ) as a practical alternative to scalar quantization for low-bit quantization-aware training (QAT). We develop a unified quantization pipeline that integrates structured lattice projections into both QAT and post-training quantization (PTQ), supporting multiple lattice choices—including E8 and D4—via a fused projection operator with straight-through estimation. Through extensive experiments across a wide range of bit-widths, lattice parameterizations, and training regimes, we show that lattice-based VQ consistently enables stable training and meaningful accuracy below 2 bits, where scalar quantization and existing PTQ methods typically underperform or are unavailable. In this low-bit regime, exploiting geometric structure across weight blocks improves robustness by reducing overload and stabilizing optimization, while at moderate and higher bit-widths, performance differences narrow and simpler quantization schemes become sufficient. We further analyze the role of lattice choice, dynamic-range scaling, and overload behavior, and demonstrate that explicit overload control is central to reliable low-bit performance. Finally, we show that lattice-based QAT extends beyond binary classification and weight-only quantization, supporting multi-class tasks, joint weight–activation quantization, and transformer encoders such as BERT, achieving substantial compression with controlled accuracy degradation

Cite this Paper

BibTeX
@InProceedings{pmlr-v328-kohli26a, title = {Lattice-Based Vector Quantization for Low-Bit Quantization-Aware Training}, author = {Kohli, Rishika and Dhavala, Soma S and Gupta, Shaifu and Gaur, Manoj Singh}, booktitle = {Conference on Parsimony and Learning}, pages = {218--241}, 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/kohli26a/kohli26a.pdf}, url = {https://proceedings.mlr.press/v328/kohli26a.html}, abstract = {Quantization is an effective approach for deploying deep learning models on resource-constrained hardware, but maintaining accuracy and training stability at extreme low precision remains a major challenge. In this work, we study lattice-based vector quantization (VQ) as a practical alternative to scalar quantization for low-bit quantization-aware training (QAT). We develop a unified quantization pipeline that integrates structured lattice projections into both QAT and post-training quantization (PTQ), supporting multiple lattice choices—including E8 and D4—via a fused projection operator with straight-through estimation. Through extensive experiments across a wide range of bit-widths, lattice parameterizations, and training regimes, we show that lattice-based VQ consistently enables stable training and meaningful accuracy below 2 bits, where scalar quantization and existing PTQ methods typically underperform or are unavailable. In this low-bit regime, exploiting geometric structure across weight blocks improves robustness by reducing overload and stabilizing optimization, while at moderate and higher bit-widths, performance differences narrow and simpler quantization schemes become sufficient. We further analyze the role of lattice choice, dynamic-range scaling, and overload behavior, and demonstrate that explicit overload control is central to reliable low-bit performance. Finally, we show that lattice-based QAT extends beyond binary classification and weight-only quantization, supporting multi-class tasks, joint weight–activation quantization, and transformer encoders such as BERT, achieving substantial compression with controlled accuracy degradation} }
Endnote
%0 Conference Paper %T Lattice-Based Vector Quantization for Low-Bit Quantization-Aware Training %A Rishika Kohli %A Soma S Dhavala %A Shaifu Gupta %A Manoj Singh Gaur %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-kohli26a %I PMLR %P 218--241 %U https://proceedings.mlr.press/v328/kohli26a.html %V 328 %X Quantization is an effective approach for deploying deep learning models on resource-constrained hardware, but maintaining accuracy and training stability at extreme low precision remains a major challenge. In this work, we study lattice-based vector quantization (VQ) as a practical alternative to scalar quantization for low-bit quantization-aware training (QAT). We develop a unified quantization pipeline that integrates structured lattice projections into both QAT and post-training quantization (PTQ), supporting multiple lattice choices—including E8 and D4—via a fused projection operator with straight-through estimation. Through extensive experiments across a wide range of bit-widths, lattice parameterizations, and training regimes, we show that lattice-based VQ consistently enables stable training and meaningful accuracy below 2 bits, where scalar quantization and existing PTQ methods typically underperform or are unavailable. In this low-bit regime, exploiting geometric structure across weight blocks improves robustness by reducing overload and stabilizing optimization, while at moderate and higher bit-widths, performance differences narrow and simpler quantization schemes become sufficient. We further analyze the role of lattice choice, dynamic-range scaling, and overload behavior, and demonstrate that explicit overload control is central to reliable low-bit performance. Finally, we show that lattice-based QAT extends beyond binary classification and weight-only quantization, supporting multi-class tasks, joint weight–activation quantization, and transformer encoders such as BERT, achieving substantial compression with controlled accuracy degradation
APA
Kohli, R., Dhavala, S.S., Gupta, S. & Gaur, M.S.. (2026). Lattice-Based Vector Quantization for Low-Bit Quantization-Aware Training. Conference on Parsimony and Learning, in Proceedings of Machine Learning Research 328:218-241 Available from https://proceedings.mlr.press/v328/kohli26a.html.

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