BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models

Junyu Chen, Jungang Li, Jing Xiong, Wenjie Wang, Qingyao Yang, He Xiao, Zhen Li, Taiqiang Wu, Mengzhao Chen, Zhen Peng, Chaofan Tao, Long Shi, Hongxia Yang, Ngai Wong
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:15272-15289, 2026.

Abstract

Large language model inference is often bounded by memory footprint and bandwidth in resource-constrained deployments, making quantization fundamental to efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. In essence, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using second-order information while progressively compensating for quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we theoretically show that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. The code is available at github.com/KingdalfGoodman/BPDQ.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26bt, title = {{BPDQ}: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models}, author = {Chen, Junyu and Li, Jungang and Xiong, Jing and Wang, Wenjie and Yang, Qingyao and Xiao, He and Li, Zhen and Wu, Taiqiang and Chen, Mengzhao and Peng, Zhen and Tao, Chaofan and Shi, Long and Yang, Hongxia and Wong, Ngai}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {15272--15289}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26bt/chen26bt.pdf}, url = {https://proceedings.mlr.press/v306/chen26bt.html}, abstract = {Large language model inference is often bounded by memory footprint and bandwidth in resource-constrained deployments, making quantization fundamental to efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. In essence, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using second-order information while progressively compensating for quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we theoretically show that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. The code is available at github.com/KingdalfGoodman/BPDQ.} }
Endnote
%0 Conference Paper %T BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models %A Junyu Chen %A Jungang Li %A Jing Xiong %A Wenjie Wang %A Qingyao Yang %A He Xiao %A Zhen Li %A Taiqiang Wu %A Mengzhao Chen %A Zhen Peng %A Chaofan Tao %A Long Shi %A Hongxia Yang %A Ngai Wong %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26bt %I PMLR %P 15272--15289 %U https://proceedings.mlr.press/v306/chen26bt.html %V 306 %X Large language model inference is often bounded by memory footprint and bandwidth in resource-constrained deployments, making quantization fundamental to efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. In essence, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using second-order information while progressively compensating for quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we theoretically show that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. The code is available at github.com/KingdalfGoodman/BPDQ.
APA
Chen, J., Li, J., Xiong, J., Wang, W., Yang, Q., Xiao, H., Li, Z., Wu, T., Chen, M., Peng, Z., Tao, C., Shi, L., Yang, H. & Wong, N.. (2026). BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:15272-15289 Available from https://proceedings.mlr.press/v306/chen26bt.html.

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