BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models
Authors: name: Junyu Chen, name: Jungang Li, name: Jing Xiong, name: Wenjie Wang, name: Qingyao Yang, name: He Xiao, name: Zhen Li, name: Taiqiang Wu, name: Mengzhao Chen, name: Zhen Peng, name: Chaofan Tao, name: Long Shi, name: Hongxia Yang, name: Ngai Wong
Organization: Hong Kong University

Large language model (LLM) inference is often bounded by memory footprint and memory bandwidth in resource-constrained deployments, making quantization a fundamental technique for efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. Fundamentally, 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 approximate second-order information while progressively compensating 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 provide theoretical analysis showing that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. Code: github.com/KingdalfGoodman/BPDQ.