Grid Games: The Power of Multiple Grids for Quantizing Large Language Models

Post-training quantization (PTQ) is widely used to reduce the memory and computational cost of large language models. Existing PTQ methods typically obtain an initial quantized model through heuristic rules or greedy optimization, and once quantization is completed the resulting integer assignments are usually treated as final. This observation motivates a complementary optimization stage within PTQ that keeps quantized weights improvable after an executable quantized model has been produced, while preserving the quantized format. We introduce ReQuant, a backpropagation-free fixed-grid refinement procedure for this stage. Agnostic to the PTQ initializer, ReQuant takes an existing quantized model as a feasible starting point and iteratively revisits its discrete weight assignments on the fixed quantization grid. Accepted updates strictly reduce the mean squared reconstruction error and remain on the original grid. In this way, ReQuant turns the initially fixed PTQ output into an iteratively optimizable discrete solution and serves as a plug-and-play post-processing stage for existing PTQ pipelines. Experiments across diverse model families, bit-widths, and downstream tasks show that ReQuant consistently improves quantized models from heterogeneous PTQ initializers, with especially large gains on simple initializers and lower bit-widths. Notably, ReQuant can refine a simple round-to-nearest initialization across multiple sweeps until it approaches or surpasses GPTAQ under the same quantization format. These results establish ReQuant as a practical complementary stage for further improving existing PTQ pipelines.

Large language models (LLMs) achieve remarkable performance but are expensive to deploy due to their enormous size. FP4 quantization, with formats such as MXFP4 and NVFP4, offers an appealing solution with native hardware support on modern accelerators. However, maintaining accuracy under FP4 precision remains difficult. A key bottleneck lies in scale optimization: existing methods tightly couple the quantization and dequantization scales, forcing both to conform to the discrete low-precision format required by hardware, such as E8M0 in MXFP4. Yet the quantization scale is never stored and need not obey this constraint, suggesting a significant untapped optimization space. In this work, we propose FOCUS, a post-training quantization framework with end-to-end scale learning for FP4 Optimization via Coupled-Relaxation and Dual-Granularity Scaling. Coupled-Relaxation Scaling (CRS) relaxes the tight coupling between quantization and dequantization scales with a learnable full-precision coefficient, enabling more effective optimization without breaking hardware compliance. Dual-Granularity Scaling (DGS) further refines the quantization scale at a finer sub-block granularity, allowing more precise adaptation to local weight distributions. Experiments across multiple LLM families and benchmarks show that FOCUS achieves state-of-the-art FP4 accuracy under both MXFP4 and NVFP4 formats, while introducing no additional inference overhead. Code and quantized models will be released at https://github.com/tencent/AngelSlim.

Post-training weight-only quantization to 4 bits is widely used to reduce the memory and compute costs of large language model inference. Existing PTQ methods, such as AWQ and GPTQ, improve how weights are mapped onto a fixed 4-bit grid through scaling, clipping, or error compensation. To further improve accuracy, methods such as OmniQuant and QuIP# uses gradient-assisted algorithms at the cost of hours of quantization time. In this work, we propose AAAC (Activation-Aware Adaptive Codebooks), a lightweight method for 4-bit LLM weight quantization. AAAC replaces the fixed scalar codebook used in standard quantization with two small learned scalar codebooks (64 bytes) per layer. Each group of weights selects the codebook that minimizes activation-weighted reconstruction error, encoding the choice in the unused sign bit of the group's positive scale and adding zero storage overhead. AAAC completes in 3--30 minutes on a single GPU, and adds no memory beyond the model itself. We evaluate against AWQ, GPTQ, IF4, GPTVQ, OmniQuant, SqueezeLLM, and QuIP# across model families. AAAC outperforms baselines at orders-of-magnitude less quantization time.