MPQ: A Message-Passing View of Post-Training Quantization

Post-training quantization (PTQ) is a practical approach to reducing the memory and computational footprint of large language models (LLMs) without retraining. GPTQ-based methods have become the de facto standard, yet they suffer from two complementary limitations. Methods with local, layer-wise objectives lack global supervision; while methods with global objectives fix their Hessian estimates at the start and ignore first-order gradients, so their guidance grows stale as quantization proceeds. This paper presents G$^2$PTQ, a unified PTQ framework with Generalized Gradient Compensation that integrates both first- and second-order information under a globally supervised, block-wise optimization objective. By refreshing gradient and Hessian estimates before quantizing each Transformer block, G$^2$PTQ avoids the staleness of prior global methods. Furthermore, to stabilize the exact first-order compensation, we introduce a trust-region scaling mechanism that dynamically bounds the gradient step to prevent exploding weight updates. Finally, we derive efficient implementations for block-wise Hessian approximation and exact gradient compensation. Experimental results on various model families and bit-widths demonstrate that G$^2$PTQ enables better alignment with the full-precision model, outperforming state-of-the-art baselines. Code is available at: https://github.com/G2PTQ/G2PTQ.

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) have shown remarkable performance in various domains, but they are constrained by massive computational and storage costs. Quantization, an effective technique for compressing models to fit resource-limited devices while preserving generative quality, encompasses two primary methods: quantization aware training (QAT) and post-training quantization (PTQ). QAT involves additional retraining or fine-tuning, thus inevitably resulting in high training cost and making it unsuitable for LLMs. Consequently, PTQ has become the research hotspot in recent quantization methods. However, existing PTQ methods usually rely on various complex computation procedures and suffer from considerable performance degradation under low-bit quantization settings. To alleviate the above issues, we propose a simple and effective post-training quantization paradigm for LLMs, named SEPTQ. Specifically, SEPTQ first calculates the importance score for each element in the weight matrix and determines the quantization locations in a static global manner. Then it utilizes the mask matrix which represents the important locations to quantize and update the associated weights column-by-column until the appropriate quantized weight matrix is obtained. Compared with previous methods, SEPTQ simplifies the post-training quantization procedure into only two steps, and considers the effectiveness and efficiency simultaneously. Experimental results on various datasets across a suite of models ranging from millions to billions in different quantization bit-levels demonstrate that SEPTQ significantly outperforms other strong baselines, especially in low-bit quantization scenarios.