# Two-Stage Grid Optimization for Group-wise Quantization of LLMs

arXiv: https://arxiv.org/abs/2602.02126 · HTML: https://mlsanity.com/paper/2602.02126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 19 of 19)

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- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
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- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [WinoGrande: An Adversarial Winograd Schema Challenge at Scale](https://mlsanity.com/paper/1907.10641/) (2019)
- [Prefixing Attention Sinks can Mitigate Activation Outliers for Large Language Model Quantization](https://mlsanity.com/paper/2406.12016/) (2024)
- [COMQ: A Backpropagation-Free Algorithm for Post-Training Quantization](https://mlsanity.com/paper/2403.07134/) (2024)
- [BoA: Attention-aware Post-training Quantization without Backpropagation](https://mlsanity.com/paper/2406.13474/) (2024)
- [Towards Next-Level Post-Training Quantization of Hyper-Scale Transformers](https://mlsanity.com/paper/2402.08958/) (2024)

## Abstract (arXiv)

Group-wise quantization is an effective strategy for mitigating accuracy degradation in low-bit quantization of large language models (LLMs). Among existing methods, GPTQ has been widely adopted due to its efficiency; however, it neglects input statistics and inter-group correlations when determining group scales, leading to a mismatch with its goal of minimizing layer-wise reconstruction loss. In this work, we propose a two-stage optimization framework for group scales that explicitly minimizes the layer-wise reconstruction loss. In the first stage, performed prior to GPTQ, we initialize each group scale to minimize the group-wise reconstruction loss, thereby incorporating input statistics. In the second stage, we freeze the integer weights obtained via GPTQ and refine the group scales to minimize the layer-wise reconstruction loss. To this end, we employ the coordinate descent algorithm and derive a closed-form update rule, which enables efficient refinement without costly numerical optimization. Notably, our derivation incorporates the quantization errors from preceding layers to prevent error accumulation. Experimental results demonstrate that our method consistently enhances group-wise quantization, achieving higher accuracy with negligible overhead.