# JARQ: Joint Alternating Refinement for Quantization

arXiv: https://arxiv.org/abs/2609.38599 · HTML: https://mlsanity.com/paper/2609.38599/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 37 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [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)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs](https://mlsanity.com/paper/2309.05516/) (2023)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [Alternating Multi-bit Quantization for Recurrent Neural Networks](https://mlsanity.com/paper/1802.00150/) (2018)
- [QuantEase: Optimization-based Quantization for Language Models](https://mlsanity.com/paper/2309.01885/) (2023)
- [Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization](https://mlsanity.com/paper/2505.11695/) (2025)
- [The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm](https://mlsanity.com/paper/2507.18553/) (2025)

## Abstract (arXiv)

Group-wise post-training quantizers for large language models round weights onto a grid that is not refit to the resulting integer codes. We show that this leaves accuracy on the table: the best grid depends on the codes, input correlations couple the errors of different groups, and useful code changes often involve many codes at once. We propose JARQ , a plug-in refinement that starts from any group-wise quantizer and alternates a joint least-squares fit of all group scales with bounded Babai proposals that move many codes of a group together on the current grid. The problem is a bilinear box-constrained mixed-integer least-squares problem; the solver is backpropagation-free, does not increase the layer-wise objective under exact scale solves, and keeps the host's bit width, groups, zero points, and inference cost. Across Llama-2, Llama-3, and Qwen models with RTN, GPTQ, OmniQuant, and AWQ hosts, JARQ lowers perplexity in 90 of 96 comparisons, cuts three-bit RTN perplexity by up to 36%, raises mean multiple-choice accuracy in 23 of 24 configurations, and improves QEP, QuaRot, and OJBKQ outputs, at under a minute per 7B block.