# Revisiting Adaptive Rounding with Vectorized Reparameterization for LLM Quantization

arXiv: https://arxiv.org/abs/2602.02151 · HTML: https://mlsanity.com/paper/2602.02151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 29 of 29)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [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)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [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)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [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#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Universal Actions for Enhanced Embodied Foundation Models](https://mlsanity.com/paper/2501.10105/) (2025)
- [VPTQ: Extreme Low-bit Vector Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2409.17066/) (2024)
- [FlexRound: Learnable Rounding based on Element-wise Division for Post-Training Quantization](https://mlsanity.com/paper/2306.00317/) (2023)
- [CBQ: Cross-Block Quantization for Large Language Models](https://mlsanity.com/paper/2312.07950/) (2023)
- [FIMA-Q: Post-Training Quantization for Vision Transformers by Fisher Information Matrix Approximation](https://mlsanity.com/paper/2506.11543/) (2025)
- [LRQ: Optimizing Post-Training Quantization for Large Language Models by Learning Low-Rank Weight-Scaling Matrices](https://mlsanity.com/paper/2407.11534/) (2024)
- [Towards Next-Level Post-Training Quantization of Hyper-Scale Transformers](https://mlsanity.com/paper/2402.08958/) (2024)

## Abstract (arXiv)

Adaptive Rounding has emerged as an alternative to round-to-nearest (RTN) for post-training quantization by enabling cross-element error cancellation. Yet, dense and element-wise rounding matrices are prohibitively expensive for billion-parameter large language models (LLMs). We revisit adaptive rounding from an efficiency perspective and propose VQRound, a parameter-efficient optimization framework that reparameterizes the rounding matrix into a compact codebook. Unlike low-rank alternatives, VQRound minimizes the element-wise worst-case error under L_∞ norm, which is critical for handling heavy-tailed weight distributions in LLMs. Beyond reparameterization, we identify rounding initialization as a decisive factor and develop a lightweight end-to-end finetuning pipeline that optimizes codebooks across all layers using only 128 samples. Extensive experiments on OPT, LLaMA, LLaMA2, and Qwen3 models demonstrate that VQRound achieves better convergence than traditional adaptive rounding at the same number of steps while using as little as 0.2% of the trainable parameters. Our results show that adaptive rounding can be made both scalable and fast-fitting. The code is available at https://github.com/zhoustan/VQRound.