Theory-optimal Quantization Based on Flatness
This paper introduces a novel metric 'Flatness' to quantify outlier distribution, leading to a theoretical optimal solution. The authors propose Bidirectional Diagonal Quantization (BDQ), which disperses outliers across matrix dimensions via learned diagonal operations, achieving new state-of-the-art results in low-bit LLM quantization.
Article intelligence
Key points
- Proposes Flatness metric to quantify outlier distribution and derive optimal solution
- BDQ framework disperses outliers through bidirectional diagonal transformations
- W4A4 quantization on LLaMA-3-8B achieves <1% accuracy drop
- 39.1% performance gap reduction on DeepSeek-R1-Distill-LLaMA-70B for W2A4KV16
Why it matters
This matters because proposes Flatness metric to quantify outlier distribution and derive optimal solution.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.18800] Theory-optimal Quantization Based on Flatness
[Submitted on 11 May 2026]
Title:Theory-optimal Quantization Based on Flatness
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Abstract:Post-training quantization has emerged as a widely adopted technique for compressing and accelerating the inference of Large Language Models (LLMs). The primary challenges in LLMs quantization stem from activation outliers, which significantly degrade model performance especially at lower bit precision. While recent approaches attempt to mitigate outliers through linear transformations across feature dimensions, our analysis reveals that the transformed weights and activations still exhibit persistent outlier patterns with concentrated magnitude distributions. In this paper, we first model the mathematical relationship between quantization error and outliers, and then introduce a new metric Flatness to quantify the distribution of outliers. Based on this, we derive the theoretical optimal solution with respect to Flatness. Building on these insights, we propose Bidirectional Diagonal Quantization (BDQ), a novel post-training quantization framework that effectively disperses outlier patterns through optimized matrix transformations. BDQ strategically distributes outlier magnitudes across matrix dimensions via learned diagonal operations. Extensive experiments demonstrate that BDQ establishes a new quantization benchmark. It achieves less than 1\% accuracy drop in W4A4 quantization on the LLaMA-3-8B model. In the more challenging W2A4KV16 experiment, compared to state-of-the-art approaches, BDQ reduces the performance gap by 39.1\% on the DeepSeek-R1-Distill-LLaMA-70B model.
Comments: 16 pages, 2 figures
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2605.18800 [cs.LG]
(or arXiv:2605.18800v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.18800
arXiv-issued DOI via DataCite
Submission history
From: Xiusheng Huang [view email] [v1] Mon, 11 May 2026 10:51:40 UTC (953 KB)
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