arXiv：cs.LG· Anthony Kostal-Vazquez, Vassil Dimitrov, Branden Butler·· 11 小时前
代数整数量化（AIQ）：面向 LLM 推理的无误差乘累加压缩格式
Algebraic Integer Quantization for Machine Learning Applications
AI 导读
研究者提出代数整数数制（AINF）与代数整数量化（AIQ），可直接归约为纯整数运算，实现无误差乘累加，并据此构建矩阵乘法引擎。AIQ 用于大语言模型推理的有损压缩，在相同 bit-per-parameter 预算下，于多种模型与基准上取得与业界标准 MX 格式相当的精度。实验采用二次代数整数，更高阶及多维代数整数留待未来探索。
正文
Abstract:In this article, we propose algebraic integer number formats (AINF) as a framework for highly configurable and accurate compressed computation. A key property of AINF is its straightforward reduction to purely integer arithmetic, enabling error-free multiply-accumulate operations. We develop a matrix multiplication engine that exploits this property, obtaining performance within a predictable factor of the most efficient numerical counterparts on modern hardware accelerators. Another key advantage of AIQ is the freedom to select algebraic integers tailored to the numerical characteristics of a given use case, offering optimization opportunities that are fundamentally unavailable in floating-point or fixed-point formats. Motivated by these properties, we introduce algebraic integer quantization (AIQ), a lossy compression format for large language model (LLM) inference, and provide results demonstrating that AIQ achieves competitive accuracy compared to the industry-standard MX format across a diverse set of models and benchmarks at equivalent bit-per-parameter budgets. The experiments presented in this article employ algebraic integers of degree two (quadratic integers); generalizations to higher-order and, in particular, multidimensional algebraic integers promise even greater computational advantages and remain a promising direction for future work.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12494 [cs.LG] |
| (or arXiv:2610.12494v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12494 arXiv-issued DOI via DataCite |
Submission history
From: Anthony Kostal-Vazquez [view email]
[v1]
Fri, 25 Sep 2026 19:36:04 UTC (26 KB)
来源：arXiv：cs.LG · arxiv.org