arXiv:2610.12494v1 Announce Type: new 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 accurac...