From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic

• URL: http://arxiv.org/abs/2601.18702v2
• Date: Sun, 01 Feb 2026 07:13:30 GMT
• Title: From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic
• Authors: Hansheng Ren,
• Abstract summary: High-order causal reasoning, a cornerstone of general intelligence, demands a substrate supporting logically consistent arithmetic.<n>We present the textbfHalo Architecture, which transitions the computational foundation from approximate reals to exact rationals.<n>Our work posits exact arithmetic as non-negotiable for advancing reasoning-capable AGI and provides a co-designed hardware-software path toward verifiable, exascale-ready AI systems.
• Score: 0.10152838128195464
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The pursuit of scale in deep learning has entrenched a trade-off: computational throughput is prioritized at the expense of numerical precision. We argue this compromise is fundamentally at odds with the requirements of general intelligence. We propose the \textbf{Exactness Hypothesis}: high-order causal reasoning -- a cornerstone of AGI -- demands a substrate supporting \textbf{arbitrary-precision, logically consistent arithmetic}. We trace prevalent LLM failures, such as logical hallucinations and incoherence, to the inherent limitations of IEEE 754 floating-point arithmetic, where approximation errors compound catastrophically in deep functions. As a solution, we present the \textbf{Halo Architecture}, which transitions the computational foundation from approximate reals ($\mathbb{R}$) to exact rationals ($\mathbb{Q}$). Halo is realized through a custom \textbf{Exact Inference Unit (EIU)}, whose design -- featuring asynchronous MIMD reduction and dual-modular redundancy -- resolves the performance and reliability bottlenecks of exact computation at scale. In rigorous simulations, 600B-parameter BF16 models fail in chaotic systems within steps, while Halo sustains \textbf{perfect numerical fidelity} indefinitely. Our work posits exact arithmetic as non-negotiable for advancing reasoning-capable AGI and provides a co-designed hardware-software path toward verifiable, exascale-ready AI systems.

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