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[2601.18702] From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic
Summary
This paper introduces the Halo Architecture, a new framework for infinite-depth reasoning using rational arithmetic, aiming to enhance the stability and efficiency of large language models.
Why It Matters
The Halo Architecture proposes a significant shift from traditional fuzzy arithmetic to a more stable exact arithmetic framework, addressing the limitations of current large language models. This advancement could lead to more efficient AI systems and accelerate convergence times, which is crucial for the development of general intelligence.
Key Takeaways
- The Halo Architecture utilizes rational arithmetic to improve model stability.
- It introduces a Dual-Ring Topology to manage memory complexity and logical consistency.
- Eliminating gradient noise can significantly reduce time-to-convergence.
- The architecture aims to simplify transformer blocks to their algebraic forms.
- This approach could pave the way for advancements in general intelligence.
Computer Science > Machine Learning arXiv:2601.18702 (cs) [Submitted on 26 Jan 2026 (v1), last revised 16 Feb 2026 (this version, v4)] Title:From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic Authors:Hansheng Ren View a PDF of the paper titled From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic, by Hansheng Ren View PDF HTML (experimental) Abstract:The prevailing scaling paradigm of Large Language Models (LLMs) rests on a substrate of "Fuzzy" floating-point arithmetic. To mitigate the inherent instability of this approximate foundation, modern architectures have erected a complex scaffolding of structural and numerical heuristics--Complex Residuals, Pre-RMSNorm, Attention Scaling, and Gradient Clipping--consuming significant compute solely to prevent numerical collapse. We propose a paradigm shift to the "Exact". We introduce the Halo Architecture, grounded in the Rational Field (Q) and powered by a custom Exact Inference Unit (EIU). To resolve the exponential bit-width growth of rational arithmetic, Halo employs a Dual-Ring Topology that unifies two complementary control mechanisms: (1) The Micro-Ring (Continuum Maintenance), which strictly bounds memory complexity via Diophantine Approximation; and (2) The Macro-Ring (Symbolic Alignment), which enforces logical consistency via periodic state collapse. This stable dual-ring substrate allows for the "Great Dismantling" of numerical sca...
