arXiv cs.AI· Hansheng Ren·· 13 小时前AI 评分20
Halo 架构：用有理算术实现无限深度推理，从模糊浮点到精确计算
From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic
AI 导读
研究者提出 Halo 架构，基于有理数域（Q）并配备定制 Exact Inference Unit（EIU），用精确算术替代 LLM 依赖的浮点运算。该架构通过 Dual-Ring Topology 解决有理算术位宽指数增长问题：Micro-Ring 用 Diophantine Approximation 约束内存复杂度，Macro-Ring 通过周期性状态坍缩保证逻辑一致性。
正文 · 原文
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 scaffolding, reducing the Transformer block to its "Clean" algebraic form (Tabula Rasa). Furthermore, we verify the "Efficiency Paradox": the elimination of gradient noise (sigma -> 0) allows for Macro-Learning Rates, potentially reducing the Total Time-to-Convergence by orders of magnitude. Halo demonstrates that General Intelligence requires the hybridization of continuous fields and discrete chains under a rigorous mathematical framework.
| Comments: | Revised in response to feedback received during the Conference on Next Generation Arithmetic (CoNGA) review process. Added formal analysis of precision-escalation termination and Diophantine approximation error bounds; expanded related work |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Hardware Architecture (cs.AR) |
| Cite as: | arXiv:2601.18702 [cs.LG] |
| (or arXiv:2601.18702v5 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2601.18702 arXiv-issued DOI via DataCite |
Submission history
From: Hansheng Ren [view email]
[v1]
Mon, 26 Jan 2026 17:24:34 UTC (974 KB)
[v2]
Sun, 1 Feb 2026 07:13:30 UTC (989 KB)
[v3]
Sat, 7 Feb 2026 17:53:30 UTC (995 KB)
[v4]
Mon, 16 Feb 2026 07:24:47 UTC (1,107 KB)
[v5]
Tue, 20 Oct 2026 19:26:19 UTC (1,123 KB)
来源：arXiv cs.AI · arxiv.org