State Representation and Termination for Recursive Reasoning Systems
State Representation and Termination for Recursive Reasoning Systems
递归推理系统的状态表示与终止条件
Abstract: Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This paper addresses both.
摘要： 递归推理系统在获取新证据与优化累积理解之间交替进行。通常有两个设计选择被隐含处理：如何表示演进中的推理状态，以及何时停止迭代。本文针对这两个问题进行了探讨。
We represent the reasoning state as an epistemic state graph encoding extracted claims, evidential relations, open questions, and confidence weights. We define the order-gap as the distance between the states reached by expand-then-consolidate versus consolidate-then-expand; a small order-gap suggests that the two orderings agree and further iteration is unlikely to help.
我们将推理状态表示为一种认知状态图，其中编码了提取出的主张、证据关系、开放性问题以及置信度权重。我们定义了“顺序间隙”（order-gap），即“先扩展后整合”与“先整合后扩展”所达到的状态之间的距离；较小的顺序间隙表明这两种顺序达成了一致，进一步迭代不太可能带来实质性帮助。
Our main result gives a necessary and sufficient condition for the linearised order-gap to be non-degenerate near the fixed point, showing when the criterion is informative rather than algebraically vacuous. This is a local condition, not a global convergence guarantee.
我们的主要研究结果给出了线性化顺序间隙在不动点附近非退化的充要条件，展示了该准则在何时具有信息量，而非代数上的空洞。这是一个局部条件，而非全局收敛保证。
We apply the framework to recursive reasoning systems and sketch its application to agent loops, tree-of-thought reasoning, theorem proving, and continual learning.
我们将该框架应用于递归推理系统，并概述了其在智能体循环、思维树推理、定理证明以及持续学习中的应用。
Paper Details:
- Authors: Debashis Guha, Amritendu Mukherjee, Sanjay Kukreja, Tarun Kumar
- Date: 2 May 2026
- arXiv ID: 2605.06690
- Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG)
论文详情：
- 作者： Debashis Guha, Amritendu Mukherjee, Sanjay Kukreja, Tarun Kumar
- 日期： 2026年5月2日
- arXiv ID: 2605.06690
- 学科分类： 人工智能 (cs.AI)；计算与语言 (cs.CL)；机器学习 (cs.LG)