提出用图结构表示推理状态，用顺序差判断何时停止迭代。
State Representation and Termination for Recursive Reasoning Systems
- 用认知图编码论点、证据、疑问和置信度，动态表征推理过程。
- 定义顺序差衡量两种推理顺序的差异，小值表明继续迭代无益。
- 给出局部条件判定该指标是否有效，适用于多种递归推理场景。
递归推理系统在获取新证据与更新理解之间交替进行。两个关键设计选择通常被隐含：如何表示不断演化的推理状态，以及何时终止迭代。本文提出将推理状态建模为包含提取命题、证据关系、待解问题和置信权重的认知状态图。定义‘顺序差’为‘先扩展再整合’与‘先整合再扩展’两种路径所达状态间的距离；若顺序差较小，说明两种顺序结果一致，进一步迭代难有帮助。本文主结果给出了线性化顺序差在不动点附近非退化的充要条件，明确了该准则何时具有实际意义而非代数上平凡。该条件为局部性质，不保证全局收敛。框架已应用于递归推理系统，并可拓展至智能体循环、思维树推理、定理证明与持续学习等任务。
原文摘要 · Abstract (English)
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. 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. 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. We apply the framework to recursive reasoning systems and sketch its application to agent loops, tree-of-thought reasoning, theorem proving, and continual learning.
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