发表机构
School of Systems Science, Beijing Normal University; Swarma Research（北京师范大学系统科学学院; Swarma研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
探讨自我进化AI中自主自我改进可持续性的问题，类比冯·诺依曼自复制自动机的复杂性阈值，论证大语言模型中需内省，基于定理证明其理论存在，指出当前模型因结构瓶颈缺乏真正内省，并给出架构突破方向及安全影响。
AI 中文摘要
对自我进化AI的追求引发关键问题：何时自主自我改进是可持续而非退化的？类比冯·诺依曼自复制自动机的复杂性阈值，我们认为大语言模型中可持续的递归自我改进需要功能类似物：内省——系统模拟自身操作和目标修改的能力。基于克林尼第二递归定理，我们证明了此类内省程序的理论存在。然而，实证研究表明，虽然当前大语言模型表现出准内省（如部分元认知），但由于结构瓶颈：缺乏完全自我访问、Transformer的前馈性质以及阻止定点迭代的计算类约束，它们仍未达到真正的内省。我们通过概述跨越这一复杂性阈值的架构路径并讨论相关安全影响来得出结论。
英文摘要
The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann's complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in Large Language Models (LLMs) requires a functional analogue: introspection -- the system's capacity to simulate its own operations and target modifications. Grounded in Kleene's Second Recursion Theorem, we demonstrate the theoretical existence of such introspective programs. However, an empirical review reveals that while current LLMs exhibit quasi-introspection (e.g., partial metacognition), they fall short of true introspection due to structural bottlenecks: a lack of complete self-access, the feedforward nature of the Transformer, and computational class constraints that prevent fixed-point iteration. We conclude by outlining architectural paths to cross this complexity threshold and discussing the associated safety implications.
Comments21 pages, 4 figures, 1 table
