大模型
arxiv.org ·
大语言模型中的自我指涉：递归自我改进的内省阈值
该 arXiv 论文类比冯·诺依曼自复制自动机的复杂度阈值，提出 LLM 可持续递归自我改进需要“内省”能力，即系统模拟自身运算并定向修改的能力。作者基于 Kleene 第二递归定理论证此类内省程序在理论上存在，但综述现有证据认为当前 LLM 仅具备准内省（如部分元认知），受限于缺乏完整自访问、Transformer 的前馈特性以及阻止不动点迭代的计算类约束，尚未达到真正内省。文末给出跨越该复杂度阈值的架构路径并讨论相关安全影响。
AI推荐理由 arXiv 预印本，理论论证清晰：以 Kleene 第二递归定理证明内省程序的理论存在性，并指出当前 LLM 因缺乏完整自访问、Transformer 前馈结构和计算类约束而仅具准内省，未达真正内省。属概念性/理论性工作，无实验验证，结论为架构路径与安全影响的讨论，需保留其理论假设性质。
72
正文
Physics > Physics and Society
arXiv:2607.04277 (physics)
[Submitted on 5 Jul 2026 (v1), last revised 18 Sep 2026 (this version, v2)]
Title:Self-Reference in Large Language Models: The Introspection Threshold for Recursive Self-Improvement
Authors:Jiang Zhang, Bing Yuan, Qian Zhang
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Abstract: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.
Comments:
Subjects:
Physics and Society (physics.soc-ph); Artificial Intelligence (cs.AI)
MSC classes:
68T99
ACM classes:
I.2.2; I.2.4
Cite as:
arXiv:2607.04277 [physics.soc-ph]
(or
arXiv:2607.04277v2 [physics.soc-ph] for this version)
https://doi.org/10.48550/arXiv.2607.04277
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arXiv-issued DOI via DataCite
Submission history
From: Bing Yuan [view email]
[v1]
Sun, 5 Jul 2026 12:40:52 UTC (15,447 KB)
[v2]
Fri, 18 Sep 2026 09:22:36 UTC (16,178 KB)
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