AI能力跃迁不能仅靠内部反复迭代，需跳出当前计算层级。
The Computational Boundary of Inference: Capability Internalization, Training, and the Turing Jump
- 用可计算性理论区分层内迭代与跨层跃迁
- 有限自我修改仍停留在原计算层，无法突破
- 适合研究AI极限与自进化理论的学者
关于AI递归自改进的讨论常混淆重复内部修正与质变能力提升之间的区别。本文在经典可计算性理论框架下，给出一个形式化分离结果：对于预言机 $A$，其对应计算层 $\\(mathcal{C}(A)=\{B : B \leq_T A\}$。我们证明，有限内部自修改仍保留在 $\\mathcal{C}(A)$ 内，而稳定化修订则由相对化的极限引理决定，受 $A'$（即 $A$ 的跳变）支配。结合局部闭包与逃逸定理，清晰划分了层内迭代与向更强相对层跃升的界限。关键在于，更强层级虽可能产生，但不能由单一已确定层内的有限重复解释。该分离结果为一类将内部更新视为充分条件的递归改进叙事设定了可计算性理论的上限。
原文摘要 · Abstract (English)
Claims about recursive self-improvement in AI often slide from repeated internal revision to the possibility of qualitatively stronger capability without clearly distinguishing the underlying computational regimes. This paper gives a formal separation result in classical computability theory that blocks that move under a precise modeling assumption. For an oracle $A$, let $\mathcal{C}(A)=\{B : B \leq_T A\}$ be the corresponding computational layer. We prove that finite internal self-modification remains inside $\mathcal{C}(A)$, while stabilized revision is governed instead by the jump $A'$ via the relativized limit lemma. Together with a local closure versus escape theorem, this yields a clean formal separation between within-layer iteration and ascent to a stronger relative level. The point is not that stronger layers never arise, but that they are not explained by finite repetition inside one already settled layer. The resulting separation gives a computability-theoretic limit on a broad class of recursive-improvement narratives in which repeated internal updating is treated as sufficient for qualitative capability ascent.
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