The Computational Boundary of Inference: Capability Internalization, Training, and the Turing Jump
arXiv:2605.27381v1 Announce Type: cross Abstract: 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
The paper provides a formal theoretical contribution at a time when 'recursive self-improvement' and 'generalized AI' capabilities are intensely debated and often conflated in public discourse.
This research provides a foundational theoretical separation in classical computability theory, potentially setting clear boundaries for discussions on AI self-improvement, which is crucial for forecasting and policy.
The formal distinction between finite internal self-modification and qualitatively stronger capability, grounded in computability theory, refines the theoretical understanding of AI's potential growth trajectories.
- · AI ethicists and philosophers
- · Academics researching foundational AI theory
- · AI safety and alignment researchers
- · Hyper-optimistic AI futurists
- · AI developers lacking theoretical rigor in capability claims
The paper formally clarifies that finite internal AI modifications remain within existing 'computational layers'.
This improved theoretical clarity could lead to more grounded, less speculative policy discussions around advanced AI capabilities.
It might influence architectural decisions in AI development by emphasizing the inherent limitations of internal improvement for generating genuinely novel computational capacity.
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Read at arXiv cs.AI