Verification and Self-Improvement in Agentic AI: Foundations and Limits

arXiv:2610.10611v1 Announce Type: new Abstract: Agentic AI systems can improve by searching longer, receiving additional support, or modifying how they propose and verify outputs. A performance score does not distinguish these mechanisms. We compare these changes through bounded verification with hidden terminal randomness. A stage specifies admissible transcripts, polynomial bounds, an alternating verification protocol, and a terminal checker. Its native reach uses default support; its closure frontier permits all support already admitted by the interface. Under a uniform pointwise probability gap and task-relative soundness, these are well-defined languages. We prove that independent majority amplification preserves both languages, whereas existential acceptance over random tapes can admit incorrect outputs. Exact verification is the zero-randomness case, with placement and completeness results. The randomized-verifier classes satisfy $\Sigma_k^{\mathrm{P}}\subseteq\Sigma_k^{\mathrm{RV}}\subseteq\Sigma_{k+1}^{\mathrm{P}}$; strict enlargement and depth separation require explicit complexity assumptions, while $\mathrm{BPP}=\mathrm{P}$ yields exact companions with the same frontiers. Representation analysis separates invariant acceptance from core-versus-support labels that can change under refactoring. For recursive self-improvement, uniformly bounded self-modification under a common sound interpreter and fixed verification protocol remains within the same verification class. A separate conditional-error budget controls false selection across adaptively chosen candidates.

Technical AI research with no clear societal implications

SOURCE     arXiv cs.AI (tier 1)
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DOCUMENT   9c9115bf-d13d-4580-94b7-3f2272ff07a1
           https://arxiv.org/abs/2610.10611
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EVIDENCE   2 extracted excerpts
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MODEL RUN  1 run, methodology 1.0.1
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SCORE      0  (Mixed or uncertain)
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CONFIDENCE 80%