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

A new arXiv paper, arXiv:2610.10611v1, presents a formal framework that separates the mechanisms by which agentic AI systems improve — longer search, additional support, or modified proposal and verification — using bounded verification with hidden terminal randomness. The authors prove that independent majority amplification preserves both the native reach and closure frontier languages, while existential acceptance over random tapes can admit incorrect outputs, and that uniformly bounded self-modification under a common sound interpreter and fixed verification protocol remains within the same verification class. The randomized-verifier classes satisfy Σ_k^P ⊆ Σ_k^RV ⊆ Σ_{k+1}^P, with strict enlargement and depth separation requiring explicit complexity assumptions.

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. A quota-enforced XOR-synthesis family separates unbounded ratios of search success from changes in the accepted languages; exact and probabilistic audits check the resulting evidence requirements. The framework ties self-improvement claims to obligations on correctness, admissible evidence, verification resources, and selection error.