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

[Submitted on 7 Oct 2026]

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

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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.

Comments: 26 pages, 5 figures. Includes proofs and reproducibility artifacts

Subjects:

Artificial Intelligence (cs.AI); Computational Complexity (cs.CC)

Cite as: arXiv:2610.10611 [cs.AI]

(or arXiv:2610.10611v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.10611

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Chien-Ping Lu [view email] [v1] Wed, 7 Oct 2026 06:47:49 UTC (90 KB)

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code/exact_audit/audit.json

code/exact_audit/fused_qbf_audit.py

code/exact_audit/patch_agent_audit.py

code/exact_audit/patch_agent_declaration.json

code/exact_audit/test_fused_qbf_audit.py

code/exact_audit/test_patch_agent_audit.py

formalization/StagedAscentFused.lean

formalization/lean-toolchain

integrated/audit.py

integrated/audit_results.json

integrated/figures/amplification.dat

integrated/figures/data_manifest.json

integrated/figures/false_acceptance.dat

integrated/figures/generate_data.py

integrated/figures/xor_success.dat

integrated/test_xor_envelope.py

integrated/xor_envelope.py

integrated/xor_envelope_results.json

reproduce.py

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