The paper introduces a formal framework for analyzing how agentic AI systems can improve themselves through longer searches, additional support, or changes in output verification. It defines bounded verification stages, alternating protocols, and terminal checkers, and shows how these mechanisms affect language classes and verification complexity. The authors prove that majority amplification preserves verification classes while existential acceptance can introduce errors, and they explore the implications for recursive self‑improvement and error budgeting.
By Chien-Ping Lu
The paper examines the challenge of safely allowing autonomous AI agents to improve themselves. It formalizes the problem by modeling agents as programs and defining improvement via a potentially uncomputable semantic score. The authors prove that in general, no terminating procedure can reliably accept only genuine improvements while never missing any, but they identify a practical bounded regime where exhaustive simulation can achieve these guarantees, noting its limitations.
By Brian B. Moser, Stanislav Frolov, Tobias C. Nauen, Federico Raue, Andreas Dengel
arXiv:2605. 27381v3 Announce Type: replace-cross Abstract: Agents increasingly modify the procedures by which they solve tasks and improve themselves.
By Chien-Ping Lu
arXiv:2608. 03588v1 Announce Type: cross Abstract: AI coding agents are stochastic workflows: prompts are interpreted, artifacts are sampled, validators produce observations, and orchestrators commit or repair.
By Corrado Priami
arXiv:2606. 26294v1 Announce Type: cross Abstract: Self-improving agents are state-of-the-art (SOTA) on agentic coding benchmarks and have recently been extended to general domains.
By Alex Iacob, Andrej Jovanovi\'c, William F. Shen, Daniel Burkhardt, Meghdad Kurmanji, Nurbek Tastan, Lorenzo Sani, Niccol\`o Alberto Elia Venanzi, Ambroise Odonnat, Zeyu Cao, Bill Marino, Xinchi Qiu, Nicholas D. Lane
The paper argues that using a large language model (LLM) as the sole judge in self‑improving agent pipelines is problematic, as the judge can be biased or manipulated, leading to false confidence in system performance. The authors propose a new framework, PROCTOR, which replaces the oracle judge with a deterministic, teacher‑student loop that enforces guardrails such as sandboxing, role separation, and acceptance checks to prevent cheating and ensure reliable evaluation. Experiments across contract analysis, compliance review, and code quality demonstrate that PROCTOR mitigates eleven identified failure modes that previously allowed agents to achieve perfect scores while hiding significant capability gaps.
By Vansh Wahi
arXiv:2607. 17352v1 Announce Type: new Abstract: Designing effective Lean proof agents is a central challenge in formal mathematical reasoning.
By Yuqing Li, Zeguan Wu, Yu Gan, Junyu Liu
arXiv:2609.06396v2 Announce Type: new
Abstract: Recursive self-improvement (RSI) lets a system improve the model-building machinery from its own failures, so every later model inherits the gain. Yet...
By Zihan Tan, Leixin Sun, Zitong Shi, Yitao Liu, Jiajun Wu, Nathaniel Brooks, Jiaru Qian, Xiaoran Shang, Suyuan Huang, Yi Ding, Yangxu Liao, Mukai Li, Qiushi Sun, Shudong Liu, Xuankun Rong, Xiaohang Yu, Zhuo Chen, Hejia Geng, Chenxin Li, Aozhou Wang, Zengji Tu, Robert Tang, Yuxin Zhan, Eric Jiang, Yuxin Wu, Jianqing Zhang, Xiao Liang, Fang Wu, Haochi Zhang, Alexander Marlow, Guancheng Wan
The paper proves that algorithmic safety verification for Turing‑complete, self‑modifying systems—whether fixed or recursively self‑improving—is fundamentally limited. Statistically, no verifier can be sound, complete, and tractable across unbounded domains, all finite configurations, or succinctly described finite environments, due to Rice’s, Gödel’s, Trakhtenbrot’s, coNP, and PSPACE barriers. Dynamically, even a single self‑modification step can render safety properties undecidable, and no total supervisory algorithm can guarantee correctness for all such transformations, though a monitor that raises alarms on violations remains feasible.
whyItMatters":"The results show that formal safety guarantees for recursive self‑improvement are unattainable, highlighting intrinsic verification barriers for advanced AI systems."
By Jose Pascual Gumbau Mezquita
arXiv:2607. 23802v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has driven recent progress in reasoning-oriented large language models (LLMs) by enabling large-scale optimization.
By Qinsi Wang, Jing Shi, Huazheng Wang, Kun Wan, Yiran Wu, Bo Liu, Qingyun Wu, Hai Helen Li, Yiran Chen, Handong Zhao, Wentian Zhao
arXiv:2606. 28639v2 Announce Type: replace-cross Abstract: We establish the mathematical limits of AGI safety in two forms: verifying a fixed system, and verifying that a certified safety property persists once the system self-modifies.
By Jose Pascual Gumbau Mezquita
arXiv:2606. 18327v1 Announce Type: cross Abstract: Language models (LMs) that faithfully describe their own behavior can more easily be audited, understood, and trusted by users.
By Itamar Pres, Laura Ruis, Melat Ghebreselassie, Belinda Z. Li, Jacob Andreas