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
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
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 compar...
arXiv:2609.26094v1 Announce Type: new
Abstract: Multi-step causal reasoning requires chaining inferences where each step constrains the next. An early error propagates silently, and a correct answer...
By Jian Zhang, Bingyi Wang, Yizhi 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
arXiv:2607. 15459v1 Announce Type: new Abstract: A trained deep reinforcement learning policy is a black box, and we ask whether it can be made explainable by rewriting it as an executable logic program that reproduces its behaviour and that a person can read, a logic engine can run, and an optimizer can edit.
By Eduardo C. Garrido-Merch\'an
SEVerA is a three‑stage framework that synthesizes self‑evolving agents with formal safety guarantees. It introduces Formally Guarded Generative Models (FGGM) that wrap parametric models in verified rejection samplers, ensuring every output satisfies a first‑order logic contract. The framework searches for candidate programs, verifies them against hard constraints, and then fine‑tunes them to improve task utility while preserving correctness, achieving zero constraint violations on tasks such as Dafny verification, symbolic math synthesis, and policy‑compliant agentic tool use.
By Debangshu Banerjee, Changming Xu, Eugene Ie, Ming Zhang, Daiyi Peng, Chu-Cheng Lin, Tarun Suresh, Gagandeep Singh
arXiv:2607. 06341v1 Announce Type: cross Abstract: Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort.
By Shuangxiang Kan, Shuanglong Kan, Sebastian Ertel
Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort. Large language models (LLMs) promise to generate these proofs automatically, yet existing approaches wire a fixed, human-designed proof strategy into the system and constrain the model to follow it (retrieving premises and predicting tactics one step at a time, or splitting goals by divide-and-conquer), and still prove only a fraction of their target theorems.
arXiv:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
By Houston Haynes
arXiv:2608. 01522v1 Announce Type: new Abstract: Teaching a language model a skill it has not mastered is obstructed by three recurring difficulties: training data is scarce, ground-truth reasoning traces are usually unavailable, and models often exhibit an apparent ceiling beyond which additional data yields no further improvement.
By Longtian Bao, Jianyou Wang, Yang Zhang, Youze Zheng, Ramamohan Paturi
arXiv:2608.30322v1 Announce Type: new
Abstract: Professional agent tasks often depend on conventions that are absent from public corpora, yet benchmarks rarely control whether an agent has access to...
By Hanlin Tian, Minhao Li, Yu Mi, Sihan Zhu, Zhao Yang, Yuxiang Wang, Hongquan Zhu, Qiufei Hu