Foundational theory of agentic evolution

Develop a foundational theoretical framework for agentic evolution in large language model systems by formalizing deployment-time evolution as optimization over a combinatorial program space of persistent artifacts, establishing separation results that prove agentic evolution achieves a higher attainable performance frontier than non-agentic heuristic methods under comparable resources, and deriving regret bounds relative to an idealized oracle fine-tuning baseline to characterize long-horizon adaptation.

Background

The paper introduces agentic evolution as a deployment-time, governed optimization process in which an evolver agent diagnoses failures and proposes validated updates to persistent artifacts and, when appropriate, parameters. It proposes A-Evolve as a general framework and advances the evolution-scaling hypothesis that adaptation capacity increases with evolution-time compute.

While empirical studies support feasibility and performance gains, the authors explicitly note the lack of a foundational theory. They identify concrete theoretical directions: formalizing evolution as optimization over a combinatorial program space, proving separation results versus non-agentic heuristics, and bounding regret relative to an idealized oracle fine-tuning baseline, to provide principled understanding of long-horizon adaptation.