arXiv:2606.01861v1 Announce Type: new Abstract: Self-play, a type of training algorithm that enables a model to self-improve, has recently shown promising empirical results in the context of formal theorem proving using Large Language Models (LLMs). (Dong & Ma, 2025) instantiate self-play with two cooperating agents: a prover, which proves theorems, and a conjecturer, which generates new theorems as a curriculum to the prover. In this paper, we provide a theoretical framework for understanding the self-improvement capabilities of self-play algorithms for theorem proving. First, we formalize th
The paper builds upon recent empirical successes of self-play in formal theorem proving using LLMs, suggesting a maturation of the field from demonstration to theoretical understanding.
A theoretical framework for self-play theorem proving could unlock more robust and generalizable AI systems, accelerating discovery in mathematics, software development, and scientific research.
The ability to formally understand and improve self-play algorithms for theorem proving significantly advances AI's capacity for autonomous reasoning and knowledge generation.
- · AI research labs
- · Mathematics communities
- · Software developers
- · Logic and formal verification sectors
- · Traditional theorem proving methods
- · Companies reliant on manual formal logic verification
Self-improving AI systems become more reliable and capable of tackling complex, abstract problems.
Accelerated discovery of new mathematical theorems and more secure software through automated formal verification.
AI agents begin to autonomously generate and prove complex theories across various scientific domains, leading to unforeseen breakthroughs.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG