Problem
Research questions and friction points this paper is trying to address.
Automated Theorem Proving
Recursive Self-Improvement
Neural Provers
ProofEvolve: Neuro-Symbolic Evolution for Formal Automated Theorem Proving
๐ค AI Summary
ไธบ่งฃๅณ่ชๅจๅฎ็่ฏๆไธญ็่ชๆๆน่ฟ้ฎ้ข๏ผProofEvolve้่ฟ็ปๅ็ฅ็ปๆจกๅๅ็ฌฆๅท้ช่ฏๆนๆณ่ฟๅๅฝขๅผๅ็่ฏๆ็ปๆ๏ผไปฅๆ้ซ่ฏๆๆ็ๅๆๅ็ใ
๐ Abstract
Automated theorem proving offers a natural foundation for recursive self-improvement in scientific discovery. However, existing neural provers do not fully preserve this recursive structure, where the learning process should be self-improving over time. Existing methods either embed proof experience into model parameters through expensive weight updates, or keep verified intermediate deductions only within the current problem. In addition, these methods also heavily rely on sparse whole-proof feedback, even when unsuccessful partial attempts contain useful discoveries. To close the gap, we propose ProofEvolve, a neuro-symbolic framework that evolves explicit, formally verified symbolic proof structures with neural models to decisively expand the knowledge boundary. In this framework, the neural model proposes variation operators, including decompositions, repairs, and schema recombinations. The symbolic Lean kernel verifies every proof transition. Over the evolution loops, ProofEvolve computes verified closure over the resulting proof directed acyclic graphs (DAGs). Within each problem, ProofEvolve evolves partial AND-OR proof DAGs in a behaviorally indexed archive. Across problems, kernel-checked schema extraction adds newly proved sub-DAGs to a persistent schema library. Proof DAGs inherit the solved results through typed schema recombination, with every residual premise exposed as a new subgoal. This evolutionary process preserves verified results from incomplete attempts and makes them available for later proofs without weakening formal soundness. Across three competition-level Lean benchmarks, ProofEvolve achieves the highest average solve rate among the evaluated proof systems.
Innovation
Methods, ideas, or system contributions that make the work stand out.
neuro-symbolic framework
automated theorem proving
proof evolution
formal verification
schema recombination
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