LEVER is a new proof‑search algorithm that lets users program the objective over correct proofs and optimizes it during search. It scores partial proofs on an AND/OR graph, combining achieved objective values with predictions for open subgoals, so the objective guides search before a proof is complete. On the PutnamBench in Lean 4, LEVER reduces computational cost by 34 % and raises the solve rate from 80 % to 96 %, while also improving topical impurity and approaching refactoring for proof length.
By Nihal Jain, Shuangjie Yao, Begum Cicekdag, Zhuo Zhang, Suman Jana
The paper presents a bounded, online step-level repair module for Lean 4 that uses compiler error messages to fix rejected tactics instead of discarding them. By sampling up to $K$ candidate tactics and allowing at most $R$ repairs per step, the method improves solve rates over a sampling-only baseline, achieving up to a 32% relative gain and solving 82 additional theorems on a 1,990-theorem subset of the LeanDojo benchmark. The approach trades extra runtime for reachable proofs, with most benefit coming from early repair attempts and shallow tactic failures, and it successfully replicates on the Lean Workbook benchmark, nearly doubling its solve rate without regressions.
By Haotian Deng, Chris Farber, Sonal Narasimha, Samskrithi Sivakumar, Yexiang Xue
The paper introduces a domain‑specific debugging agent for repairing near‑miss accelerator kernels, arguing that debugging is more efficient than regenerating kernels from scratch. It tackles knowledge scarcity, integrity, and cost control through pattern retrieval, anti‑cheat detection, and convergence safeguards. Empirical results show the debug agent achieves a 66.7% Pass@1 rate and uses 92.8% fewer tokens per success compared to traditional regeneration methods.
By Yansong Sun, Shenxiu Wu, Siyuan Chen, Runlin Hou, Junhao Qiu, Junming Cao, Shudi Shao, Zhichao Lu, Qingfu Zhang
arXiv:2608. 02712v1 Announce Type: cross Abstract: Kernel generation for hardware accelerators such as GPUs and NPUs has become a proving ground for large language models (LLMs), and state-of-the-art systems raise correctness through pipelines that couple LLMs with agentic reinforcement learning and evolutionary search.
By Yansong Sun, Shenxiu Wu, Siyuan Chen, Runlin Hou, Junhao Qiu, Junming Cao, Shudi Shao, Zhichao Lu, Qingfu Zhang
arXiv:2606. 12594v1 Announce Type: new Abstract: Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive.
By Joshua Ong Jun Leang, Zheng Zhao, Mihaela C\u{a}t\u{a}lina Stoian, Qiyuan Xu, Haonan Li, Wenda Li, Shay B. Cohen, Eleonora Giunchiglia
arXiv:2606. 30852v1 Announce Type: new Abstract: Reasoning models spend different amounts of useful computation across instances, but it remains unclear when a learned stopping rule improves over simple confidence or convergence thresholds.
By Zhe Dong (University of Maine at Presque Isle), Fang Qin (Stanford University), Manish Shah (Independent Researcher)