arXiv AI
Agentic Algorithm Design: LLMs that Propose, Formalise, and Prove Runtime Bounds for Evolutionary Algorithms in Lean
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arXiv Machine Learning
Oct 23
Agentic Verified Optimization of Real-World Software
The paper introduces agentic verified optimization, where an AI agent produces a faster implementation of a program along with a machine‑checked proof that it is behaviorally equivalent to the original. The authors implement this in Lean 4, creating Aqueduct to migrate C, C++, Go, and Rust code into Lean and validate the ports via differential testing. On 189 reference functions, agents achieved 156 faster, proved rewrites, and on 17 migrated applications, 92 rewrites improved 47 of 51 scenarios, demonstrating the feasibility of verified optimization for real‑world software.
arXiv AI
Jul 21
Self-Modifying Lean Proof Agents with Verifier-Grounded Benchmark Coevolution
arXiv:2607. 17352v1 Announce Type: new Abstract: Designing effective Lean proof agents is a central challenge in formal mathematical reasoning.
arXiv AI
Oct 19
Hard Instances on Demand
The paper presents a method for generating hard problem instances by treating instance creation as an optimization problem, using solver runtime as the objective. Leveraging the Nevergrad platform, the authors generate challenging instances for four NP‑hard problems—satisfiability, traveling salesperson, Hamiltonian cycle, and non‑permutation flow‑shop scheduling—that outperform random draws and rival curated benchmark sets. The approach requires only a solver, an instance encoder, and a compute budget, and it can uncover structural insights such as phase‑transition behavior in SAT.
arXiv AI
Jun 6
Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement
arXiv:2606. 06468v1 Announce Type: new Abstract: We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement.
arXiv AI
Jun 3
Don't Gamble, GAMBLe: An Analytical Framework for AI-Driven Research Systems
arXiv:2606. 02863v1 Announce Type: new Abstract: AI-Driven Research Systems (ADRS) -- systems coupling LLMs with automated evaluation to discover algorithms, proofs, and designs -- are being optimized and adopted across domains, but the tools to analyze them have not kept pace.
arXiv AI
Oct 1
Growing an Agent/Prover Interface: Evolutionary Tool Design for Cost-Efficient Theorem Proving in Rocq and Lean
arXiv:2609.39544v1 Announce Type: new Abstract: Recent achievements in AI-assisted mathematics require intensive interaction of agents with proof assistants to generate machine-checked proof certific...