arXiv AI
Jun 9
TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
Lean Graph Search for Formal Theorem Proving
LeanGraphSearch is a graph‑based retrieval method for the Lean 4 theorem prover that builds a dependency graph from Mathlib’s forward dependencies and traverses it to find supporting lemmas via multi‑hop chains. By linking each declaration to its premises, propagating relevance through a graph‑ranking algorithm, and re‑ranking candidates against the original query, it improves recall by up to 12% over LeanSearch v2 on MathlibQR and increases coverage of complete annotated proof routes on MathlibMPR by up to 3.7%. When integrated into an iterative proving loop, LeanGraphSearch raises pass rates at 8, 16, and 32 reflection turns by as much as 40% compared to a vanilla prover and up to 10% compared to LeanSearch v2, demonstrating higher accuracy‑cost efficiency.
Related stories
Hugging Face Trending Papers
Jun 8
TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.
arXiv AI
Oct 9
LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs
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.
arXiv Machine Learning
Sep 23
VeriSoftBench: Repository-Scale Formal Verification Benchmarks for Lean
arXiv:2602.18307v2 Announce Type: replace-cross Abstract: Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-b...
arXiv AI
Jun 12
Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation
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.
arXiv AI
Jun 2
Automated Conjecture Resolution with Formal Verification
arXiv:2604. 03789v2 Announce Type: replace-cross Abstract: Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems.
arXiv AI
Sep 1
Reward-Oracle MCTS for Formal Theorem Proving: Sample-Efficient Search and the Need for Kernel-Level Proof Auditing
arXiv:2608.28639v1 Announce Type: new Abstract: Formal theorem proving with large language models remains challenging due to the difficulty of navigating large proof search spaces efficiently. Existi...
arXiv AI
Sep 25
Learning to Discover Interesting Mathematics
The paper introduces a method for evaluating the intrinsic interestingness of mathematical theorems by comparing the length of their proofs to the length of their statements. It trains a 27B language model to predict proof difficulty, enabling the generation and selection of more interesting theorems while significantly reducing overlap with existing Mathlib. The approach allows iterative expansion of a self‑building, machine‑verified mathematical library guided by quantifiable metrics.
arXiv AI
Jun 30
LAMP: Lean-based Agentic framework with MCP and Proof Repair
arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.
arXiv AI
Jul 3
Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph
arXiv:2510. 04520v2 Announce Type: replace Abstract: Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their inability to synthesize new definitions.
arXiv Computation and Language
Sep 7
Compiler-Guided Adaptive Proof Search with Cross-Model Synergy on Context-Dependent Theorem Proving
The paper introduces a compiler-guided adaptive proof search framework for Lean 4 theorem proving, addressing the challenge of context-dependent proofs in real-world projects. It balances exploration and exploitation by generating diverse starting points via dual-model generation and resampling when stagnation occurs, while refining promising states using compiler-grounded pairwise comparison. Experiments on seven Lean 4 projects from miniCTX‑v2 demonstrate that the method improves average pass rates by 12.8 percentage points within a pass@32 budget and reduces LLM calls by 21.9 % compared to pass@k baselines.
arXiv AI
Aug 17
MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinement
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.