AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.
arXiv:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
arXiv:2608. 11211v1 Announce Type: new Abstract: Conway's 99-graph problem asks whether a strongly regular graph with parameters $\mathrm{srg}(99,14,1,2)$ exists.
arXiv:2608. 14999v1 Announce Type: cross Abstract: Constructing special graphs is an important task within graph theory and computer science.
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv:2610.03556v1 Announce Type: new Abstract: Empirical claims about the connection between over-squashing and long-range interactions in GNNs, can only be trusted if the benchmarks used to validat...
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
arXiv:2606. 11562v1 Announce Type: new Abstract: Graph analysis underlies many applications whose answers cannot be looked up in a single record or retrieved along a path: laundering rings, drug repurposing, user preference, and scientific theme are all inferred from a node together with its neighbourhood.
arXiv:2610. 07503v1 Announce Type: cross Abstract: Two populations of graphs often have to be compared without any correspondence between their vertices, for instance when networks come from different communities, or when a graph generative model is evaluated against held-out graphs.
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.
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.
ProofEvolve is a neuro‑symbolic framework that evolves formally verified symbolic proof structures alongside neural models to expand the knowledge boundary in automated theorem proving. The neural component proposes variation operators such as decompositions, repairs, and schema recombinations, while the Lean kernel verifies every proof transition, ensuring formal soundness. Across three competition‑level Lean benchmarks, ProofEvolve achieves the highest average solve rate among evaluated proof systems.
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.