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: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: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.
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.
arXiv:2608. 11431v1 Announce Type: new Abstract: Graph learning presupposes a graph, and tables and relational databases do not come with one.
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...
The paper investigates a failure mode in Graph-JEPA, a joint‑embedding predictive model trained on a large scientific‑reasoning graph. Despite achieving high linear‑probe accuracy and effective rank, the learned representation contains almost no usable instance information, as shown by retrieval metrics. The authors diagnose the issue to variance allocation in the objective, propose a repair that restores near‑perfect information recovery, and demonstrate that the problem persists even after repair, highlighting limitations in the evaluation metrics used.