VALG: An Agentic System for ML Theory Research.

Researchers have developed VALG, an innovative agentic system aimed at automating and streamlining machine learning theory research. This system integrates several advanced capabilities: multi-level verification ensures the rigor of mathematical statements, adaptive problem formulation allows for dynamic adjustment of research questions, and a graph-structured approach facilitates the development and organization of proofs. VALG is designed to mimic the iterative process of human researchers, formulating hypotheses, conducting preliminary analyses, and refining both assumptions and proofs. VALG's sophisticated architecture enables it to maintain fixed mathematical specifications within theorem branches, verify the composition of proof-dependency graphs, and construct or review local proofs in a structured order. A key feature is its ability to diagnose proof failures, determining whether the issue lies in a derivation, the proof structure, or the initial theorem formulation. Depending on the obstruction, VALG can then initiate related variants or relaxations of the problem, preserving the mathematical relationship to the original challenge. Initial evaluations on subproblems from COLT 2026 open problems show VALG producing internally finalized theorem candidates and various restricted or conditional results, demonstrating its potential to significantly accelerate theoretical ML advancements.