VALG: An Agentic System for ML Theory Research

2026-08-13

AI Summary

This work proposes the first framework that formalizes machine learning theory research as an autonomous agent workflow. By integrating typed proof dependency graphs, multi-level verification mechanisms, and adaptive problem modeling strategies, the system dynamically sets theorem objectives, diagnoses failures, and iteratively refines problem formulations while preserving mathematical relationships between the original problem and its variants. Evaluated on nine subtasks derived from five open problems at COLT 2026, the framework successfully generated two complete theorem candidates consistent with the scope of the original questions; the remaining outputs comprised conditional theorems, special cases, or results under restricted assumptions. These outcomes demonstrate the system’s effectiveness and potential in autonomously advancing theoretical research in machine learning.

Abstract

Machine learning theory studies learning procedures through mathematical setups in which the data model, training protocol, oracle access, loss, metric, and randomness define the phenomenon that a theorem is meant to explain. Solving an open problem therefore requires the problem formulation, theorem target, and proof mechanism to be developed in concert. Researchers formulate hypotheses, test them through preliminary theoretical or empirical analysis, and refine both assumptions and proofs. We investigate whether this process can be organized as an autonomous agentic workflow for ML theory research. We develop VALG, an agentic system that combines multi-level Verification, Adaptive formulation of Learning-theory problems, and Graph-structured proof development. Within each source-relative theorem branch, VALG maintains a fixed mathematical specification, checks the theorem-level composition of a typed proof-dependency graph, and constructs and reviews local proofs in dependency order. When a proof attempt fails, VALG identifies whether the obstruction lies in a derivation, the proof structure, or the theorem formulation and routes the next attempt accordingly. Formulation-level obstructions initiate an explicitly related variant or relaxation, preserving the mathematical relation between the resulting theorem and the source problem. We evaluate VALG on nine subproblems from five COLT 2026 open problems. Two runs produce internally finalized theorem candidates that match the scope of their source briefs; the remaining seven yield restricted-method results, special cases, or conditional theorems. These case studies show how VALG keeps source-scope matches, relaxations, conditional results, and blocked attempts mathematically distinct. VALG is open source at https://github.com/DechenZhang/VALG-ML-Theory-Agent.

Problem

• machine learning theory
• open problem solving
• theorem formulation
• autonomous agentic workflow
• mathematical reasoning

Innovation

• agentic system
• machine learning theory
• adaptive problem formulation
• graph-structured proof
• automated theorem exploration