Aria: An Agent for Retrieval and Iterative Auto-Formalization via Dependency Graph

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. To tackle these issues, we present Aria (**A**gent for **R**etrieval and **I**terative **A**utoformalization), a system for conjecture-level formalization in Lean that emulates human expert reasoning via a two-phase Graph-of-Thought process: recursively decomposing statements into a dependency graph and then constructing formalizations from grounded concepts. To ensure semantic correctness, we introduce **AriaScorer**, a checker that retrieves definitions from Mathlib for term-level grounding, enabling rigorous and reliable verification. We evaluate Aria on diverse benchmarks. On ProofNet, it achieves 91.6\% compilation success rate and 68.5\% final accuracy, surpassing previous methods. On FATE-X, a suite of challenging algebra problems from research literature, it outperforms the best baseline with 44.0\% vs. 24.0\% final accuracy. On a dataset of homological conjectures, Aria reaches 42.9\% final accuracy while all other models score 0\%.