@inproceedings{jiang-etal-2026-sair,
    title = "{SAIR}-Comb : A Structure-Aware Iterative Refinement Framework for Combinatorics Autoformalization",
    author = "Jiang, Weijie  and
      He, Gaolei  and
      Xiong, Beibei  and
      Wang, Jianlin  and
      Yang, Zhengfeng",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.1075/",
    pages = "23452--23473",
    ISBN = "979-8-89176-390-6",
    abstract = "Autoformalization aims to bridge the gap between human mathematical intuition and formal proof by automating the translation of informal reasoning into machine-verifiable languages. Despite significant breakthroughs catalyzed by Large Language Models (LLMs), autoformalizing Combinatorics remains a formidable challenge due to its intricate structural dependencies and the severe scarcity of high-quality formal datasets. To address these challenges, we propose SAIR-Comb, a Structure-Aware Iterative Refinement framework for Combinatorics powered by Lean 4 and LLMs. SAIR-Comb employs a multi-stage pipeline: first, it performs data augmentation and refinement by rectifying syntactic, semantic, and structural errors, guided by a curated manual combinatorics dataset. The model then undergoes a two-stage training regime: expert iteration with syntactic grounding, followed by reinforcement learning (RL) to align formal reasoning trajectories. Furthermore, we introduce Structural Consistency{---}a rigorous new metric designed to expose formalizing failures that elude traditional semantic-only evaluations. Experiments demonstrate that SAIR-Comb achieves strong performance on the specialized CombiBench while remaining highly competitive on general-domain benchmarks, including PutnamBench and ProverBench."
}