@inproceedings{obozov-etal-2025-synthetic,
    title = "Synthetic Proofs with Tool-Integrated Reasoning: Contrastive Alignment for {LLM} Mathematics with Lean",
    author = "Obozov, Mark  and
      Diskin, Michael  and
      Beznosikov, Aleksandr  and
      Gasnikov, Alexander  and
      Barannikov, Serguei",
    editor = "Valentino, Marco  and
      Ferreira, Deborah  and
      Thayaparan, Mokanarangan  and
      Ranaldi, Leonardo  and
      Freitas, Andre",
    booktitle = "Proceedings of The 3rd Workshop on Mathematical Natural Language Processing (MathNLP 2025)",
    month = nov,
    year = "2025",
    address = "Suzhou, China",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-emnlp/2025.mathnlp-main.15/",
    pages = "195--202",
    ISBN = "979-8-89176-348-7",
    abstract = "Modern mathematical reasoning benchmarks primarily focus on answer finding rather than proof verification, creating a gap in evaluating the proving capabilities of large language models (LLMs). We present a methodology for generating diverse mathematical proof tasks using formal tools. Our approach combines Lean-based synthetic problem generation with a Tool-Integrated Reasoning (TiR) framework for partial (sampling-based) proof validation, and it uses contrastive preference optimization to align the model{'}s proof outputs. Experiments on the Qwen-2.5 family of models demonstrate meaningful improvements in mathematical reasoning, particularly for smaller models. Our aligned models achieve up to a 57{\%} higher success rate than baselines on the MiniF2F benchmark (across 0.5B, 1.5B, and 7B parameter models). These results highlight the potential of synthetic data and integrated validation for advancing LLM-based mathematical reasoning."
}