@inproceedings{wang-zhang-2026-implicit,
    title = "From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in {LLM}s",
    author = "Wang, Shaojie  and
      Zhang, Liang",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.1420/",
    pages = "28486--28500",
    ISBN = "979-8-89176-395-1",
    abstract = "Recent studies reveal that large language models (LLMs) exhibit limited logical reasoning abilities in mathematical problem-solving, instead often relying on pattern-matching and memorization. We systematically analyze this limitation, focusing on logical relationship understanding, which is a core capability underlying genuine logical reasoning, and reveal that errors related to this capability account for over 90{\%} of incorrect predictions, with Chain-of-Thought Supervised Fine-Tuning (CoT-SFT) failing to substantially reduce these errors. To address this bottleneck, we propose **F**irst-**S**tep **L**ogical **R**easoning (**FSLR**), a lightweight training framework targeting logical relationship understanding. Our key insight is that the first planning step-identifying which variables to use and which operation to apply-encourages the model to derive logical relationships directly from the problem statement. By training models on this isolated step, FSLR provides explicit supervision for logical relationship understanding, unlike CoT-SFT which implicitly embeds such relationships within complete solution trajectories. Extensive experiments across multiple models and datasets demonstrate that FSLR consistently outperforms CoT-SFT under both in-distribution and out-of-distribution settings, with average improvements of 3.2{\%} and 4.6{\%}, respectively. Moreover, FSLR achieves 4-6{\texttimes} faster training and reduces training token consumption by over 80{\%}."
}