From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in LLMs

arXiv:2601.03682v2 Announce Type: replace-cross 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 predicti