Go to ACL ARR 2025 May homepageMDToC: Metacognitive Dynamic Tree of Concepts for Boosting Mathematical Problem-Solving of Large Language Models
Abstract: Despite advances in mathematical reasoning capabilities, Large Language Models (LLMs) still struggle with calculation verification when using established prompting techniques. We present MDToC (Metacognitive Dynamic Tree of Concepts), a three-phase approach that constructs a concept tree, develops accuracy-verified calculations for each concept, and employs majority voting to evaluate competing solutions. Evaluations across CHAMP, MATH, and Game-of-24 benchmarks demonstrate our MDToC's effectiveness, with GPT-4-Turbo achieving 58.1% on CHAMP, 86.6% on MATH, and 85% on Game-of-24 - outperforming GoT by 5%, 5.4%, and 4% on all these tasks, respectively, without hand-engineered hints. MDToC consistently surpasses existing prompting methods across all backbone models, yielding improvements of up to 7.6% over ToT and 6.2% over GoT, establishing metacognitive calculation verification as a promising direction for enhanced mathematical reasoning.
Paper Type: Long
Research Area: Language Modeling
Research Area Keywords: Chain-of-thought, prompting
Contribution Types: Model analysis & interpretability, NLP engineering experiment
Languages Studied: English
Submission Number: 4875
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