{"ID":2826597,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.18841","arxiv_id":"2512.18841","title":"MDToC: 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.","short_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 cal...","url_abs":"https://arxiv.org/abs/2512.18841","url_pdf":"https://arxiv.org/pdf/2512.18841v2","authors":"[\"Tung Duong Ta\",\"Tim Oates\",\"Thien Van Luong\",\"Huan Vu\",\"Tien Cuong Nguyen\"]","published":"2025-12-21T18:11:24Z","proceeding":"cs.CL","tasks":"[\"cs.CL\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}