MDToC: Metacognitive Dynamic Tree of Concepts for Boosting Mathematical Problem-Solving of Large Language Models
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914222995144704 |
|---|---|
| author | Ta, Tung Duong Oates, Tim Van Luong, Thien Vu, Huan Nguyen, Tien Cuong |
| author_facet | Ta, Tung Duong Oates, Tim Van Luong, Thien Vu, Huan Nguyen, Tien Cuong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MDToC: Metacognitive Dynamic Tree of Concepts for Boosting Mathematical Problem-Solving of Large Language Models Ta, Tung Duong Oates, Tim Van Luong, Thien Vu, Huan Nguyen, Tien Cuong Computation and Language 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. |
| title | MDToC: Metacognitive Dynamic Tree of Concepts for Boosting Mathematical Problem-Solving of Large Language Models |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2512.18841 |