Conditional Performance Guarantee for Large Reasoning Models
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915763489603584 |
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| author | Huang, Jianguo Zeng, Hao Jing, Bingyi Wei, Hongxin An, Bo |
| author_facet | Huang, Jianguo Zeng, Hao Jing, Bingyi Wei, Hongxin An, Bo |
| contents | Large reasoning models have shown strong performance through extended chain-of-thought reasoning, yet their computational cost remains significant. Probably approximately correct (PAC) reasoning provides statistical guarantees for efficient reasoning by adaptively switching between thinking and non-thinking models, but the guarantee holds only in the marginal case and does not provide exact conditional coverage. We propose G-PAC reasoning, a practical framework that provides PAC-style guarantees at the group level by partitioning the input space. We develop two instantiations: Group PAC (G-PAC) reasoning for known group structures and Clustered PAC (C-PAC) reasoning for unknown groupings. We prove that both G-PAC and C-PAC achieve group-conditional risk control, and that grouping can strictly improve efficiency over marginal PAC reasoning in heterogeneous settings. Our experiments on diverse reasoning benchmarks demonstrate that G-PAC and C-PAC successfully achieve group-conditional risk control while maintaining substantial computational savings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22790 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conditional Performance Guarantee for Large Reasoning Models Huang, Jianguo Zeng, Hao Jing, Bingyi Wei, Hongxin An, Bo Artificial Intelligence Statistics Theory Large reasoning models have shown strong performance through extended chain-of-thought reasoning, yet their computational cost remains significant. Probably approximately correct (PAC) reasoning provides statistical guarantees for efficient reasoning by adaptively switching between thinking and non-thinking models, but the guarantee holds only in the marginal case and does not provide exact conditional coverage. We propose G-PAC reasoning, a practical framework that provides PAC-style guarantees at the group level by partitioning the input space. We develop two instantiations: Group PAC (G-PAC) reasoning for known group structures and Clustered PAC (C-PAC) reasoning for unknown groupings. We prove that both G-PAC and C-PAC achieve group-conditional risk control, and that grouping can strictly improve efficiency over marginal PAC reasoning in heterogeneous settings. Our experiments on diverse reasoning benchmarks demonstrate that G-PAC and C-PAC successfully achieve group-conditional risk control while maintaining substantial computational savings. |
| title | Conditional Performance Guarantee for Large Reasoning Models |
| topic | Artificial Intelligence Statistics Theory |
| url | https://arxiv.org/abs/2601.22790 |