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| Autores principales: | , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2510.10168 |
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| _version_ | 1866914091202772992 |
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| author | Gao, Chengqian Li, Haonan Killian, Taylor W. She, Jianshu Wang, Renxi Ma, Liqun Cheng, Zhoujun Hao, Shibo Xu, Zhiqiang |
| author_facet | Gao, Chengqian Li, Haonan Killian, Taylor W. She, Jianshu Wang, Renxi Ma, Liqun Cheng, Zhoujun Hao, Shibo Xu, Zhiqiang |
| contents | Concise reasoning in large language models seeks to generate only essential intermediate steps needed to arrive at a final answer, thereby alleviating issues of overthinking. Most proposed approaches hinge on carefully hand-crafted heuristics, struggling to balance concision with performance, often failing to adapt across domains and model scales. In this work, we address these challenges by introducing a principled and pragmatic strategy, performance-aware length updating (PALU). As a principled algorithm, PALU formulates concise reasoning as a constrained optimization problem, minimizing response length subject to a performance constraint, and then applies Lagrangian optimization to convert it into a tractable unconstrained problem. As a pragmatic solution, PALU streamlines complicated update rules through three approximations: (i) estimating performance with off-policy rollouts, (ii) truncating the Lagrange multiplier to two extremes, and (iii) replacing gradient-based updates with quantile-driven length adjustments. PALU reduces output length by 65% while improving accuracy by 15% when applied to DeepSeek-Distill-Qwen-1.5B, averaged over five benchmarks, outperforming a range of alternative methods. Furthermore, PALU is demonstrated to adapt across both domain (logic, STEM and math) and model scale (1.5B, 7B, 14B) entrenching the algorithm as a practical and effective concise reasoning approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concise Reasoning in the Lens of Lagrangian Optimization Gao, Chengqian Li, Haonan Killian, Taylor W. She, Jianshu Wang, Renxi Ma, Liqun Cheng, Zhoujun Hao, Shibo Xu, Zhiqiang Artificial Intelligence Concise reasoning in large language models seeks to generate only essential intermediate steps needed to arrive at a final answer, thereby alleviating issues of overthinking. Most proposed approaches hinge on carefully hand-crafted heuristics, struggling to balance concision with performance, often failing to adapt across domains and model scales. In this work, we address these challenges by introducing a principled and pragmatic strategy, performance-aware length updating (PALU). As a principled algorithm, PALU formulates concise reasoning as a constrained optimization problem, minimizing response length subject to a performance constraint, and then applies Lagrangian optimization to convert it into a tractable unconstrained problem. As a pragmatic solution, PALU streamlines complicated update rules through three approximations: (i) estimating performance with off-policy rollouts, (ii) truncating the Lagrange multiplier to two extremes, and (iii) replacing gradient-based updates with quantile-driven length adjustments. PALU reduces output length by 65% while improving accuracy by 15% when applied to DeepSeek-Distill-Qwen-1.5B, averaged over five benchmarks, outperforming a range of alternative methods. Furthermore, PALU is demonstrated to adapt across both domain (logic, STEM and math) and model scale (1.5B, 7B, 14B) entrenching the algorithm as a practical and effective concise reasoning approach. |
| title | Concise Reasoning in the Lens of Lagrangian Optimization |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2510.10168 |