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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.08659 |
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| _version_ | 1866917385076736000 |
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| author | Wu, Siye Xie, Jian Zhang, Yikai Xiao, Yanghua |
| author_facet | Wu, Siye Xie, Jian Zhang, Yikai Xiao, Yanghua |
| contents | The emergence of large reasoning models demonstrates that scaling inference-time compute significantly enhances performance on complex tasks. However, it often falls into another trap: overthinking simple problems, where repetitive rationales yield minimal accuracy gains at a disproportionately high cost. This motivates adaptive reasoning: dynamically aligning reasoning depth with instance difficulty. In this paper, we study adaptive reasoning from an optimality perspective, formalizing it as a utility maximization problem where tokens are allocated until the marginal accuracy gain falls below the incremental cost. Based on this, we propose CODA (Compute Allocation by Difficulty Awareness), a method that operationalizes this principle by allocating tokens via a policy-internal difficulty signal. Specifically, CODA estimates difficulty via group-based rollouts and maps it to two non-negative gates that modulate a length-dependent shaping term on top of the binary base reward. The easy-side gate penalizes verbosity on simple instances, whereas the hard-side gate encourages more deliberative rollouts on challenging ones. Across model scales and benchmarks, CODA achieves adaptive reasoning without external annotations or user-provided budgets: on easy tasks, CODA reduces token costs by over 60% while maintaining strong accuracy, whereas on hard tasks it incentivizes more deliberative rollouts to maximize performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CODA: Difficulty-Aware Compute Allocation for Adaptive Reasoning Wu, Siye Xie, Jian Zhang, Yikai Xiao, Yanghua Computation and Language The emergence of large reasoning models demonstrates that scaling inference-time compute significantly enhances performance on complex tasks. However, it often falls into another trap: overthinking simple problems, where repetitive rationales yield minimal accuracy gains at a disproportionately high cost. This motivates adaptive reasoning: dynamically aligning reasoning depth with instance difficulty. In this paper, we study adaptive reasoning from an optimality perspective, formalizing it as a utility maximization problem where tokens are allocated until the marginal accuracy gain falls below the incremental cost. Based on this, we propose CODA (Compute Allocation by Difficulty Awareness), a method that operationalizes this principle by allocating tokens via a policy-internal difficulty signal. Specifically, CODA estimates difficulty via group-based rollouts and maps it to two non-negative gates that modulate a length-dependent shaping term on top of the binary base reward. The easy-side gate penalizes verbosity on simple instances, whereas the hard-side gate encourages more deliberative rollouts on challenging ones. Across model scales and benchmarks, CODA achieves adaptive reasoning without external annotations or user-provided budgets: on easy tasks, CODA reduces token costs by over 60% while maintaining strong accuracy, whereas on hard tasks it incentivizes more deliberative rollouts to maximize performance. |
| title | CODA: Difficulty-Aware Compute Allocation for Adaptive Reasoning |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2603.08659 |