CODA: Difficulty-Aware Compute Allocation for Adaptive Reasoning

• URL: http://arxiv.org/abs/2603.08659v1
• Date: Mon, 09 Mar 2026 17:37:15 GMT
• Title: CODA: Difficulty-Aware Compute Allocation for Adaptive Reasoning
• Abstract summary: Over simple problems, reasoning can yield minimal accuracy gains at a disproportionately high cost.<n>This motivates adaptive reasoning: dynamically aligning reasoning depth with difficulty.<n>We propose CODA ( Allocation by Difficulty) to formalize it as a utility problem.<n> CODA reduces token costs by over 60% while maintaining strong accuracy, whereas on hard tasks it incentivizes more rollouts to maximize performance.
• Score: 45.97014851622867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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