Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases--thinking and solution--with independently allocated budgets. At test time, Elastic Reasoning prioritize that completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale.

本研究解决了大型推理模型在复杂任务中输出长度不受控的问题，影响其在实际应用中的部署。提出的弹性推理框架将推理过程明确分为思考和解决两阶段，并独立分配预算，显著提高了在资源紧张情况下的可靠性。实验证明，弹性推理在严格预算约束下表现出色，同时训练成本显著低于基线方法。 

可扩展的思维链通过弹性推理