Scalable Chain of Thoughts via Elastic Reasoning

2025-05-08

AI Summary

Uncontrollable chain-of-thought (CoT) length in large reasoning models hinders deployment under resource constraints. This paper proposes an elastic inference framework that, for the first time, decouples CoT into two independently budget-allocatable phases: “thinking” and “solving.” Methodologically, we introduce budget-aware rollout sampling, truncation-robust training, and a lightweight GRPO-based reinforcement learning policy—enabling zero-shot generalization across arbitrary computational budgets and, conversely, improving inference conciseness in unconstrained settings. Experiments on AIME, MATH500, LiveCodeBench, and Codeforces demonstrate significant improvements over baselines: enhanced reliability under strict budget constraints, substantially reduced training cost, and more efficient, concise reasoning when budgets are unconstrained. The framework achieves cross-budget zero-shot adaptability without fine-tuning, establishing a new paradigm for controllable, resource-aware reasoning.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Control uncontrolled output lengths in large reasoning models
• Balance reasoning completeness under strict resource constraints
• Train models robust to truncated thinking without extra training

Innovation

• Elastic Reasoning splits thinking and solution phases
• Budget-constrained rollout strategy enhances robustness
• Prioritizes solution completeness under tight constraints