# Scalable Chain of Thoughts via Elastic Reasoning

arXiv: https://arxiv.org/abs/2505.05315 · HTML: https://mlsanity.com/paper/2505.05315/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 36 of its 44 references that are in the map.
- First posted on arXiv 8 May 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 36)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [A Long Way to Go: Investigating Length Correlations in RLHF](https://mlsanity.com/paper/2310.03716/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [C3oT: Generating Shorter Chain-of-Thought without Compromising Effectiveness](https://mlsanity.com/paper/2412.11664/) (2024)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [o1-Coder: an o1 Replication for Coding](https://mlsanity.com/paper/2412.00154/) (2024)
- [Efficient Reasoning with Hidden Thinking](https://mlsanity.com/paper/2501.19201/) (2025)

## Built on by (most cited first, 30 of 34)

- [GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning](https://mlsanity.com/paper/2507.01006/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [SelfBudgeter: Adaptive Token Allocation for Efficient LLM Reasoning](https://mlsanity.com/paper/2505.11274/) (2025)
- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [Interleaved Reasoning for Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2505.19640/) (2025)
- [DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning](https://mlsanity.com/paper/2510.02212/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [DRPO: Efficient Reasoning via Decoupled Reward Policy Optimization](https://mlsanity.com/paper/2510.04474/) (2025)
- [Multi-Turn On-Policy Distillation with Prefix Replay](https://mlsanity.com/paper/2607.04763/) (2026)
- [Making Small Language Models Efficient Reasoners: Intervention, Supervision, Reinforcement](https://mlsanity.com/paper/2505.07961/) (2025)
- [LAPO: Internalizing Reasoning Efficiency via Length-Adaptive Policy Optimization](https://mlsanity.com/paper/2507.15758/) (2025)
- [Thinker: Learning to Think Fast and Slow](https://mlsanity.com/paper/2505.21097/) (2025)
- [How Far Are We from Optimal Reasoning Efficiency?](https://mlsanity.com/paper/2506.07104/) (2025)
- [Hierarchical Budget Policy Optimization for Adaptive Reasoning](https://mlsanity.com/paper/2507.15844/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Procedural Knowledge at Scale Improves Reasoning](https://mlsanity.com/paper/2604.01348/) (2026)
- [RADAR: Reasoning-Ability and Difficulty-Aware Routing for Reasoning LLMs](https://mlsanity.com/paper/2509.25426/) (2025)
- [Mid-Think: Training-Free Intermediate-Budget Reasoning via Token-Level Triggers](https://mlsanity.com/paper/2601.07036/) (2026)
- [When Is Thinking Enough? Early Exit via Sufficiency Assessment for Efficient Reasoning](https://mlsanity.com/paper/2604.06787/) (2026)
- [PEAR: Phase Entropy Aware Reward for Efficient Reasoning](https://mlsanity.com/paper/2510.08026/) (2025)
- [When Domains Interact: Asymmetric and Order-Sensitive Cross-Domain Effects in Reinforcement Learning for Reasoning](https://mlsanity.com/paper/2602.01365/) (2026)
- [When to Think, When to Speak: Learning Disclosure Policies for LLM Reasoning](https://mlsanity.com/paper/2605.03314/) (2026)
- [Pruning Long Chain-of-Thought of Large Reasoning Models via Small-Scale Preference Optimization](https://mlsanity.com/paper/2508.10164/) (2025)
- [Before you <think>, monitor: Implementing Flavell's metacognitive framework in LLMs](https://mlsanity.com/paper/2510.16374/) (2025)
- [Beyond Variance: Prompt-Efficient RLVR via Rare-Event Amplification and Bidirectional Pairing](https://mlsanity.com/paper/2602.03452/) (2026)
- [Stop Unnecessary Reflection: Training LRMs for Efficient Reasoning with Adaptive Reflection and Length Coordinated Penalty](https://mlsanity.com/paper/2602.12113/) (2026)
- [Buy versus Build an LLM: A Decision Framework for Governments](https://mlsanity.com/paper/2602.13033/) (2026)
- [The Coupling Tax: How Shared Token Budgets Undermine Visible Chain-of-Thought Under Fixed Output Limits](https://mlsanity.com/paper/2605.07686/) (2026)

## Abstract (arXiv)

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 prioritizes the 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. Our code has been made available at https://github.com/SalesforceAIResearch/Elastic-Reasoning.