# How Far Are We from Optimal Reasoning Efficiency?

arXiv: https://arxiv.org/abs/2506.07104 · HTML: https://mlsanity.com/paper/2506.07104/

## Key facts

- Cited by 8 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 51 of its 60 references that are in the map.
- First posted on arXiv 8 Jun 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 51)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (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)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Model](https://mlsanity.com/paper/2504.07615/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [DAST: Difficulty-Adaptive Slow-Thinking for Large Reasoning Models](https://mlsanity.com/paper/2503.04472/) (2025)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [C3oT: Generating Shorter Chain-of-Thought without Compromising Effectiveness](https://mlsanity.com/paper/2412.11664/) (2024)

## Built on by (most cited first, 8 of 8)

- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoT](https://mlsanity.com/paper/2509.19284/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [Your Models Have Thought Enough: Training Large Reasoning Models to Stop Overthinking](https://mlsanity.com/paper/2509.23392/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [TERMINATOR: Learning Optimal Exit Points for Early Stopping in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2603.12529/) (2026)
- [Draft-Thinking: Learning Efficient Reasoning in Long Chain-of-Thought LLMs](https://mlsanity.com/paper/2603.00578/) (2026)
- [CAM: A Causality-based Analysis Framework for Multi-Agent Code Generation Systems](https://mlsanity.com/paper/2602.02138/) (2026)

## Abstract (arXiv)

Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency incurs high inference costs and limits practical deployment. While existing fine-tuning methods aim to improve reasoning efficiency, assessing their efficiency gains remains challenging due to inconsistent evaluations. In this work, we introduce the reasoning efficiency frontiers, empirical upper bounds derived from fine-tuning base LRMs across diverse approaches and training configurations. Based on these frontiers, we propose the Reasoning Efficiency Gap (REG), a unified metric quantifying deviations of any fine-tuned LRMs from these frontiers. Systematic evaluation on challenging mathematical benchmarks reveals significant gaps in current methods: they either sacrifice accuracy for short length or still remain inefficient under tight token budgets. To reduce the efficiency gap, we propose REO-RL, a class of Reinforcement Learning algorithms that minimizes REG by targeting a sparse set of token budgets. Leveraging numerical integration over strategically selected budgets, REO-RL approximates the full efficiency objective with low error using a small set of token budgets. Through systematic benchmarking, we demonstrate that our efficiency metric, REG, effectively captures the accuracy-length trade-off, with low-REG methods reducing length while maintaining accuracy. Our approach, REO-RL, consistently reduces REG by >=50 across all evaluated LRMs and matching Qwen3-4B/8B efficiency frontiers under a 16K token budget with minimal accuracy loss. Ablation studies confirm the effectiveness of our exponential token budget strategy. Finally, our findings highlight that fine-tuning LRMs to perfectly align with the efficiency frontiers remains an open challenge.