# The Price of a Second Thought: On the Evaluation of Reasoning Efficiency in Large Language Models

arXiv: https://arxiv.org/abs/2505.22017 · HTML: https://mlsanity.com/paper/2505.22017/

## Key facts

- Cited by 18 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 41 of its 49 references that are in the map.
- First posted on arXiv 28 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 41)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [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)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [Inductive Biases and Variable Creation in Self-Attention Mechanisms](https://mlsanity.com/paper/2110.10090/) (2021)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (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)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Sketch-of-Thought: Efficient LLM Reasoning with Adaptive Cognitive-Inspired Sketching](https://mlsanity.com/paper/2503.05179/) (2025)

## Built on by (most cited first, 18 of 18)

- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [The Markovian Thinker: Architecture-Agnostic Linear Scaling of Reasoning](https://mlsanity.com/paper/2510.06557/) (2025)
- [SABER: Switchable and Balanced Training for Efficient LLM Reasoning](https://mlsanity.com/paper/2508.10026/) (2025)
- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Probing the Trajectories of Reasoning Traces in Large Language Models](https://mlsanity.com/paper/2601.23163/) (2026)
- [SLR: Automated Synthesis for Scalable Logical Reasoning](https://mlsanity.com/paper/2506.15787/) (2025)
- [Accordion-Thinking: Self-Regulated Step Summaries for Efficient and Readable LLM Reasoning](https://mlsanity.com/paper/2602.03249/) (2026)
- [System 1&2 Synergy via Dynamic Model Interpolation](https://mlsanity.com/paper/2601.21414/) (2026)
- [Expanding Computation Spaces of LLMs at Inference Time](https://mlsanity.com/paper/2509.24884/) (2025)
- [PACE: Prefix-Protected and Difficulty-Aware Compression for Efficient Reasoning](https://mlsanity.com/paper/2602.11639/) (2026)
- [Stop Unnecessary Reflection: Training LRMs for Efficient Reasoning with Adaptive Reflection and Length Coordinated Penalty](https://mlsanity.com/paper/2602.12113/) (2026)
- [TRiMS: Real-Time Tracking of Minimal Sufficient Length for Efficient Reasoning via RL](https://mlsanity.com/paper/2603.17449/) (2026)
- [Reasoning about Reasoning: BAPO Bounds on Chain-of-Thought Token Complexity in LLMs](https://mlsanity.com/paper/2602.02909/) (2026)
- [When Less is Enough: Efficient Inference via Collaborative Reasoning](https://mlsanity.com/paper/2605.01111/) (2026)
- [Token-Operations-Oriented Inference Optimization Techniques for Large Models](https://mlsanity.com/paper/2606.20295/) (2026)
- [Revisiting Complete Reasoning Traces for Post-Training](https://mlsanity.com/paper/2609.07103/) (2026)

## Abstract (arXiv)

Recent thinking models trained with reinforcement learning and backward-checking CoT often suffer from overthinking: they produce excessively long outputs even on simple problems, wasting computation. Existing evaluations, based on token efficiency, give an incomplete view as they neglect problem difficulty and intermediate computation costs. We formalize reasoning efficiency as a relative measure between thinking and instruct models, treating instruct models as the minimal-effort baseline. A systematic study across four thinking models and multiple benchmarks reveals two consistent patterns: (i) instruct models achieve higher efficiency overall, and (ii) problem difficulty affects efficiency, with thinking models wasting computation on easy problems but providing value on harder ones. Building on this insight, we propose COTHINK, a simple two-stage pipeline: an instruct model drafts a brief outline, and a thinking model expands it. On GSM8K, MATH500, and AIME24, COTHINK cuts token usage by 21.1% while keeping accuracy on four thinking models, and remains competitive with strong efficiency baselines.