# Hawkeye:Efficient Reasoning with Model Collaboration

arXiv: https://arxiv.org/abs/2504.00424 · HTML: https://mlsanity.com/paper/2504.00424/

## Key facts

- Cited by 11 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 23 of its 33 references that are in the map.
- First posted on arXiv 1 Apr 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, 23 of 23)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [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)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [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)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [Skeleton-of-Thought: Prompting LLMs for Efficient Parallel Generation](https://mlsanity.com/paper/2307.15337/) (2023)
- [Efficiently Scaling LLM Reasoning with Certaindex](https://mlsanity.com/paper/2412.20993/) (2024)
- [Rethinking Chain-of-Thought from the Perspective of Self-Training](https://mlsanity.com/paper/2412.10827/) (2024)

## Built on by (most cited first, 11 of 11)

- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Shorten After You're Right: Lazy Length Penalties for Reasoning RL](https://mlsanity.com/paper/2505.12284/) (2025)
- [HAPO: Training Language Models to Reason Concisely via History-Aware Policy Optimization](https://mlsanity.com/paper/2505.11225/) (2025)
- [A Survey on Collaborative Mechanisms Between Large and Small Language Models](https://mlsanity.com/paper/2505.07460/) (2025)
- [Don't Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models](https://mlsanity.com/paper/2505.21765/) (2025)
- [Exploring the System 1 Thinking Capability of Large Reasoning Models](https://mlsanity.com/paper/2504.10368/) (2025)
- [SPRINT: Enabling Interleaved Planning and Parallelized Execution in Reasoning Models](https://mlsanity.com/paper/2506.05745/) (2025)
- [How Far Are We from Optimal Reasoning Efficiency?](https://mlsanity.com/paper/2506.07104/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Concise Reasoning in the Lens of Lagrangian Optimization](https://mlsanity.com/paper/2510.10168/) (2025)
- [How Does Controllability Emerge In Language Models During Pretraining?](https://mlsanity.com/paper/2508.01892/) (2025)

## Abstract (arXiv)

Chain-of-Thought (CoT) reasoning has demonstrated remarkable effectiveness in enhancing the reasoning abilities of large language models (LLMs). However, its efficiency remains a challenge due to the generation of excessive intermediate reasoning tokens, which introduce semantic redundancy and overly detailed reasoning steps. Moreover, computational expense and latency are significant concerns, as the cost scales with the number of output tokens, including those intermediate steps. In this work, we observe that most CoT tokens are unnecessary, and retaining only a small portion of them is sufficient for producing high-quality responses. Inspired by this, we propose HAWKEYE, a novel post-training and inference framework where a large model produces concise CoT instructions to guide a smaller model in response generation. HAWKEYE quantifies redundancy in CoT reasoning and distills high-density information via reinforcement learning. By leveraging these concise CoTs, HAWKEYE is able to expand responses while reducing token usage and computational cost significantly. Our evaluation shows that HAWKEYE can achieve comparable response quality using only 35% of the full CoTs, while improving clarity, coherence, and conciseness by approximately 10%. Furthermore, HAWKEYE can accelerate end-to-end reasoning by up to 3.4x on complex math tasks while reducing inference cost by up to 60%. HAWKEYE will be open-sourced and the models will be available soon.