In this work, we introduce the reasoning efficiency frontiers, empirical upper bounds derived from fine-tuning base LRMs (DeepSeek-R1-Distill-Qwen-1.5B/7B and Qwen3-4B/8B) across diverse approaches and training configurations. Our major contributions are:

• REG (Reasoning Efficiency Gap): an unified metric that measures the gap of a fine-tuned LRM to the efficiency frontiers.
• REO-RL: a class of RL algorithms that minimizes the efficiency gap by improving rewards under a sparse set of token budgets.

Reasoning Efficiency Frontiers

We evaluate the reasoning efficiency frontiers for DeepSeek-R1-Distill-Qwen-1.5B/7B and Qwen3-4B/8B on four mathematical reasoning benchmarks: AMC 2023, AIME 2024&2025, and Minerva Math. These frontiers are provided in data/frontiers.

TODO

• Efficiency Frontiers
• Evaluation Scripts for REG
• REO-RL Implementation

Citation

@misc{gao2025faroptimalreasoningefficiency,
      title={How Far Are We from Optimal Reasoning Efficiency?}, 
      author={Jiaxuan Gao and Shu Yan and Qixin Tan and Lu Yang and Shusheng Xu and Wei Fu and Zhiyu Mei and Kaifeng Lyu and Yi Wu},
      year={2025},
      eprint={2506.07104},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2506.07104}, 
}