# Fast on the Easy, Deep on the Hard: Efficient Reasoning via Powered Length Penalty Source: [Fast on the Easy, Deep on the Hard: Efficient Reasoning via Powered Length Penalty]() Collection index: [llms.txt]() Data updated: 2025-10-26T04:56:50.224Z Authors: Zehui Ling, Deshu Chen, Hongwei Zhang, Yifeng Jiao, Xin Guo, Yuan Cheng Published: 2025-06-12T07:49:24.000Z ## Abstract Large language models (LLMs) have demonstrated significant advancements in reasoning capabilities, performing well on various challenging benchmarks. Techniques like Chain-of-Thought prompting have been introduced to further improve reasoning. However, these approaches frequently generate longer outputs, which in turn increase computational latency. Although some methods use reinforcement learning to shorten reasoning, they often apply uniform penalties without considering the problem's complexity, leading to suboptimal outcomes. In this study, we seek to enhance the efficiency of LLM reasoning by promoting conciseness for simpler problems while preserving sufficient reasoning for more complex ones for accuracy, thus improving the model's overall performance. Specifically, we manage the model's reasoning efficiency by dividing the reward function and including a novel penalty for output length. Our approach has yielded impressive outcomes in benchmark evaluations across three datasets: GSM8K, MATH500, and AIME2024. For the comparatively simpler datasets GSM8K and MATH500, our method has effectively shortened output lengths while preserving or enhancing accuracy. On the more demanding AIME2024 dataset, our approach has resulted in improved accuracy. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Mathematical Reasoning on OlympiadBench (Acc, Tokens, EFF)](): Mathematical Reasoning; OlympiadBench; Accuracy: 63.5. - [Mathematical Reasoning on AIME 2025 (Acc, Tokens, EFF)](): Mathematical Reasoning; AIME 2025; Accuracy: 46.7. ## Original sources and implementation [Original paper]() [PDF]()