Sprint or Delve: A Distribution-Aware Approach to Efficient Reasoning
TL;DR
The Powered Length Penalty (PLP) is proposed, an adaptive regularizer that penalizes redundancy in short sequences while gradually reducing penalties for longer sequences, preserving deep reasoning.
Abstract
Reasoning chains in Large Language Models (LLMs) often exhibit heavy-tailed length distributions, yet existing efficiency methods rely on suboptimal linear penalties that suppress complex reasoning, limiting both accuracy and generalization. To address this, we first empirically observe that reasoning lengths are well approximated by a log-normal distribution, and provide an intuitive explanation for this phenomenon. Based on this insight, we propose the Powered Length Penalty (PLP), an adaptive regularizer that penalizes redundancy in short sequences while gradually reducing penalties for longer sequences, preserving deep reasoning. Trained solely on the elementary GSM8K dataset, PLP significantly improves reasoning efficiency by reducing inference costs on GSM8K and MATH500, while simultaneously enhancing accuracy on the challenging AIME2024 benchmark. Furthermore, PLP transfers effectively to diverse domains, including MMLU and GPQA. These results suggest that modeling reasoning length distributions and adapting penalties accordingly can mitigate the typical trade-off between efficiency and performance, enabling more reliable and cost-effective reasoning across tasks.