ETR: Entropy Trend Reward for Efficient Chain-of-Thought Reasoning

TL;DR

This paper introduces Entropy Trend Reward (ETR), a new training objective that enhances the efficiency of chain-of-thought reasoning in language models by promoting decreasing uncertainty trajectories.

Contribution

The paper proposes ETR, a trajectory-aware reward that improves reasoning efficiency by encouraging uncertainty reduction, integrated into policy optimization for better accuracy and shorter reasoning traces.

Findings

ETR achieves a 9.9% accuracy improvement on DeepSeek-R1-Distill-7B.

ETR reduces chain-of-thought length by 67% across four benchmarks.

ETR outperforms existing length penalties and entropy reduction methods.

Abstract

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy-efficiency tradeoff, improving DeepSeek-R1-Distill-7B by 9.9% in accuracy while reducing CoT length by 67% across four benchmarks. Code is available at https://github.com/Xuan1030/ETR