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

arXiv:2604.05355v1 Announce Type: new 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 lengt

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Xuan Xiong, Huan Liu, Li Gu, Zhixiang Chi, Yue Qiu, Yuanhao Yu, Yang Wang · · 1 min read · 7 views
#cs.AI #cs.CL

arXiv:2604.05355v1 Announce Type: new 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

Executive Summary

The paper introduces Entropy Trend Reward (ETR), a novel trajectory-aware objective designed to optimize chain-of-thought (CoT) reasoning in large language models (LLMs). By shifting focus from static uncertainty reduction to dynamic uncertainty trajectories, ETR encourages progressive uncertainty reduction while permitting controlled local exploration. Integrated with Group Relative Policy Optimization (GRPO), ETR demonstrates significant improvements in accuracy-efficiency tradeoffs across multiple benchmarks. Notably, it enhances DeepSeek-R1-Distill-7B's accuracy by 9.9% while reducing CoT length by 67%. This work challenges conventional assumptions about CoT optimization and offers a scalable solution for more efficient and effective LLM reasoning.

Key Points

  • ▸ ETR redefines CoT optimization by prioritizing entropy trend dynamics over static uncertainty reduction, enabling more efficient reasoning paths.
  • ▸ The method leverages trajectory-aware rewards within GRPO, allowing progressive uncertainty reduction while tolerating localized exploration to avoid premature convergence.
  • ▸ Empirical results across multiple models and benchmarks validate ETR’s superior accuracy-efficiency tradeoff, with substantial reductions in CoT length and improvements in task performance.

Merits

Theoretical Innovation

ETR introduces a paradigm shift from static to dynamic uncertainty optimization, addressing a critical gap in CoT reasoning research. Its trajectory-aware approach aligns with cognitive science principles of progressive problem decomposition.

Empirical Robustness

The method demonstrates consistent performance gains across diverse benchmarks and models, including a 9.9% accuracy improvement and 67% reduction in CoT length for DeepSeek-R1-Distill-7B, indicating broad applicability and scalability.

Computational Efficiency

By shortening CoT lengths without sacrificing accuracy, ETR reduces computational overhead, making it a practical solution for deploying LLMs in resource-constrained environments.

Demerits

Limited Generalizability

While ETR shows strong performance on reasoning benchmarks, its effectiveness in real-world, open-ended tasks or multimodal reasoning remains untested, warranting further validation.

Dependence on GRPO Integration

ETR’s efficacy is demonstrated in conjunction with GRPO; its standalone performance or compatibility with other optimization frameworks is not explored, potentially limiting its adoption.

Hyperparameter Sensitivity

The method’s reliance on trajectory-aware rewards may introduce sensitivity to hyperparameters, such as reward shaping or exploration thresholds, which could affect reproducibility.

Expert Commentary

The authors present a compelling case for rethinking CoT optimization through the lens of entropy trends, challenging the prevailing paradigm of static uncertainty reduction. Their integration of trajectory-aware rewards with GRPO is both innovative and empirically validated, offering a nuanced solution to the inefficiency plaguing CoT reasoning. The results are particularly striking given the substantial improvements in both accuracy and efficiency, which are often inversely correlated in LLM optimization. However, the method’s reliance on GRPO and untested generalizability to non-reasoning tasks warrant caution. Future work should explore the theoretical underpinnings of entropy trends in cognitive architectures and assess ETR’s robustness in more complex, real-world scenarios. This paper marks a significant advancement in the field, with implications that extend beyond LLMs to broader AI systems where dynamic uncertainty management is critical.

Recommendations

  • ✓ Further research should evaluate ETR’s performance in open-ended, multimodal, and real-world tasks to validate its generalizability beyond benchmark settings.
  • ✓ Investigate the method’s compatibility with alternative RL frameworks (e.g., PPO, DPO) to assess its standalone efficacy and broaden its adoption potential.
  • ✓ Develop standardized metrics for uncertainty trajectory optimization to enable fairer comparisons across different methods and models.
  • ✓ Explore the integration of ETR with interpretability tools to enhance the explainability of LLM reasoning processes, particularly in high-stakes applications.

Sources

Original: arXiv - cs.AI

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