When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions

2026-05-19

AI Summary

This work challenges the prevailing assumption that large language models (LLMs) universally require explicit reasoning strategies—such as chain-of-thought prompting—and demonstrates that their necessity varies by task, with indiscriminate application often leading to computational waste or even performance degradation. The authors propose that reasoning emerges dynamically during decoding rather than being an inherent property of a task, and introduce, for the first time, an analogy to entropy phase transitions. Leveraging entropy trajectories from early decoding stages, they construct a lightweight, interpretable Entropy-based Decoding Reasoning Manifold (EDRM) that enables training-free, instance-level adaptive reasoning routing. Experiments across 15 benchmarks and four mainstream LLMs show that with only 50 calibration samples, EDRM reduces token consumption by 41–55% at the dataset level while improving accuracy; at the instance level, it achieves up to a 4.7% absolute accuracy gain alongside 27–45% fewer tokens used.

Abstract

Chain-of-thought (CoT) reasoning has become the default strategy for enhancing LLM capabilities, yet its application raises a fundamental question: when is explicit reasoning actually beneficial? Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption. In this work, we show that LLM reasoning is not a static property of tasks or models, but a \emph{dynamic decoding state} that emerges during generation. Through systematic analysis, we find early-stage entropy dynamics provide a reliable signal of this state: tasks benefiting from CoT exhibit consistent entropy reduction, while others display unstable or increasing patterns. This behavior can be interpreted as a phase-transition-like shift from a high-entropy exploratory regime to a low-entropy structured reasoning regime. Based on these insights, we propose \textbf{EDRM} (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing framework that leverages early decoding entropy to adaptively select inference strategies. EDRM embeds entropy trajectories into a compact and interpretable manifold representation, enabling both zero-shot deployment and fine-grained instance-level adaptation. Across 15 benchmarks and 4 LLMs of varying scales and architectures, EDRM consistently outperforms static baselines. At the dataset level, EDRM achieves \textbf{41--55\%} token reduction while improving accuracy with as few as 50 calibration samples. At the instance level, it further improves accuracy by up to \textbf{4.7\%} while maintaining \textbf{27--45\%} token savings. These results suggest that reasoning should be invoked selectively rather than by default, and demonstrate the effectiveness of entropy-driven decoding control for efficient and adaptive LLM inference.

Problem

• LLM reasoning
• Chain-of-thought
• entropy dynamics
• phase transition
• inference efficiency

Innovation

• entropy dynamics
• chain-of-thought reasoning
• adaptive inference
• phase transition
• decoding control