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

• URL: http://arxiv.org/abs/2605.22873v1
• Date: Wed, 20 May 2026 03:15:46 GMT
• Title: When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions
• Abstract summary: 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?<n> Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption.<n>We show that LLM reasoning is not a static property of tasks or models, but a emphdynamic decoding state that emerges during generation.<n>We propose textbfEDRM (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing
• Score: 42.557327309177175
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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