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

Background

The effectiveness of chain-of-thought (CoT) reasoning in enhancing the capabilities of large language models (LLMs) is widely acknowledged. However, empirical evidence suggests that CoT can sometimes lead to marginal gains or even negative outcomes on certain tasks, particularly those involving factual and open-ended questions. This phenomenon raises a critical question: when is explicit reasoning truly beneficial?

Key Points

This research delves into the dynamic nature of LLM reasoning during task generation. It introduces EDRM (Entropy Dynamics-based Reasoning Manifold), which leverages early decoding entropy to adaptively select inference strategies, aiming to achieve efficient and adaptive LLM performance.

Entropy Dynamics Analysis

The study systematically examines the relationship between entropy dynamics and CoT reasoning effectiveness. Early-stage entropy reduction is identified as a reliable indicator of tasks that benefit from CoT. Tasks showing consistent entropy decrease are more likely to profit from structured reasoning processes. Conversely, those displaying unstable or increasing entropy patterns may not benefit significantly.

EDRM Framework

EDRM proposes a lightweight and training-free routing framework that dynamically selects inference strategies based on early decoding entropy. Entropy trajectories are embedded into a compact manifold representation, facilitating both zero-shot deployment and fine-grained instance-level adaptation. The framework's core concept is to invoke reasoning selectively rather than by default.

Significance

The findings demonstrate that EDRM can effectively reduce token consumption while maintaining or improving accuracy across various tasks and LLMs. At the dataset level, EDRM achieves a 41–55% reduction in tokens without compromising accuracy, with as few as 50 calibration samples. Instance-level analysis reveals up to a 4.7% improvement in accuracy alongside token savings of 27–45%.

Key Insights

• Dynamic Reasoning: LLM reasoning is not a static property but a dynamic decoding state that emerges during generation.
• Entropy-based Selection: Early-stage entropy reduction reliably predicts tasks benefiting from CoT, allowing for adaptive strategy selection.
• Efficiency and Adaptability: EDRM offers both reduced token consumption and enhanced accuracy through selective invocation of reasoning.

These results highlight the potential of entropy-driven decoding control in achieving efficient and adaptive LLM inference, suggesting a shift away from default CoT strategies to more contextually informed approaches.