How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories

ACL ARR 2026 May Submission15423 Authors

Keywords: Chain-of-Thoughts, Reasoning Energy, Explainability, Large Language Model

Abstract: Understanding how computational effort is allocated across individual reasoning steps in chain-of-thought (CoT) trajectories is a key open challenge for LLM interpretability, yet existing methods either rely on output-level signals or collapse processing depth into a single trajectory-level scalar, leaving step-wise reasoning effort opaque. We propose Step-Aware Reasoning Energy (SARE), a geometric framework that quantifies computational effort at the granularity of individual CoT steps via Centered Kernel Alignment (CKA) between Gram matrices of token hidden states across adjacent transformer layers. Unlike token-level or output-based proxies, SARE captures inter-token relational structure without requiring eigenvector alignment or cluster correspondence, and further contextualizes energy within the semantic progression of reasoning by modeling CoT trajectories as transitions among latent semantic states. Experiments across six reasoning benchmarks and three open-weight LLMs reveal three consistent findings: reasoning energy is highly non-uniform across semantic step types, exhibiting structured phase-like transitions invisible to trajectory-level metrics; incorrect trajectories are associated with systematically lower energy at critical reasoning junctions; and SARE-based features match or outperform output-based confidence baselines across most evaluated settings, demonstrating that internal geometric dynamics encode predictive information beyond surface-level signals.

Paper Type: Long

Research Area: Interpretability and Analysis of Models for NLP

Research Area Keywords: probing, calibration/uncertainty, hardness of samples

Contribution Types: Model analysis & interpretability

Languages Studied: English

EMNLP 2026 AI Reviewing Experiment: yes

Submission Number: 15423