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

Computer Science > Artificial Intelligence [Submitted on 28 Jul 2026] How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories Hui Wei, Junda Wu, Sheldon Yu, Sizhe Zhou, Yizhu Jiao, Ming Zhong, Bowen Jin, Tong Yu, Shijia Pan, Jiawei Han, Julian McAuley Understanding how computational effort is allocated across individual chain-of-thought (CoT) reasoning steps remains an open challenge: existing interpretability methods rely on output-level signals or collapse processing depth into a single trajectory-level scalar, leaving step-wise effort opaque. We propose Step-Aware Reasoning Energy (SARE), a geometric framework that quantifies effort at the granularity of individual CoT steps via Centered Kernel Alignment (CKA) between Gram matrices of token hidden states across adjacent transformer layers, capturing inter-token relational structure without requiring eigenvector alignment or cluster correspondence. SARE further contextualizes this energy within reasoning's semantic progression by modeling CoT trajectories as transitions among latent semantic states. Across six reasoning benchmarks and three open-weight LLMs, we find that reasoning energy is highly non-uniform across step types, exhibiting phase-like transitions invisible to trajectory-level metrics; incorrect trajectories show systematically lower energy at critical reasoning junctions; and SARE-based features match or outperform output-based confidence baselines in most settings, indicating that internal geometric dynamics encode predictive information beyond surface-level signals. Comments: 13 pages, 3 figures Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG) Cite as: arXiv:2607.28674 [cs.AI]   (or arXiv:2607.28674v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2607.28674 Focus to learn more Submission history From: Hui Wei [view email] [v1] Tue, 28 Jul 2026 06:15:51 UTC (2,030 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-07 Change to browse by: cs cs.CL cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)