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--> [Submitted on 28 Jul 2026] Title:How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories View a PDF of the paper titled How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories, by Hui Wei and 10 other authors View PDF HTML (experimental) Abstract: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 arXiv-issued DOI via DataCite Submission history From: Hui Wei [view email] [v1] Tue, 28 Jul 2026 06:15:51 UTC (2,030 KB) Full-text links: Access Paper: View a PDF of the paper titled How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories, by Hui Wei and 10 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-07 Change to browse by: cs cs.CL cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)