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[Submitted on 4 Sep 2026] Title:Capsule Lens: Locating and Tracking Concept Geometry in Model Representations View a PDF of the paper titled Capsule Lens: Locating and Tracking Concept Geometry in Model Representations, by Yiming Tang and 5 other authors View PDF HTML (experimental) Abstract:Understanding how concepts are encoded in the internal representations of machine learning models is a central problem in mechanistic interpretability, essential both for the science of deep learning and for the trustworthy deployment of increasingly capable models. Existing approaches to interpret model representations mainly map representations onto more interpretable spaces and do not directly characterize how concepts occupy representation space; various hypotheses have been proposed, but often lack of rigorous validation and largely focus on static representations. In this work, we introduce Capsule Lens, a framework that matches the region a concept occupies with a simple, trackable geometric form, a capsule, defined by several interpretable parameters, fitted in closed form to each concept's geometry and validated on held-out samples. We apply Capsule Lens in two major settings: static and dynamic representations. On static representations, we demonstrate how to locate concept geometry across various models, and how the span and norm curves uncover important geometric characteristics. On dynamic representations, we present three case studies tracking representation drifts induced by distinct training settings, CLIP pretraining, RL post-training on visual question answering, and RL post-training on mathematical reasoning. These analyses reveal qualitatively different geometric dynamics, ranging from broad network-wide restructuring in CLIP pretraining to localized and concept-specific changes in RL post-training. Our results include findings aligned with existing literature as well as novel observations. We believe Capsule Lens stands as a promising tool for locating, analyzing, and tracking concept geometry in both static and dynamic representations. Subjects: Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2609.05575 [cs.LG] (or arXiv:2609.05575v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.05575 arXiv-issued DOI via DataCite Submission history From: Yiming Tang [view email] [v1] Fri, 4 Sep 2026 09:15:04 UTC (2,675 KB) Full-text links: Access Paper: View a PDF of the paper titled Capsule Lens: Locating and Tracking Concept Geometry in Model Representations, by Yiming Tang and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs cs.CV 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?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) 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?)