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[Submitted on 3 Oct 2026] Title:Beyond the Linear Representation Hypothesis: Non-Linear Activation Steering in Text-to-Image Models View a PDF of the paper titled Beyond the Linear Representation Hypothesis: Non-Linear Activation Steering in Text-to-Image Models, by Muhammad Atif Butt and 3 other authors View PDF HTML (experimental) Abstract:Mechanistic interpretability often relies on the Linear Representation Hypothesis (LRH), which assumes that high-level concepts are encoded as linear directions in activation space. Yet a natural visual concept does not necessarily require a linear visual transition: between sunny and stormy lies an intermediate weather state such as a sky with a few white clouds, not simply a weaker storm; between a caterpillar and a butterfly, the progression is not a caterpillar with continuously growing wings. This raises the question of whether such true intermediate states are also represented nonlinearly by the model. Indeed, when we prompt text-to-image models directly for intermediate attributes, their activations rarely fall along the straight direction connecting the endpoints. Therefore, we propose KANSteer, which models concept traversal as a curve passing through its intermediate states. Seeking a representation that is both simple and interpretable, we propose to use Kolmogorov-Arnold Networks (KANs), which provide a one-dimensional coordinate whose learned functions define the trajectory. This allows the steering direction to vary along the concept while preserving an interpretable representation. Across several concepts and text-to-image diffusion transformers, we find that their activation trajectories substantially deviate from straight lines, and that KANSteer provide a closer fit and smoother traversal of intermediate attributes than linear steering. Subjects: Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2610.06945 [cs.CV] (or arXiv:2610.06945v1 [cs.CV] for this version) https://doi.org/10.48550/arXiv.2610.06945 arXiv-issued DOI via DataCite (pending registration) Submission history From: Muhammad Atif Butt [view email] [v1] Sat, 3 Oct 2026 10:32:28 UTC (43,730 KB) Full-text links: Access Paper: View a PDF of the paper titled Beyond the Linear Representation Hypothesis: Non-Linear Activation Steering in Text-to-Image Models, by Muhammad Atif Butt and 3 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CV new | recent | 2026-10 Change to browse by: cs 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?)