[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
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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)
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