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Functional Attentive Interpretable Regression

arXiv · AI, language, vision and robotics · article · Sep 5, 2026 · UTC

In function-on-function regression, the coefficient surface $β(s,t)$ may exhibit complex support structure---from localized patches to global patterns such as disconnected regions, bands, or rings---where effect similarity does not align with Euclidean proximity. Projection-based methods that rely on fixed basis expansions can obscure such structure, while direct smoothing approaches risk oversmoothing the surface and its boundaries. We propose Functional Attentive Interpretable Regression (FAIR), which represents $β(s,t)$ directly through coordinate features and uses self-attention to learn e

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