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The dominant formulation attaches one such function to every kernel entry and lets it act on pixel values, expressive but parameter-heavy and prone to overfitting. We argue that the learnable functions are better placed in the \\emph{structure} of the convolution than on each edge, and we organise the design space along a single axis: whether the function acts on the pixel \\emph{values} or on the filter \\emph{shape}. We study three realisations. SV-KAN applies one shared univariate function to the values and leaves the spatial filter free and static, aa classical convolution with a single learnable shared activation. AG-KAN keeps the shared value function but supplies the spatial structure through a content-adaptive Gaussian gate. RF-KAN instead moves the learnable functions onto the filter shape, bui","title":"Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs","url":"https://arxiv.org/abs/2606.24371","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.24371v1 Announce Type: cross \nAbstract: Convolutional Kolmogorov--Arnold Networks (KANs) replace the fixed weights of a convolutional kernel with learnable univariate functions. The dominant formulation attaches one such function to every kernel entry and lets it act on pixel values, expressive but parameter-heavy and prone to overfitting. We argue that the learnable functions are better placed in the \\emph{structure} of the convolution than on each edge, and we organise the design space along a single axis: whether the function acts on the pixel \\emph{values} or on the filter \\emph{shape}. We study three realisations. 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