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arXiv · 2510.18813

A Geometric Approach to Steerable Convolutions

Soumyabrata Kundu·Risi Kondor
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Abstract

In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on geometric arguments and fundamental principles of pattern matching. We offer an intuitive explanation for the appearance of the Clebsch--Gordan decomposition and spherical harmonic basis functions. Furthermore, we suggest a novel way to construct steerable convolution layers using interpolation kernels that improve upon existing implementation, and offer greater robustness to noisy data.

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Soumyabrata Kundu, Risi Kondor. 2025-10-21. A Geometric Approach to Steerable Convolutions. https://arxiv.org/abs/2510.18813

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