A Geometric Approach to Steerable Convolutions
This work offers a clearer understanding and improved implementation for researchers in geometric deep learning, though it appears incremental as it builds on existing steerable convolution frameworks.
The paper tackles the abstract derivation of steerable convolutional neural networks by providing a more intuitive geometric approach based on pattern matching principles, which also leads to a novel construction using interpolation kernels that improves robustness to noisy data.
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.