Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces. (arXiv:2206.08362v3 [cs.CV] UPDATED)

We introduce a unified framework for group equivariant networks on
homogeneous spaces derived from a Fourier perspective. We consider
tensor-valued feature fields, before and after a convolutional layer. We
present a unified derivation of kernels via the Fourier domain by leveraging
the sparsity of Fourier coefficients of the lifted feature fields. The sparsity
emerges when the stabilizer subgroup of the homogeneous space is a compact Lie
group. We further introduce a nonlinear activation, via an elementwise
nonlinearity on the regular …

arxiv cv design kernel networks