Paper Info
Title
Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis.
Abstract
Neural network on Riemannian symmetric space such as hyperbolic space and the manifold of symmetric positive definite (SPD) matrices is an emerging subject of research in geometric deep learning. Based on the well-established framework of the Helgason-Fourier transform on the noncompact symmetric space, we present a fully-connected network and its associated ridgelet transform on the noncompact symmetric space, covering the hyperbolic neural network (HNN) and the SPDNet as special cases. The ridgelet transform is an analysis operator of a depth-2 continuous network spanned by neurons, namely, it maps an arbitrary given function to the weights of a network. Thanks to the coordinate-free reformulation, the role of nonlinear activation functions is revealed to be a wavelet function. Moreover, the reconstruction formula is applied to present a constructive proof of the universality of finite networks on symmetric spaces.
Year
Venue
DocType
2022
International Conference on Machine Learning
Conference
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Sho Sonoda162.95
Isao Ishikawa200.68
Masahiro Ikeda323.75