40 citations · 139 across the 37 of their papers we have counts for
5 papers · 1 filter
Joint Group Invariant Functions on Data-Parameter Domain Induce Universal Neural Networks
Sho Sonoda, Hideyuki Ishi, Isao Ishikawa +1
The symmetry and geometry of input data are considered to be encoded in the internal data representation inside the neural network, but the specific encoding rule has been less inv…
Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
Sho Sonoda, Yuka Hashimoto, Isao Ishikawa +1
We identify hidden layers inside a deep neural network (DNN) with group actions on the data domain, and formulate a formal deep network as a dual voice transform with respect to th…
Koopman spectral analysis of skew-product dynamics on Hilbert -modules
Dimitrios Giannakis, Yuka Hashimoto, Masahiro Ikeda +2
We introduce a linear operator on a Hilbert -module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it ad…
Koopman-based generalization bound: New aspect for full-rank weights
Yuka Hashimoto, Sho Sonoda, Isao Ishikawa +2
We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight…
Boundedness of composition operators on higher order Besov spaces in one dimension
Masahiro Ikeda, Isao Ishikawa, Koichi Taniguchi
This paper aims to characterize boundedness of composition operators on Besov spaces of higher order derivatives on the one-dimensional Euclidean space. In co…