12 citations · 24 across the 14 of their papers we have counts for
4 papers · 1 filter
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…
Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator
Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri
Reproducing kernel Hilbert -module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of -algebra, and the Perron-Frobenius operator is a line…
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…
Noncommutative -algebra Net: Learning Neural Networks with Powerful Product Structure in -algebra
Ryuichiro Hataya, Yuka Hashimoto
We propose a new generalization of neural network parameter spaces with noncommutative -algebra, which possesses a rich noncommutative structure of products. We show that this…