40 citations · 139 across the 37 of their papers we have counts for
3 papers · 1 filter
Why High-rank Neural Networks Generalize?: An Algebraic Framework with RKHSs
Yuka Hashimoto, Sho Sonoda, Isao Ishikawa +1
We derive a new Rademacher complexity bound for deep neural networks using Koopman operators, group representations, and reproducing kernel Hilbert spaces (RKHSs). The proposed bou…
Why and When Deep is Better than Shallow: Implementation-Agnostic State-Transition Model of Deep Learning
Sho Sonoda, Yuka Hashimoto, Isao Ishikawa +1
We ask when adding hidden layers improves generalization, in a model that keeps the layers fixed and varies only their number. A hidden layer is a self-map of a state space, a dept…
A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Yuanchao Xu, Kaidi Shao, Isao Ishikawa +3
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing meth…