4 citations · 5 across the 10 of their papers we have counts for
6 papers · 1 filter
Unified generalization analysis for physics informed neural networks
Yuka Hashimoto, Tomoharu Iwata
Physics-Informed Neural Networks (PINNs) and their variational counterparts (VPINNs) are neural networks that incorporate physical laws, making them useful for scientific problems.…
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…
Deep Ridgelet Transform and Unified Universality Theorem for Deep and Shallow Joint-Group-Equivariant Machines
Sho Sonoda, Yuka Hashimoto, Isao Ishikawa +1
We present a constructive universal approximation theorem for learning machines equipped with joint-group-equivariant feature maps, called the joint-equivariant machines, based on…
-Algebraic Machine Learning: Moving in a New Direction
Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri
Machine learning has a long collaborative tradition with several fields of mathematics, such as statistics, probability and linear algebra. We propose a new direction for machine l…
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…