40 citations · 139 across the 37 of their papers we have counts for
38 papers
Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform
Sho Sonoda, Luca Galimberti, Yuanchao Xu +2
Neural networks whose inputs are functions, as in operator learning, are usually shown to be universal by existence arguments, either by reduction to finite-dimensional networks or…
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…
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…
Boundedness of composition operator in Orlicz-Morrey spaces
Masahiro Ikeda, Isao Ishikawa, Ryota Kawasumi
In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesg…
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda +1
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what…
A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks
Sho Sonoda, Isao Ishikawa, Masahiro Ikeda
To investigate neural network parameters, it is easier to study the distribution of parameters than to study the parameters in each neuron. The ridgelet transform is a pseudo-inver…
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…
Global universality of the two-layer neural network with the -rectified linear unit
N. Hatano, M. Ikeda, I. Ishikawa +1
This paper concerns the universality of the two-layer neural network with the -rectified linear unit activation function with with a suitable norm without any res…
Dynamic Structure Estimation from Bandit Feedback using Nonvanishing Exponential Sums
Motoya Ohnishi, Isao Ishikawa, Yuko Kuroki +1
This work tackles the dynamic structure estimation problems for periodically behaved discrete dynamical system in the Euclidean space. We assume the observations become sequentiall…
Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groups
Sho Sonoda, Isao Ishikawa, Masahiro Ikeda
We show the universality of depth-2 group convolutional neural networks (GCNNs) in a unified and constructive manner based on the ridgelet theory. Despite widespread use in applica…
Universal approximation property of invertible neural networks
Isao Ishikawa, Takeshi Teshima, Koichi Tojo +3
Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various m…
Koopman and Perron-Frobenius Operators on reproducing kernel Banach spaces
Masahiro Ikeda, Isao Ishikawa, Corbinian Schlosser
Koopman and Perron-Frobenius operators for dynamical systems have been getting popular in a number of fields in science these days. Properties of the Koopman operator essentially d…
Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis
Sho Sonoda, Isao Ishikawa, Masahiro Ikeda
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…
Generalized eigenvalues of the Perron-Frobenius operators of symbolic dynamical systems
Hayato Chiba, Masahiro Ikeda, Isao Ishikawa
The generalized spectral theory is an effective approach to analyze a linear operator on a Hilbert space with a continuous spectrum. The generalized spectrum is compu…
Koopman Spectrum Nonlinear Regulators and Efficient Online Learning
Motoya Ohnishi, Isao Ishikawa, Kendall Lowrey +3
Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, beh…
Ghosts in Neural Networks: Existence, Structure and Role of Infinite-Dimensional Null Space
Sho Sonoda, Isao Ishikawa, Masahiro Ikeda
We study parameter nonuniqueness in continuous-width depth-two fully connected neural networks. Our main contribution is a direct method for solving the neural-network equation $S[…
Bounded composition operators on functional quasi-Banach spaces and stability of dynamical systems
Isao Ishikawa
In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prov…
Reproducing kernel Hilbert C*-module and kernel mean embeddings
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda +3
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In th…