4 citations · 11 across the 11 of their papers we have counts for
13 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…
High-Probability Guarantees for SGD under -Heavy-Tailed Gradient Noise
Qijun Tong, Masahiro Ikeda, Ryota Kawasumi
Stochastic gradient descent (SGD) is widely used to train machine learning models, but subsampling the training data introduces noise into its updates. The strength and applicabili…
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…
Spectral Truncation Kernels: Noncommutativity in -algebraic Kernel Machines
Yuka Hashimoto, Ayoub Hafid, Masahiro Ikeda +1
A central question in vector- and function-valued learning is how to design kernels that capture both local and non-local interactions while remaining computationally tractable. Ex…
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…
-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…
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…
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…