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05/23/2023
Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator
Reproducing kernel Hilbert C^*-module (RKHM) is a generalization of repr...
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10/21/2022
Learning in RKHM: a C^*-Algebraic Twist for Kernel Machines
Supervised learning in reproducing kernel Hilbert space (RKHS) and vecto...
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06/02/2022
Dynamic Structure Estimation from Bandit Feedback
This work present novel method for structure estimation of an underlying...
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05/30/2022
Universality of group convolutional neural networks based on ridgelet analysis on groups
We investigate the approximation property of group convolutional neural ...
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04/15/2022
Universal approximation property of invertible neural networks
Invertible neural networks (INNs) are neural network architectures with ...
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03/03/2022
Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis
Neural network on Riemannian symmetric space such as hyperbolic space an...
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06/30/2021
Koopman Spectrum Nonlinear Regulator and Provably Efficient Online Learning
Most modern reinforcement learning algorithms optimize a cumulative sing...
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06/09/2021
Ghosts in Neural Networks: Existence, Structure and Role of Infinite-Dimensional Null Space
Overparametrization has been remarkably successful for deep learning stu...
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01/27/2021
Reproducing kernel Hilbert C*-module and kernel mean embeddings
Kernel methods have been among the most popular techniques in machine le...
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12/04/2020
Universal Approximation Property of Neural Ordinary Differential Equations
Neural ordinary differential equations (NODEs) is an invertible neural n...
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11/20/2020
A global universality of two-layer neural networks with ReLU activations
In the present study, we investigate a universality of neural networks, ...
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07/29/2020
Kernel Mean Embeddings of Von Neumann-Algebra-Valued Measures
Kernel mean embedding (KME) is a powerful tool to analyze probability me...
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07/07/2020
Gradient Descent Converges to Ridgelet Spectrum
Deep learning achieves a high generalization performance in practice, de...
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06/20/2020
Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators
Invertible neural networks based on coupling flows (CF-INNs) have variou...
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06/15/2020
Hypergraph Clustering Based on PageRank
A hypergraph is a useful combinatorial object to model ternary or higher...
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03/02/2020
Analysis via Orthonormal Systems in Reproducing Kernel Hilbert C^*-Modules and Applications
Kernel methods have been among the most popular techniques in machine le...
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11/27/2019
Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions
Composition operators have been extensively studied in complex analysis,...
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06/17/2019
Metric on random dynamical systems with vector-valued reproducing kernel Hilbert spaces
The development of a metric on structural data-generating mechanisms is ...
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09/12/2018
Finding Cheeger Cuts in Hypergraphs via Heat Equation
Cheeger's inequality states that a tightly connected subset can be extra...
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05/31/2018
Metric on Nonlinear Dynamical Systems with Koopman Operators
The development of a metric for structural data is a long-term problem i...
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05/19/2018
Integral representation of the global minimizer
We have obtained an integral representation of the shallow neural networ...
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02/24/2017