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02/12/2023
Koopman-Based Bound for Generalization: New Aspect of Neural Networks Regarding Nonlinear Noise Filtering
We propose a new bound for generalization of neural networks using Koopm...
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01/27/2023
Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation
Ridgelet transform has been a fundamental mathematical tool in the theor...
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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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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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02/10/2022
Deep Learning in Random Neural Fields: Numerical Experiments via Neural Tangent Kernel
A biological neural network in the cortex forms a neural field. Neurons ...
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06/16/2021
Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning
Random features are a central technique for scalable learning algorithms...
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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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06/07/2021
Differentiable Multiple Shooting Layers
We detail a novel class of implicit neural models. Leveraging time-paral...
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08/19/2020
On the Approximation Lower Bound for Neural Nets with Random Weights
A random net is a shallow neural network where the hidden layer is froze...
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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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04/22/2020
Fast Quantum Algorithm for Learning with Optimized Random Features
Kernel methods augmented with random features give scalable algorithms f...
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02/02/2019
Numerical Integration Method for Training Neural Network
We propose a new numerical integration method for training a shallow neu...
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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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12/12/2017
Transportation analysis of denoising autoencoders: a novel method for analyzing deep neural networks
The feature map obtained from the denoising autoencoder (DAE) is investi...
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05/10/2016
Decoding Stacked Denoising Autoencoders
Data representation in a stacked denoising autoencoder is investigated. ...
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05/14/2015
Neural Network with Unbounded Activation Functions is Universal Approximator
This paper presents an investigation of the approximation property of ne...
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12/23/2013