20 citations · 59 across the 18 of their papers we have counts for
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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…
Universal Approximation Property of Neural Ordinary Differential Equations
Takeshi Teshima, Koichi Tojo, Masahiro Ikeda +2
Neural ordinary differential equations (NODEs) is an invertible neural network architecture promising for its free-form Jacobian and the availability of a tractable Jacobian determ…
A global universality of two-layer neural networks with ReLU activations
Naoya Hatano, Masahiro Ikeda, Isao Ishikawa +1
In the present study, we investigate a universality of neural networks, which concerns a density of the set of two-layer neural networks in a function spaces. There are many works…
Ridge Regression with Over-Parametrized Two-Layer Networks Converge to Ridgelet Spectrum
Sho Sonoda, Isao Ishikawa, Masahiro Ikeda
Characterization of local minima draws much attention in theoretical studies of deep learning. In this study, we investigate the distribution of parameters in an over-parametrized…
Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators
Takeshi Teshima, Isao Ishikawa, Koichi Tojo +3
Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirabl…
Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noise
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda +2
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods…