Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators. - Isao Ishikawa; Keisuke Fujii 001; Masahiro Ikeda; Yuka Hashimoto; Yoshinobu Kawahara (NeurIPS, 2018)

Integral representation of the global minimizer. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda; Kei Hagihara; Yoshihiro Sawano; Takuo Matsubara; Noboru Murata (CoRR, 2018)

Metric on Nonlinear Dynamical Systems with Koopman Operators. - Isao Ishikawa; Keisuke Fujii 001; Masahiro Ikeda; Yuka Hashimoto; Yoshinobu Kawahara (CoRR, 2018)

Metric on random dynamical systems with vector-valued reproducing kernel Hilbert spaces. - Isao Ishikawa; Akinori Tanaka; Masahiro Ikeda; Yoshinobu Kawahara (CoRR, 2019)

Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators. - Takeshi Teshima; Isao Ishikawa; Koichi Tojo; Kenta Oono; Masahiro Ikeda; Masashi Sugiyama (NeurIPS, 2020)

Analysis via Orthonormal Systems in Reproducing Kernel Hilbert C*-Modules and Applications. - Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda; Fuyuta Komura; Takeshi Katsura; Yoshinobu Kawahara (CoRR, 2020)

Gradient Descent Converges to Ridgelet Spectrum. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda (CoRR, 2020)

Kernel Mean Embeddings of Von Neumann-Algebra-Valued Measures. - Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda; Fuyuta Komura; Yoshinobu Kawahara (CoRR, 2020)

A global universality of two-layer neural networks with ReLU activations. - Naoya Hatano; Masahiro Ikeda; Isao Ishikawa; Yoshihiro Sawano (CoRR, 2020)

Universal Approximation Property of Neural Ordinary Differential Equations. - Takeshi Teshima; Koichi Tojo; Masahiro Ikeda; Isao Ishikawa; Kenta Oono (CoRR, 2020)

Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noise. - Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda; Yoichi Matsuo; Yoshinobu Kawahara (J. Mach. Learn. Res., 2020)

Ridge Regression with Over-parametrized Two-Layer Networks Converge to Ridgelet Spectrum. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda (AISTATS, 2021)

Ghosts in Neural Networks: Existence, Structure and Role of Infinite-Dimensional Null Space. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda (CoRR, 2021)

Koopman Spectrum Nonlinear Regulator and Provably Efficient Online Learning. - Motoya Ohnishi; Isao Ishikawa; Kendall Lowrey; Masahiro Ikeda; Sham M. Kakade; Yoshinobu Kawahara (CoRR, 2021)

Reproducing kernel Hilbert C*-module and kernel mean embeddings. - Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda; Fuyuta Komura; Takeshi Katsura; Yoshinobu Kawahara (J. Mach. Learn. Res., 2021)

Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda (ICML, 2022)

Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groups. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda (NeurIPS, 2022)

Dynamic Structure Estimation from Bandit Feedback. - Motoya Ohnishi; Isao Ishikawa; Yuko Kuroki; Masahiro Ikeda (CoRR, 2022)

Joint Group Invariant Functions on Data-Parameter Domain Induce Universal Neural Networks. - Sho Sonoda; Hideyuki Ishi; Isao Ishikawa; Masahiro Ikeda (NeurReps, 2023)

Koopman-Based Bound for Generalization: New Aspect of Neural Networks Regarding Nonlinear Noise Filtering. - Yuka Hashimoto; Sho Sonoda; Isao Ishikawa; Atsushi Nitanda; Taiji Suzuki (CoRR, 2023)

Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks. - Sho Sonoda; Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda (CoRR, 2023)

Universal Approximation Property of Invertible Neural Networks. - Isao Ishikawa; Takeshi Teshima; Koichi Tojo; Kenta Oono; Masahiro Ikeda; Masashi Sugiyama (J. Mach. Learn. Res., 2023)

Generalized Eigenvalues of the Perron-Frobenius Operators of Symbolic Dynamical Systems. - Hayato Chiba; Masahiro Ikeda; Isao Ishikawa (SIAM J. Appl. Dyn. Syst., 2023)

Koopman-based generalization bound: New aspect for full-rank weights. - Yuka Hashimoto; Sho Sonoda; Isao Ishikawa; Atsushi Nitanda; Taiji Suzuki (ICLR, 2024)

A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks. - Sho Sonoda; Isao Ishikawa; Masahiro Ikeda (CoRR, 2024)

Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces. - Isao Ishikawa; Yuka Hashimoto; Masahiro Ikeda; Yoshinobu Kawahara (CoRR, 2024)

Finite-dimensional approximations of push-forwards on locally analytic functionals and truncation of least-squares polynomials. - Isao Ishikawa (CoRR, 2024)

Constructive Universal Approximation Theorems for Deep Joint-Equivariant Networks by Schur's Lemma. - Sho Sonoda; Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda (CoRR, 2024)

Dynamic Structure Estimation from Bandit Feedback using Nonvanishing Exponential Sums. - Motoya Ohnishi; Isao Ishikawa; Yuko Kuroki; Masahiro Ikeda (Trans. Mach. Learn. Res., 2024)

Koopman Spectrum Nonlinear Regulators and Efficient Online Learning. - Motoya Ohnishi; Isao Ishikawa; Kendall Lowrey; Masahiro Ikeda; Sham M. Kakade; Yoshinobu Kawahara (Trans. Mach. Learn. Res., 2024)

Generalization Through Growth: Hidden Dynamics Controls Depth Dependence. - Sho Sonoda; Yuka Hashimoto; Isao Ishikawa; Masahiro Ikeda (CoRR, 2025)