4 papers · 1 filter
Zero Generalization Error Theorem for Random Interpolators via Algebraic Geometry
Naoki Yoshida, Isao Ishikawa, Masaaki Imaizumi
We theoretically demonstrate that the generalization error of interpolators for machine learning models under teacher-student settings becomes 0 once the number of training samples…
Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections
Yuanchao Xu, Itsushi Sakata, Isao Ishikawa
Finite-dimensional Koopman eigenvalues do not characterize resolvent growth, particularly for nonnormal compressions. We study the singular-value structure of empirical Koopman fin…
Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspective
Yuanchao Xu, Fengyi Li, Masahiro Fujisawa +3
We propose Koopman Spectral Wasserstein Gradient Descent (KSWGD), a particle-based generative modeling framework that learns the Langevin generator via Koopman theory and integrate…
Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups
Yuanchao Xu, Jing Liu, Weiping Ding +2
Koopman spectral analysis turns nonlinear stochastic dynamics into a linear evolution of observables and gives access to decay rates, oscillatory modes, and metastable behavior. In…