7 papers
Backward Kolmogorov Transport: Sampling Invariant Laws of Reversible Diffusions from Trajectory Data
Yuanchao Xu, Isao Ishikawa
We consider a reversible diffusion with unknown drift, observed through trajectories, and construct samplers of its invariant law. The trajectories contain samples of this law, but…
Dynamical rigidity for weighted composition operators on holomorphic function spaces
Isao Ishikawa
We study weighted composition operators on quasi-Banach spaces of holomorphic functions via their induced action on jets along periodic orbits. Under a natural graded nondegeneracy…
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…
Finite-dimensional approximations of push-forwards on locally analytic functionals
Isao Ishikawa
This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the m…