The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems.

PW A systems allow for discontinuities across the separate regions ("pieces"), and are thus a simplified

Y et in recurrent networks, computations are implemented at the level of dynamics, and two networks performing the same computation with equivalent dynamics need not exhibit the same geometry.

In this work, we treat variational flows as dynamical systems, and leverage shadowing theory to elucidate this behavior via theoretical guarantees on the error of sampling, density evaluation, and ELBO estimation.

Learning the Koopman operator and its spectral decomposition from data is enabled by a number of algorithms.