A Constructive Approach to Function Realization by Neural Stochastic Differential Equations
Abstract
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given architecture. This can lead to high-complexity controls which are impractical in applications. In this paper, we take the opposite, constructive approach: We impose various structural restrictions on system dynamics and consequently characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural stochastic differential equation (Neural SDE), a deterministic dynamical system, and a readout map. Both probabilistic and geometric (Lie-theoretic) methods are used to characterize the classes of functions realized by such systems.
Cite
@article{arxiv.2307.00215,
title = {A Constructive Approach to Function Realization by Neural Stochastic Differential Equations},
author = {Tanya Veeravalli and Maxim Raginsky},
journal= {arXiv preprint arXiv:2307.00215},
year = {2023}
}
Comments
6 pages, 1 pdf figure; final version accepted to IEEE Conference on Decision and Control