A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

Tanya Veeravalli, Maxim Raginsky
7/1/2023
math.OCcs.LG

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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.

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Cite this paper

@article{veeravalli2023constructive,
  title  = {A Constructive Approach to Function Realization by Neural Stochastic Differential Equations},
  author = {Tanya Veeravalli and Maxim Raginsky},
  year   = {2023},
  eprint = {2307.00215},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2307.00215v2}
}

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