A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

Tanya Veeravalli; Maxim Raginsky

doi:10.1109/CDC49753.2023.10383274

A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

Original language	English (US)
Title of host publication	2023 62nd IEEE Conference on Decision and Control, CDC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6364-6369
Number of pages	6
ISBN (Electronic)	9798350301243
DOIs	https://doi.org/10.1109/CDC49753.2023.10383274
State	Published - 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: Dec 13 2023 → Dec 15 2023

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Country/Territory	Singapore
City	Singapore
Period	12/13/23 → 12/15/23

Keywords

geometric control theory
neural dynamical systems
stochastic differential equations

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC49753.2023.10383274

Library availability

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Veeravalli, T., & Raginsky, M. (2023). A Constructive Approach to Function Realization by Neural Stochastic Differential Equations. In 2023 62nd IEEE Conference on Decision and Control, CDC 2023 (pp. 6364-6369). (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC49753.2023.10383274

A Constructive Approach to Function Realization by Neural Stochastic Differential Equations. / Veeravalli, Tanya; Raginsky, Maxim.
2023 62nd IEEE Conference on Decision and Control, CDC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 6364-6369 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Veeravalli, T & Raginsky, M 2023, A Constructive Approach to Function Realization by Neural Stochastic Differential Equations. in 2023 62nd IEEE Conference on Decision and Control, CDC 2023. Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6364-6369, 62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, 12/13/23. https://doi.org/10.1109/CDC49753.2023.10383274

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A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

Abstract

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Keywords

ASJC Scopus subject areas

Online availability

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