A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

• URL: http://arxiv.org/abs/2307.00215v2
• Date: Thu, 21 Sep 2023 17:25:50 GMT
• Title: A Constructive Approach to Function Realization by Neural Stochastic Differential Equations
• Authors: Tanya Veeravalli, Maxim Raginsky
• Abstract summary: We introduce structural restrictions on system dynamics and characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural differential equation (Neural SDE), a deterministic dynamical system, and a readout map.
• Score: 8.04975023021212
• License: http://creativecommons.org/licenses/by/4.0/
• 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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