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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