Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks
Abstract
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the exponential scaling often associated with analyses over high-dimensional spaces. This paper presents automated methods for constructing functional decompositions used to form set-based over-approximations of nonlinear functions, with particular focus on the hybrid zonotope set representation. To demonstrate these methods, we construct a hybrid zonotope set that over-approximates the input-output graph of a long short-term memory neural network, and use functional decomposition to represent a discrete hybrid automaton via a hybrid zonotope.
Keywords
Cite
@article{arxiv.2503.15336,
title = {Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks},
author = {Jonah J. Glunt and Jacob A. Siefert and Andrew F. Thompson and Justin Ruths and Herschel C. Pangborn},
journal= {arXiv preprint arXiv:2503.15336},
year = {2025}
}