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arXiv · 2503.15336

Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks

Jonah J. Glunt·Jacob A. Siefert·Andrew F. Thompson·Justin Ruths·Herschel C. Pangborn
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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.

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Jonah J. Glunt, Jacob A. Siefert, Andrew F. Thompson, Justin Ruths, Herschel C. Pangborn. 2025-03-19. Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks. https://arxiv.org/abs/2503.15336

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