Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909543260225536 |
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| author | Glunt, Jonah J. Siefert, Jacob A. Thompson, Andrew F. Ruths, Justin Pangborn, Herschel C. |
| author_facet | Glunt, Jonah J. Siefert, Jacob A. Thompson, Andrew F. Ruths, Justin Pangborn, Herschel C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks Glunt, Jonah J. Siefert, Jacob A. Thompson, Andrew F. Ruths, Justin Pangborn, Herschel C. Systems and Control 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. |
| title | Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2503.15336 |