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DISCO Verification: Division of Input Space into COnvex polytopes for neural network verification

Abstract : The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a piecewise linear structure. However, such networks yields subregions that are linear and thus simpler to analyse independently. In this paper, we propose a method to simplify the verification problem by operating a partitionning into multiple linear subproblems. To evaluate the feasibility of such an approach, we perform an empirical analysis of neural networks to estimate the number of linear regions, and compare them to the bounds currently known. We also present the impact of a technique aiming at reducing the number of linear regions during training.
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https://hal.inria.fr/hal-03227439
Contributor : Julien Girard-Satabin Connect in order to contact the contributor
Submitted on : Monday, May 17, 2021 - 11:54:27 AM
Last modification on : Wednesday, March 16, 2022 - 3:46:52 AM
Long-term archiving on: : Wednesday, August 18, 2021 - 6:30:01 PM

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  • HAL Id : hal-03227439, version 1
  • ARXIV : 2105.07776

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Julien Girard-Satabin, Aymeric Varasse, Marc Schoenauer, Guillaume Charpiat, Zakaria Chihani. DISCO Verification: Division of Input Space into COnvex polytopes for neural network verification. 2021. ⟨hal-03227439⟩

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