no code implementations • 8 Aug 2022 • Saber Jafarpour, Alexander Davydov, Matthew Abate, Francesco Bullo, Samuel Coogan
Third, we use the upper bounds of the Lipschitz constants and the upper bounds of the tight inclusion functions to design two algorithms for the training and robustness verification of implicit neural networks.
1 code implementation • 1 Apr 2022 • Alexander Davydov, Saber Jafarpour, Matthew Abate, Francesco Bullo, Samuel Coogan
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs).
no code implementations • 10 Dec 2021 • Saber Jafarpour, Matthew Abate, Alexander Davydov, Francesco Bullo, Samuel Coogan
First, given an implicit neural network, we introduce a related embedded network and show that, given an $\ell_\infty$-norm box constraint on the input, the embedded network provides an $\ell_\infty$-norm box overapproximation for the output of the given network.
no code implementations • 7 Oct 2021 • Kerianne Hobbs, Mark Mote, Matthew Abate, Samuel Coogan, Eric Feron
An important quality of an RTA system is that the assurance mechanism is constructed in a way that is entirely agnostic to the underlying structure of the primary controller.
no code implementations • 2 Oct 2020 • Matthew Abate, Samuel Coogan
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system.