52 citations · 111 across the 30 of their papers we have counts for
4 papers · 1 filter
Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach
Saber Jafarpour, Alexander Davydov, Matthew Abate +2
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The…
The Yakubovich S-Lemma Revisited: Stability and Contractivity in Non-Euclidean Norms
Anton V. Proskurnikov, Alexander Davydov, Francesco Bullo
The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic Lyapunov function in the Lur'e problem of absolute stability. A quadratic Lyapunov function is…
Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks
Alexander Davydov, Saber Jafarpour, Anton V. Proskurnikov +1
We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces and . We first establish properties of mappings…
Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks
Alexander Davydov, Saber Jafarpour, Matthew Abate +2
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations…