52 citations · 111 across the 30 of their papers we have counts for
6 papers · 1 filter
Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach
Saber Jafarpour, Matthew Abate, Alexander Davydov +2
Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional…
From Contraction Theory to Fixed Point Algorithms on Riemannian and Non-Euclidean Spaces
Francesco Bullo, Pedro Cisneros-Velarde, Alexander Davydov +1
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control.…
Non-Euclidean Contraction Analysis of Continuous-Time Neural Networks
Alexander Davydov, Anton V. Proskurnikov, Francesco Bullo
Critical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational eff…
Robust Implicit Networks via Non-Euclidean Contractions
Saber Jafarpour, Alexander Davydov, Anton V. Proskurnikov +1
Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation.…
Non-Euclidean Contraction Theory for Monotone and Positive Systems
Saber Jafarpour, Alexander Davydov, Francesco Bullo
In this note we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix mea…
Non-Euclidean Contraction Theory for Robust Nonlinear Stability
Alexander Davydov, Saber Jafarpour, Francesco Bullo
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings a…