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Euclidean Contractivity of Neural Networks with Symmetric Weights by Centorrino, Veronica; Gokhale, Anand; Davydov, Alexander; Russo, Giovanni; Bullo, Francesco is a scholarly article available to read on EtoBox.

What is Euclidean Contractivity of Neural Networks with Symmetric Weights about?

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of symmetric matrices. Then, we give sufficient conditions for strong and weak Euclidean contractivity, i.e., contractivity with respect to the $\ell_2$ norm, of both models with symmetric weights and (possibly) non-smooth activation functions. Our contraction analysis leads to contraction rates which are log-optimal in almost all symmetric synaptic matrices. Finally, we use our results to propose a firing-rate neural network model to solve a quadratic optimization problem with box constraints.

Author

Centorrino, Veronica; Gokhale, Anand; Davydov, Alexander; Russo, Giovanni; Bullo, Francesco

Published

2023

Language

EN