Physics-informed machine learning (PIML) is a set of methods and tools that systematically
integrate machine learning (ML) algorithms with physical constraints and abstract …

Recently, deep equilibrium models (DEQs) have drawn increasing attention from the
machine learning community. However, DEQs are much less understood in terms of certified …

Flow networks are ubiquitous in natural and engineered systems, and in order to understand
and manage these networks, one must quantify the flow of commodities across their edges …

Deep neural networks can be fragile and sensitive to small input perturbations that might
cause a significant change in the output. In this letter, we employ contraction theory to …

Implicit graph neural networks (IGNNs)–that solve a fixed-point equilibrium equation using
Picard iteration for representation learning–have shown remarkable performance in learning …

Contraction theory is a mathematical framework for studying the convergence, robustness,
and modularity properties of dynamical systems and algorithms. In this opinion paper, we …

This letter investigates stability conditions of continuous-time Hopfield and firing-rate neural
networks by leveraging contraction theory. First, we present a number of useful general …

Critical questions in dynamical neuroscience and machine learning are related to the study
of recurrent neural networks and their stability, robustness, and computational efficiency …

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of
local neural activity. Many properties of single RNNs are well characterized theoretically, but …

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 …