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We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…

We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…

This paper presents a new neural network (NN) paradigm for scalable and generalizable stability analysis of power systems. The paradigm consists of two parts: the neural stability descriptor and the sample-augmented iterative training…

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

In recent years, Deep Neural Network models have been developed in different fields, where they have brought many advances. However, they have also started to be used in tasks where risk is critical. A misdiagnosis of these models can lead…

Adversarial examples resulting from instability of current computer vision models are an extremely important topic due to their potential to compromise any application. In this paper we demonstrate that instability is inevitable due to a)…

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence…

Recent advancements in artificial intelligence, particularly deep neural networks, have pushed the boundaries of what is achievable in complex tasks. Traditional methods for training neural networks in classification problems often rely on…

Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems…

Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture…

Deep learning's success comes with growing energy demands, raising concerns about the long-term sustainability of the field. Spiking neural networks, inspired by biological neurons, offer a promising alternative with potential computational…

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…

We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…

This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…

Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of…

The problem of designing learners that provide guarantees that their predictions are provably correct is of increasing importance in machine learning. However, learning theoretic guarantees have only been considered in very specific…

Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…

We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective…

We introduce a novel artificial neural network architecture that integrates robustness to adversarial input in the network structure. The main idea of our approach is to force the network to make predictions on what the given instance of…

In this paper, we examine both stability and sustainability of a network-based model of natural resource consumption. Stability is studied from a dynamical systems perspective, though we argue that sustainability is a fundamentally…