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This paper studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity…

The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…

The high computational complexity and increasing parameter counts of deep neural networks pose significant challenges for deployment in resource-constrained environments, such as edge devices or real-time systems. To address this, we…

From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…

Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own payoffs. There exists a game among these…

We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are…

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…

A growing body of literature in networked systems research relies on game theory and mechanism design to model and address the potential lack of cooperation between self-interested users. Most game-theoretic models applied to system…

We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…

Deep learning has excelled on complex pattern recognition tasks such as image classification and object recognition. However, it struggles with tasks requiring nontrivial reasoning, such as algorithmic computation. Humans are able to solve…

Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…

We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron…

Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…

Neuronal ensemble activity, including coordinated and oscillatory patterns, exhibits hallmarks of nonequilibrium systems with time-asymmetric trajectories to maintain their organization. However, assessing time asymmetry from neuronal…

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the…

Structured prediction in natural language processing (NLP) has a long history. The complex models of structured application come at the difficulty of learning and inference. These difficulties lead researchers to focus more on models with…

Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the…

Brain network is remarkably cost-efficient while the fundamental physical and dynamical mechanisms underlying its economical optimization in network structure and activity are not clear. Here we study intricate cost-efficient interplay…

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…