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In this article, we explore the potential of artificial neural networks, which are trained using an exceptionally simplified catalog of ideal configurations encompassing both order and disorder. We explore the generalisation power of these…

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity…

We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or…

Neural circuits often face the problem of classifying stimuli into discrete groups and making decisions based on such classifications. Neurons of these circuits can be distinguished according to their correlations with different features of…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

Recurrent neural networks (RNNs) have yielded promising results for both recognizing objects in challenging conditions and modeling aspects of primate vision. However, the representational dynamics of recurrent computations remain poorly…

In this contribution we give an overview over recent work on the theory of interacting neural networks. The model is defined in Section 2. The typical teacher/student scenario is considered in Section 3. A static teacher network is…

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 analyze the input-output behavior of residual networks from a dynamical system point of view by disentangling the residual dynamics from the output activities before the classification stage. For a network with simple skip connections…

A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…

The analysis of networks affects the research of many real phenomena. The complex network structure can be viewed as a network's state at the time of the analysis or as a result of the process through which the network arises. Research…

Models of the consensus of the individual state in social systems have been the subject of recent researches in the physics literature. We investigate how network structures coevolve with the individual state under the framework of social…

The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…

We study possible applications of artificial neural networks to examine the string landscape. Since the field of application is rather versatile, we propose to dynamically evolve these networks via genetic algorithms. This means that we…

Recurrent Neural Networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a Machine Learning…

Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints.…

We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…

We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functional analysis, and find (in contrast to the…

In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high…

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…