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A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized…
Recurrent neural networks have shown excellent performance in many applications, however they require increased complexity in hardware or software based implementations. The hardware complexity can be much lowered by minimizing the…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…
This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…
In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This…
A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the…
Algebraic neural networks (AlgNNs) are composed of a cascade of layers each one associated to and algebraic signal model, and information is mapped between layers by means of a nonlinearity function. AlgNNs provide a generalization of…
Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we…
Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections…
Weight thresholding is a simple technique that aims at reducing the number of edges in weighted networks that are otherwise too dense for the application of standard graph theoretical methods. We show that the group structure of real…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
It has been argued by Thom and Palm that sparsely-connected neural networks (SCNs) show improved performance over fully-connected networks (FCNs). Super-regular networks (SRNs) are neural networks composed of a set of stacked sparse layers…
The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according to the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social…
Due to the fact much of today's data can be represented as graphs, there has been a demand for generalizing neural network models for graph data. One recent direction that has shown fruitful results, and therefore growing interest, is the…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks…