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Hopfield model is one of the few neural networks for which analytical results can be obtained. However, most of them are derived under the assumption of random uncorrelated patterns, while in real life applications data to be stored show…
The Hopfield network model and its generalizations were introduced as a model of associative, or content-addressable, memory. They were widely investigated both as an unsupervised learning method in artificial intelligence and as a model of…
Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic…
Cortical networks exhibit synchronized activity which often occurs in spontaneous events in the form of spike avalanches. Since synchronization has been causally linked to central aspects of brain function such as selective signal…
A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality…
The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…
Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…
We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitrary degree distribution $p(k)$ and applied to…
We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
Hebbian synaptic plasticity inevitably leads to interference and forgetting when different, overlapping memory patterns are sequentially stored in the same network. Recent work on artificial neural networks shows that an…
Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…
It is well-known that the synchronization of diffusively-coupled systems on networks strongly depends on the network topology. In particular, the so-called algebraic connectivity $\mu_{N-1}$, or the smallest non-zero eigenvalue of the…
We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…