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The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…

Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…

The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian…

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising…

Biological neural networks continuously adapt and modify themselves in response to experiences throughout their lifetime - a capability largely absent in artificial neural networks. Hebbian plasticity offers a promising path toward rapid…

While advances in artificial intelligence and neuroscience have enabled the emergence of neural networks capable of learning a wide variety of tasks, our understanding of the temporal dynamics of these networks remains limited. Here, we…

We investigated how the stability of macroscopic states in the associative memory model is affected by synaptic depression. To this model, we applied the dynamical mean-field theory, which has recently been developed in stochastic neural…

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

Animals learn to predict external contingencies from experience through a process of conditioning. A natural mechanism for conditioning is stimulus substitution, whereby the neuronal response to a stimulus with no prior behavioral…

Link prediction models are increasingly used to recommend interactions in evolving networks, yet their impact on network structure is typically assessed from static snapshots. In particular, observed homophily conflates intrinsic…

Brain plasticity refers to brain's ability to change neuronal connections, as a result of environmental stimuli, new experiences, or damage. In this work, we study the effects of the synaptic delay on both the coupling strengths and…

Learning features invariant to arbitrary transformations in the data is a requirement for any recognition system, biological or artificial. It is now widely accepted that simple cells in the primary visual cortex respond to features while…

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…

Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…

Neuromorphic chips embody computational principles operating in the nervous system, into microelectronic devices. In this domain it is important to identify computational primitives that theory and experiments suggest as generic and…

Artificial neural networks (ANNs) have been extensively used for the description of problems arising from biological systems and for constructing neuromorphic computing models. The third generation of ANNs, namely, spiking neural networks…

Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic…

We study the dynamics of a two-qubit system coupled through time dependent anisotropic $XYZ$ Heisenberg interaction in presence of a time varying non-uniform external magnetic field. Exact results are presented for the time evolution of the…

We propose a modification of the cost function of the Hopfield model whose salient features shine in its Taylor expansion and result in more than pairwise interactions with alternate signs, suggesting a unified framework for handling both…