Related papers: A new mathematical model for brain memory working.…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…

In the mammalian brain, newly acquired memories depend on the hippocampus for maintenance and recall, but over time the neocortex takes over these functions, rendering memories hippocampus-independent. The process responsible for this…

Neural network models capable of storing memory have been extensively studied in computer science and computational neuroscience. The Hopfield network is a prototypical example of a model designed for associative, or content-addressable,…

Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…

We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…

We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…

We investigate the theory of observers in the quantum mechanical world by using a novel model of the human brain which incorporates the glial network into the Hopfield model of the neural network. Our model is based on a microscopic…

The brain can reproduce memories from partial data; this ability is critical for memory recall. The process of memory recall has been studied using auto-associative networks such as the Hopfield model. This kind of model reliably converges…

We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions are of interests to engineers, mathematicians, and physicists from the last several decades. With a motivation of…

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…

Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where…

Over the past two decades, an increasing array of control-theoretic methods have been used to study the brain as a complex dynamical system and better understand its structure-function relationship. This article provides an overview on one…

Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…

At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral…

Gradient-based neural network training traditionally enforces symmetry between forward and backward propagation, requiring activation functions to be differentiable (or sub-differentiable) and strictly monotonic in certain regions to…

Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it…

Ever since the last two decades of the past century pioneering studies in the field of statistical physics had focused their efforts on developing models of neural networks that could display memory storage and retrieval. Though many…

We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical…