Related papers: Efficient Hopfield pattern recognition on a scale-…

We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…

Brain-inspired computing aims to mimic cognitive functions like associative memory, the ability to recall complete patterns from partial cues. Memristor technology offers promising hardware for such neuromorphic systems due to its potential…

The exponential rise in data generation has led to vast, heterogeneous datasets crucial for predictive analytics and decision-making. Ensuring data quality and semantic integrity remains a challenge. This paper presents a brain-inspired…

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…

Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…

We consider the Hopfield model with $n$ neurons and an increasing number $p=p(n)$ of randomly chosen patterns and use Stein's method to obtain rates of convergence for the central limit theorem of overlap parameters, which holds for every…

Intracortical brain-machine interfaces require decoders that adapt continuously to neural signal instability while operating within strict memory budgets. We introduce a dual-timescale Hebbian accumulator learning rule for spiking neural…

In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be…

A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

This article delves into the Hopfield neural network model, drawing inspiration from biological neural systems. The exploration begins with an overview of the model's foundations, incorporating insights from mechanical statistics to deepen…

Attractor neural network is an important theoretical scenario for modeling memory function in the hippocampus and in the cortex. In these models, memories are stored in the plastic recurrent connections of neural populations in the form of…

We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing…

We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…

Associative memories are structures that store data in such a way that it can later be retrieved given only a part of its content -- a sort-of error/erasure-resilience property. They are used in applications ranging from caches and memory…

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…

Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…

The task of a neural associative memory is to retrieve a set of previously memorized patterns from their noisy versions using a network of neurons. An ideal network should have the ability to 1) learn a set of patterns as they arrive, 2)…

On the basis of the general form for the energy needed to adapt the connection strengths of a network in which learning takes place, a local learning rule is found for the changes of the weights. This biologically realizable learning rule…