Related papers: Storage and Learning phase transitions in the Rand…
It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we…
The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…
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…
Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…
While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student…
Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
Networks in machine learning offer examples of complex high-dimensional dynamical systems reminiscent of biological systems. Here, we study the learning dynamics of Generalized Hopfield networks, which permit a visualization of internal…
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…
Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…
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…
We associate learning and adaptation in living systems with the shaping of the velocity vector field in the respective dynamical systems in response to external, generally random, stimuli. With this, a mathematical concept of self-shaping…
In neural network's Literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i.e., definite patterns that are experienced just once to form the synaptic…
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…
The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…
The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…
We study a variant of the pseudo-inverse learning rule for Hopfield-like Neural Networks, which allows the network to infer archetypal concepts on the basis of a limited number of examples. The mean-field replica theory for this model…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…
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…