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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…
In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different…
We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach…
Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…
The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-states of the network dynamics.…
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…
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…
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…
The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We…
We consider the class of Hopfield models of associative memory with activation function $F$ and state space $\{-1,1\}^N$, where each vertex of the cube describes a configuration of $N$ binary neurons. $M$ randomly chosen configurations,…
Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…
We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…
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…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
The potential for associative recall of diluted neuronal networks is investigated with respect to several biologically relevant configurations, more specifically the position of the cells along the input space and the spatial distribution…
We introduce a three-dimensional vectorial extension of the Hopfield associative-memory model in which each neuron is a unit vector on $S^2$ and synaptic couplings are $3\times 3$ blocks generated through a vectorial Hebbian rule. The…
Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…
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…
The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix,…