Related papers: Non-Convex Multi-species Hopfield models
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…
A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…
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,…
Models of interacting complex systems provide the fundamental statistical physics reference frame for the study and the understanding of associative memories, machine learning, and the dynamics of neural networks. On the other hand,…
Associative memory has been a prominent candidate for the computation performed by the massively recurrent neocortical networks. Attractor networks implementing associative memory have offered mechanistic explanation for many cognitive…
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 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…
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…
Hopfield networks and Boltzmann machines (BMs) are fundamental energy-based neural network models. Recent studies on modern Hopfield networks have broaden the class of energy functions and led to a unified perspective on general Hopfield…
Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the…
Neural networks with recurrent asymmetric couplings are important to understand how episodic memories are encoded in the brain. Here, we integrate the experimental observation of wide synaptic integration window into our model of sequence…
Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…
We introduce Graph Hopfield Networks, whose energy function couples associative memory retrieval with graph Laplacian smoothing for node classification. Gradient descent on this joint energy yields an iterative update interleaving Hopfield…
Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…
Among the performance-enhancing procedures for Hopfield-type networks that implement associative memory, Hebbian Unlearning (or dreaming) strikes for its simplicity and its clear biological interpretation. Yet, it does not easily lend…
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…
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 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…
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.…
Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations (belief-propagation and TAP equations) in the best understood such machine, namely…