Related papers: Graph Hopfield Networks: Energy-Based Node Classif…

Associative memory models, such as Hopfield networks and their modern variants, have garnered renewed interest due to advancements in memory capacity and connections with self-attention in transformers. In this work, we introduce a unified…

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…

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for…

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

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…

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…

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…

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,…

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…

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…

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,…

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 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…

We study the problem of learning associative memory -- a system which is able to retrieve a remembered pattern based on its distorted or incomplete version. Attractor networks provide a sound model of associative memory: patterns are stored…

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…

Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…

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 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…

Associative memory, traditionally modeled by Hopfield networks, enables the retrieval of previously stored patterns from partial or noisy cues. Yet, the local computational principles which are required to enable this function remain…

Associative memory retrieves complete patterns from partial or corrupted inputs and constitutes a primitive form of generative inference. Classical Hopfield networks (CHN) provide a canonical framework for associative memory but suffer from…