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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…
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…
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,…
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…
Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…
We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes, eight GABAergic interneuron classes), forty-seven…
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…
In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…
The Hopfield model describes a neural network that stores memories using all-to-all-coupled spins. Memory patterns are recalled under equilibrium dynamics. Storing too many patterns breaks the associative recall process because frustration…
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…
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…
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
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…
Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it…
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 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…
In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small…
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…
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…
A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…