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In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…

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…

Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very…

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the…

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…

We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval…

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…

We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to…

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

A set of fixed points of the Hopfield type neural network was 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…

Feedback-rich neural architectures can regenerate earlier representations and inject temporal context, making them a natural setting for strictly local synaptic plasticity. Existing literature raises doubt about whether a minimal,…

Associative memory models retrieve stored information through content-based addressing, mimicking the neural processes of animal brains. The classical Hopfield network-based models store memories as vectors of discrete values and have good…

Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures…

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…

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…

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…

Memory and computation efficient deep learning architec- tures are crucial to continued proliferation of machine learning capabili- ties to new platforms and systems. Binarization of operations in convo- lutional neural networks has shown…

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…

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…

The organizational principles behind the connectivity of a complex network are known to influence its behavior. In this work we investigate, using the Hopfield model, the influence of the network architecture on the performance for…