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Related papers: Robust exponential memory in Hopfield networks

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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…

Machine Learning · Computer Science 2021-09-17 Tommaso Salvatori , Yuhang Song , Yujian Hong , Simon Frieder , Lei Sha , Zhenghua Xu , Rafal Bogacz , Thomas Lukasiewicz

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological…

Machine Learning · Statistics 2023-11-20 Luca Ambrogioni

We consider the problem of training a neural network to store a set of patterns with maximal noise robustness. A solution, in terms of optimal weights and state update rules, is derived by training each individual neuron to perform either…

Neural and Evolutionary Computing · Computer Science 2024-07-24 Georgios Iatropoulos , Johanni Brea , Wulfram Gerstner

Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…

Disordered Systems and Neural Networks · Physics 2022-03-08 Agnish Kumar Behera , Madan Rao , Srikanth Sastry , Suriyanarayanan Vaikuntanathan

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…

Disordered Systems and Neural Networks · Physics 2012-09-28 Elena Agliari , Lorenzo Asti , Adriano Barra , Raffaella Burioni , Guido Uguzzoni

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

Neurons and Cognition · Quantitative Biology 2022-05-17 Jakob Jordan , Mihai A. Petrovici , Oliver Breitwieser , Johannes Schemmel , Karlheinz Meier , Markus Diesmann , Tom Tetzlaff

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…

Machine Learning · Computer Science 2025-10-28 Saul Santos , Vlad Niculae , Daniel McNamee , André F. T. Martins

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…

Machine Learning · Computer Science 2024-11-01 Benjamin Hoover , Duen Horng Chau , Hendrik Strobelt , Parikshit Ram , Dmitry Krotov

High-capacity associative memory models, such as Kernel Logistic Regression (KLR) Hopfield networks, have demonstrated strong storage capabilities but typically rely on computationally expensive synchronous updates. This reliance poses a…

Neural and Evolutionary Computing · Computer Science 2026-05-12 Akira Tamamori

A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…

Disordered Systems and Neural Networks · Physics 2009-10-31 Francesco P. Battaglia , Alessandro Treves

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,…

Probability · Mathematics 2025-04-08 Véronique Gayrard

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…

Neurons and Cognition · Quantitative Biology 2026-01-21 Nurani Rajagopal Rohan , V. Srinivasa Chakravarthy , Sayan Gupta

The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…

Neural and Evolutionary Computing · Computer Science 2024-09-24 Hayden McAlister , Anthony Robins , Lech Szymanski

We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…

Machine Learning · Computer Science 2020-08-18 Tri Huynh , Michael Maire , Matthew R. Walter

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one…

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…

Neural and Evolutionary Computing · Computer Science 2017-09-26 Eliott Coyac , Vincent Gripon , Charlotte Langlais , Claude Berrou

A fundamental aspect of limitations in learning any computation in neural architectures is characterizing their optimal capacities. An important, widely-used neural architecture is known as autoencoders where the network reconstructs the…

Neurons and Cognition · Quantitative Biology 2017-05-23 Alireza Alemi , Alia Abbara

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…

Statistical Mechanics · Physics 2009-11-07 Dietrich Stauffer , Amnon Aharony , Luciano da Fontoura Costa , Joan Adler

In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…

Analysis of PDEs · Mathematics 2025-10-27 Yuncheng You

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…

Disordered Systems and Neural Networks · Physics 2026-02-17 Ramón Nartallo-Kaluarachchi , Renaud Lambiotte , Alain Goriely