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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…

Neural and Evolutionary Computing · Computer Science 2021-07-29 Dmitry Krotov

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,…

Neurons and Cognition · Quantitative Biology 2021-04-29 Dmitry Krotov , John Hopfield

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…

Neural and Evolutionary Computing · Computer Science 2022-06-20 Beren Millidge , Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz

An autoassociative memory model is a function that, given a set of data points, takes as input an arbitrary vector and outputs the most similar data point from the memorized set. However, popular memory models fail to retrieve images even…

Machine Learning · Computer Science 2024-02-19 Tommaso Salvatori , Beren Millidge , Yuhang Song , Rafal Bogacz , Thomas Lukasiewicz

Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…

Machine Learning · Computer Science 2017-07-06 Vincent Gripon , Matthias Löwe , Franck Vermet

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

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…

Machine Learning · Computer Science 2025-11-26 Shurong Wang , Yuqi Pan , Zhuoyang Shen , Meng Zhang , Hongwei Wang , Guoqi Li

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…

Statistical Mechanics · Physics 2015-06-24 Luciano da Fontoura Costa , Dietrich Stauffer

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…

Neural and Evolutionary Computing · Computer Science 2020-10-06 Pavel Tolmachev , Jonathan H. Manton

Associative memory architectures such as the Hopfield network have long been important conceptual and theoretical models for neuroscience and artificial intelligence. However, translating these abstract models into spiking neural networks…

Neurons and Cognition · Quantitative Biology 2025-07-02 William F. Podlaski , Christian K. Machens

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 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…

Neurons and Cognition · Quantitative Biology 2023-08-28 Louis Kang , Taro Toyoizumi

The primate heteromodal cortex presents an evident functional modularity at a mesoscopic level, with physiological and anatomical evidence pointing to it as likely substrate of long-term memory. In order to investigate some of its…

Neurons and Cognition · Quantitative Biology 2021-12-09 Carlo Fulvi Mari

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

A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others.…

Disordered Systems and Neural Networks · Physics 2020-05-14 Carlo Fulvi Mari

Identifying computational mechanisms for memorization and retrieval of data is a long-standing problem at the intersection of machine learning and neuroscience. Our main finding is that standard overparameterized deep neural networks…

Machine Learning · Computer Science 2022-05-25 Adityanarayanan Radhakrishnan , Mikhail Belkin , Caroline Uhler

A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used…

Neural and Evolutionary Computing · Computer Science 2017-03-28 Dmitry Krotov , John J Hopfield

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…

Neural and Evolutionary Computing · Computer Science 2016-05-20 Ivo Danihelka , Greg Wayne , Benigno Uria , Nal Kalchbrenner , Alex Graves

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

We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…

Disordered Systems and Neural Networks · Physics 2017-04-26 Weishun Zhong , David J. Schwab , Arvind Murugan
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