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The communication bottleneck in federated learning (FL) has spurred extensive research into techniques to reduce the volume of data exchanged between client devices and the central parameter server. In this paper, we systematically classify…

Information Theory · Computer Science 2026-04-17 Adrian Edin , Michel Kieffer , Mikael Johansson , Zheng Chen

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

Dense Associative Memories (DenseAMs) are generalizations of Hopfield networks, which have superior information storage capacity and can store training data points (memories) at local minima of the energy landscape. When the amount of…

Machine Learning · Computer Science 2026-03-18 Bao Pham , Gabriel Raya , Matteo Negri , Mohammed J. Zaki , Luca Ambrogioni , Dmitry Krotov

Neural networks augmented with external memory have the ability to learn algorithmic solutions to complex tasks. These models appear promising for applications such as language modeling and machine translation. However, they scale poorly in…

Machine Learning · Computer Science 2016-10-31 Jack W Rae , Jonathan J Hunt , Tim Harley , Ivo Danihelka , Andrew Senior , Greg Wayne , Alex Graves , Timothy P Lillicrap

Transformers face scalability challenges due to the quadratic cost of attention, which involves dense similarity computations between queries and keys. We propose CAMformer, a novel accelerator that reinterprets attention as an associative…

Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and…

Factorization Machines (FMs) are a supervised learning approach that enhances the linear regression model by incorporating the second-order feature interactions. Despite effectiveness, FM can be hindered by its modelling of all feature…

Machine Learning · Computer Science 2017-08-17 Jun Xiao , Hao Ye , Xiangnan He , Hanwang Zhang , Fei Wu , Tat-Seng Chua

The increasing computational demands of modern AI systems have exposed fundamental limitations of digital hardware, driving interest in alternative paradigms for efficient large-scale inference. Dense Associative Memory (DenseAM) is a…

Neural and Evolutionary Computing · Computer Science 2025-12-18 Marc Gong Bacvanski , Xincheng You , John Hopfield , Dmitry Krotov

Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as…

Computational Physics · Physics 2020-12-11 Alexander Goscinski , Guillaume Fraux , Giulio Imbalzano , Michele Ceriotti

Despite recent progress in memory augmented neural network (MANN) research, associative memory networks with a single external memory still show limited performance on complex relational reasoning tasks. Especially the content-based…

Machine Learning · Computer Science 2021-08-30 Taewon Park , Inchul Choi , Minho Lee

Long-context understanding is crucial for many NLP applications, yet transformers struggle with efficiency due to the quadratic complexity of self-attention. Sparse attention methods alleviate this cost but often impose static, predefined…

Computation and Language · Computer Science 2025-06-16 Hanzhi Zhang , Heng Fan , Kewei Sha , Yan Huang , Yunhe Feng

Recently, Hopfield and Krotov introduced the concept of {\em dense associative memories} [DAM] (close to spin-glasses with $P$-wise interactions in a disordered statistical mechanical jargon): they proved a number of remarkable features…

Disordered Systems and Neural Networks · Physics 2020-02-19 Francesco Alemanno , Martino Centonze , Alberto Fachechi

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

The Transformer architecture, underpinned by the self-attention mechanism, has become the de facto standard for sequence modeling tasks. However, its core computational primitive scales quadratically with sequence length (O(N^2)), creating…

Computation and Language · Computer Science 2025-09-03 Rishiraj Acharya

Hopfield model is one of the few neural networks for which analytical results can be obtained. However, most of them are derived under the assumption of random uncorrelated patterns, while in real life applications data to be stored show…

Statistical Mechanics · Physics 2023-02-01 Giordano De Marzo , Giulio Iannelli

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training…

High Energy Physics - Phenomenology · Physics 2022-12-02 Ranit Das , Gregor Kasieczka , David Shih

Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…

Neurons and Cognition · Quantitative Biology 2021-12-22 Stefano Fusi

The impact of device and circuit-level effects in mixed-signal Resistive Random Access Memory (RRAM) accelerators typically manifest as performance degradation of Deep Learning (DL) algorithms, but the degree of impact varies based on…

Emerging Technologies · Computer Science 2022-01-26 Corey Lammie , Jason K. Eshraghian , Chenqi Li , Amirali Amirsoleimani , Roman Genov , Wei D. Lu , Mostafa Rahimi Azghadi

A low-power Content-Addressable-Memory (CAM) is introduced employing a new mechanism for associativity between the input tags and the corresponding address of the output data. The proposed architecture is based on a recently developed…

Hardware Architecture · Computer Science 2016-11-17 Hooman Jarollahi , Vincent Gripon , Naoya Onizawa , Warren J. Gross

Recurrent neural networks (RNNs) and self-attention are both widely used sequence-mixing layers that maintain an internal memory. However, this memory is constructed using two orthogonal mechanisms: RNNs compress the entire past into a…

Machine Learning · Computer Science 2026-03-30 Leon Lufkin , Tomás Figliolia , Beren Millidge , Kamesh Krishnamurthy