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In this work we propose an energy functional along the lines of Modern Hopfield Networks (MNH), the stationary points of which correspond to the attention due to Vaswani et al. [12], thus unifying both frameworks. The minima of this…

Machine Learning · Statistics 2025-06-16 Ahmed Farooq

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…

Machine Learning · Statistics 2025-06-10 Jerry Yao-Chieh Hu , Bo-Yu Chen , Dennis Wu , Feng Ruan , Han Liu

Modern Hopfield Neural Networks (HNNs), also known as Dense Associative Memories (DAMs), enhance the performance of simple recurrent neural networks by leveraging the nonlinearities in their energy functions. They have broad applications in…

Optics · Physics 2026-01-12 Khalid Musa , Santosh Kumar , Michael Katidis , Yu-Ping Huang

Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative…

Machine Learning · Computer Science 2026-05-29 Ken Takeda , Masafumi Oizumi , Ryo Karakida

The exponential rise in data generation has led to vast, heterogeneous datasets crucial for predictive analytics and decision-making. Ensuring data quality and semantic integrity remains a challenge. This paper presents a brain-inspired…

Machine Learning · Computer Science 2025-03-06 Ashwin Viswanathan Kannan , Johnson P Thomas , Abhimanyu Mukerji

We describe a hybrid analog-digital computing approach to solve important combinatorial optimization problems that leverages memristors (two-terminal nonvolatile memories). While previous memristor accelerators have had to minimize analog…

In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an…

Neural and Evolutionary Computing · Computer Science 2011-05-03 C. Ramya , G. Kavitha , Dr. K. S. Shreedhara

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…

Adaptation and Self-Organizing Systems · Physics 2015-06-09 Christopher Hillar , Ngoc M. Tran

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…

Neural and Evolutionary Computing · Computer Science 2023-11-06 Hamza Tahir Chaudhry , Jacob A. Zavatone-Veth , Dmitry Krotov , Cengiz Pehlevan

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…

Most existing Heterogeneous Information Network (HIN) embedding methods focus on static environments while neglecting the evolving characteristic of realworld networks. Although several dynamic embedding methods have been proposed, they are…

Social and Information Networks · Computer Science 2020-11-13 Zhenghao Zhang , Jianbin Huang , Qinglin Tan

Despite success across diverse tasks, current artificial recurrent network architectures rely primarily on implicit hidden-state memories, limiting their interpretability and ability to model long-range dependencies. In contrast, biological…

Neural and Evolutionary Computing · Computer Science 2025-07-30 Daniel Szelogowski

Machine comprehension(MC) style question answering is a representative problem in natural language processing. Previous methods rarely spend time on the improvement of encoding layer, especially the embedding of syntactic information and…

Artificial Intelligence · Computer Science 2017-07-31 Boyuan Pan , Hao Li , Zhou Zhao , Bin Cao , Deng Cai , Xiaofei He

Graph neural networks (GNNs) have achieved great success in various graph problems. However, most GNNs are Message Passing Neural Networks (MPNNs) based on the homophily assumption, where nodes with the same label are connected in graphs.…

Machine Learning · Computer Science 2022-10-18 Junjie Xu , Enyan Dai , Xiang Zhang , Suhang Wang

Neuroscience and Artificial Intelligence (AI) have progressed in tandem, each contributing to our understanding of the brain, and inspiring recent developments in biologically-plausible neural networks (NNs) and learning rules. Predictive…

Neural and Evolutionary Computing · Computer Science 2024-06-24 Ehsan Ganjidoost , Mallory Snow , Jeff Orchard

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

We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories. We present a tight analysis by establishing a connection between the…

Machine Learning · Statistics 2024-11-04 Jerry Yao-Chieh Hu , Dennis Wu , Han Liu

Graph Transformers have recently achieved remarkable progress in graph representation learning by capturing long-range dependencies through self-attention. However, their quadratic computational complexity and inability to effectively model…

Machine Learning · Computer Science 2025-12-17 Yifan Lu , Ziyun Zou , Belal Alsinglawi , Islam Al-Qudah , Izzat Alsmadi , Feilong Tang , Pengfei Jiao , Shoaib Jameel , Imran Razzak

Hypergraphs provide a natural representation for many real world datasets. We propose a novel framework, HNHN, for hypergraph representation learning. HNHN is a hypergraph convolution network with nonlinear activation functions applied to…

Machine Learning · Computer Science 2020-07-15 Yihe Dong , Will Sawin , Yoshua Bengio

Most real-world datasets are inherently heterogeneous graphs, which involve a diversity of node and relation types. Heterogeneous graph embedding is to learn the structure and semantic information from the graph, and then embed it into the…

Artificial Intelligence · Computer Science 2021-03-12 Bang Lin , Xiuchong Wang , Yu Dong , Chengfu Huo , Weijun Ren , Chuanyu Xu