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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…

Deep neural networks, including transformers and convolutional neural networks, have significantly improved multivariate time series classification (MTSC). However, these methods often rely on supervised learning, which does not fully…

Machine Learning · Computer Science 2024-05-28 Xiwen Chen , Peijie Qiu , Wenhui Zhu , Huayu Li , Hao Wang , Aristeidis Sotiras , Yalin Wang , Abolfazl Razi

Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…

Biological Physics · Physics 2021-06-07 Oskar H Schnaack , Luca Peliti , Armita Nourmohammad

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 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

We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…

Machine Learning · Computer Science 2024-06-04 Jerry Yao-Chieh Hu , Thomas Lin , Zhao Song , Han Liu

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

Modern Hopfield Networks (MHNs) have emerged as powerful components in deep learning, serving as effective replacements for pooling layers, LSTMs, and attention mechanisms. While recent advancements have significantly improved their storage…

Computational Complexity · Computer Science 2026-01-26 Yang Cao , Xiaoyu Li , Yuanpeng Li , Yingyu Liang , Zhenmei Shi , Zhao Song

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

We present the first application of modern Hopfield networks to the problem of portfolio optimization. We performed an extensive study based on combinatorial purged cross-validation over several datasets and compared our results to both…

Machine Learning · Computer Science 2025-07-08 Carlo Nicolini , Monisha Gopalan , Jacopo Staiano , Bruno Lepri

Histopathology image analysis can be considered as a Multiple instance learning (MIL) problem, where the whole slide histopathology image (WSI) is regarded as a bag of instances (i.e, patches) and the task is to predict a single class label…

Computer Vision and Pattern Recognition · Computer Science 2019-06-28 Meng Li , Lin Wu , Arnold Wiliem , Kun Zhao , Teng Zhang , Brian C. Lovell

Whole-slide image classification represents a key challenge in computational pathology and medicine. Attention-based multiple instance learning (MIL) has emerged as an effective approach for this problem. However, the effect of attention…

Quantitative Methods · Quantitative Biology 2025-03-14 Rajiv Krishnakumar , Julien Baglio , Frederik F. Flöther , Christian Ruiz , Stefan Habringer , Nicole H. Romano

Immune repertoire classification, a typical multiple instance learning (MIL) problem, is a frontier research topic in computational biology that makes transformative contributions to new vaccines and immune therapies. However, the…

Machine Learning · Computer Science 2023-08-01 Mingcai Chen , Yu Zhao , Zhonghuang Wang , Bing He , Jianhua Yao

Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…

Machine Learning · Computer Science 2025-04-11 Saul Santos , António Farinhas , Daniel C. McNamee , André F. T. Martins

In this study we introduce a novel energy functional for long-sequence memory, building upon the framework of dense Hopfield networks which achieves exponential storage capacity through higher-order interactions. Building upon earlier work…

Machine Learning · Computer Science 2025-07-03 Ahmed Farooq

The classification of gigapixel histopathology images with deep multiple instance learning models has become a critical task in digital pathology and precision medicine. In this work, we propose a Transformer-based multiple instance…

Computer Vision and Pattern Recognition · Computer Science 2023-11-21 Josef Cersovsky , Sadegh Mohammadi , Dagmar Kainmueller , Johannes Hoehne

Motivation: The analysis of antibodies and T-cell receptors (TCRs) concentrations in serum is a fundamental problem in immunoinformatics. Repertoire construction is a preliminary step of analysis of clonal lineages, understanding of immune…

Genomics · Quantitative Biology 2016-04-11 Alexander Shlemov , Sergey Bankevich , Andrey Bzikadze , Yana Safonova

The computer-aided analysis of medical scans is a longstanding goal in the medical imaging field. Currently, deep learning has became a dominant methodology for supporting pathologists and radiologist. Deep learning algorithms have been…

Machine Learning · Computer Science 2017-12-06 Jakub M. Tomczak , Maximilian Ilse , Max Welling

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 hippocampus plays a vital role in the diagnosis and treatment of many neurological disorders. Recent years, deep learning technology has made great progress in the field of medical image segmentation, and the performance of related…

Computer Vision and Pattern Recognition · Computer Science 2022-11-16 Heyu Huang , Runmin Cong , Lianhe Yang , Ling Du , Cong Wang , Sam Kwong
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