A Federated Many-to-One Hopfield model for associative Neural Networks
Università del Salento（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Lecce（意大利国家核物理研究所（INFN）莱切分部）；Istituto Nazionale di Alta Matematica Francesco Severi (INdAM)（弗朗切斯科·塞韦里高等数学国立研究所（INdAM））；Sapienza Università di Roma（罗马智慧大学）
Andrea Alessandrelli, Fabrizio Durante, Andrea Ladiana, Andrea Lepre
Federated learning enables collaborative training without sharing raw data, but struggles under client heterogeneity and streaming distribution shifts, where drift and novel data can impair convergence and cause forgetting. We propose a federated associative-memory framework that learns shared archetypes in heterogeneous, continual settings, where client data are independent but not necessarily balanced. Each client encodes its experience as a low-rank Hebbian operator, sent to a central server for aggregation and factorization into global archetypes. This approach preserves privacy, avoids centralized replay buffers, and is robust to small, noisy, or evolving datasets. We cast aggregation as a low-rank-plus-noise spectral inference problem, deriving theoretical thresholds for detectability and retrieval robustness. An entropy-based controller balances stability and plasticity in streaming regimes. Experiments with heterogeneous clients, drift, and novelty show improved global archetype reconstruction and associative retrieval, supporting the spectral view of federated consolidation.
A Hardware-aware Hopfield Network with a Nonlinear Memristor Array for Robust Associative Memory with Superlinear Capacity
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Seoul National University（首尔大学）；Korea University（韩国大学）；KIST School, University of Science and Technology（韩国科学技术院科学技术研究生院）
Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories
Sapienza Università di Roma（罗马大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Istituto Nazionale d’Alta Matematica, GNFM（意大利高等数学研究所）；Università del Salento（莱切萨伦托大学）
The University of Tokyo（东京大学）；Department of Physics, The University of Tokyo（东京大学物理系）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理研究所）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
Large Associative Memory Problem in Neurobiology and Machine Learning
MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；Princeton Neuroscience Institute（普林斯顿神经科学研究所）；Princeton University（普林斯顿大学）
密集关联记忆或现代Hopfield网络允许存储和可靠检索指数级大（在特征空间的维度上）数量的记忆。与此同时，它们的朴素实现是非生物的，因为它似乎需要神经元之间存在多体突触连接。我们表明，这些模型是一个更微观的（书面的生物自由度）理论，有额外的（隐藏的）神经元，只需要两个身体之间的相互作用的有效描述。由于这个原因，我们提出的微观理论是一个有效的模型，大联想记忆与一定程度的生物相容性。我们的网络的动力学和它的降维等效都最小化能量（李雅普诺夫）函数。当某些动态变量（隐藏神经元）从我们的微观理论中整合出来时，可以恢复许多以前在文献中讨论过的模型，例如“Hopfield Networks is All You Need”论文中提出的模型。我们还提供了另一种推导的能量函数和更新规则中提出的上述文件，并澄清这一类的各种模型之间的关系。
Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University（哈佛学院肯普纳自然与人工智能研究所）；Zuckerman Institute, Columbia University（哥伦比亚大学祖克曼研究所）；Kavli Institute for Brain Science, Columbia University（哥伦比亚大学卡弗里脑科学研究所）
Electrolyte Bonding Engineering for Highly Uniform GeTe-based CBRAM and Parallel Hebbian Learning in Selector-free Hopfield Networks
Center for Semiconductor Technology, Korea Institute of Science and Technology（韩国科学技术院半导体技术中心）；Nanoscience and Technology, KIST School, University of Science and Technology（韩国科学技术院KIST学院纳米科学与技术）；Department of Materials Science and Engineering, Seoul National University（首尔大学材料科学与工程系）；Department of Physics and Astronomy, Seoul National University（首尔大学物理与天文学系）；Department of Electrical Engineering, Korea University（高丽大学电气工程系）；Department of Materials Science and Engineering, Korea University（高丽大学材料科学与工程系）
A Bifurcation Theory for the Equilibria of Modern Hopfield Networks
Max-Planck-Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Ludwig-Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）；Gurdon Institute, University of Cambridge（剑桥大学格登研究所）
Phases in a class of associative memories via hidden neurons
CyberAgent AI Lab（CyberAgent AI实验室）；RIKEN iTHEMS（RIKEN跨学科理论科学研究所）；Graduate School of Artificial Intelligence and Science, Rikkyo University（立教大学人工智能与科学研究科）
Thermodynamics of bidirectional associative memories
Università del Salento（萨伦托大学）；Istituto Nazionale di Fisica Nucleare（国家核物理研究所）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；INRIA（法国国家信息与自动化研究所）
Statistical mechanics of vector Hopfield network near and above saturation
Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学）；Sapienza Università di Roma（罗马第一大学）；National Research Council of Italy, CNR - NANOTEC, Rome Unit（意大利国家研究委员会纳米技术研究所罗马分部）
John A. Paulson School of Engineering and Applied Sciences（约翰·A·保尔森工程与应用科学学院）；Center for Brain Science（脑科学中心）；Department of Physics（物理系）；MIT-IBM Watson AI Lab, IBM Research（MIT-IBM沃森人工智能实验室，IBM研究院）；Kempner Institute for the Study of Natural and Artificial Intelligence（肯普纳自然与人工智能研究所）
Observation of associative-memory retrieval and spin-glass phases on a photonic quantum simulator
Sapienza Università di Roma（罗马大学）；Università del Salento（萨伦托大学）；Institute of Nanotechnology of the National Research Council of Italy, CNR-NANOTEC（意大利国家研究委员会纳米技术研究所）；Università degli Studi di Salerno（萨莱诺大学）；INFN, Sezione di Napoli, Gruppo Collegato di Salerno（意大利国家核物理研究所那不勒斯分部萨莱诺协作组）；Department of Computing Sciences, Bocconi University（博科尼大学计算科学系）；Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR)（意大利国家研究委员会光子和纳米技术研究所）
Partial annealing and pattern decorrelation in associative neural networks
Università del Salento（萨伦托大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Lecce（意大利国家核物理研究所莱切分部）；Sapienza Università di Roma（罗马第一大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1（意大利国家核物理研究所罗马一分部）；CNR-Nanotec, unità di Lecce（国家研究委员会纳米技术研究所莱切单元）；Université Paris-Saclay（巴黎萨克雷大学）
McGovern Institute for Brain Research, Massachusetts Institute of Technology（麻省理工学院麦戈文脑科学研究所）；The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), Massachusetts Institute of Technology（麻省理工学院美国国家科学基金会人工智能基础相互作用研究所）
Firing Rate Models as Associative Memory: Excitatory-Inhibitory Balance for Robust Retrieval
Department of Information Engineering（信息工程系）；Università degli Studi di Padova（帕多瓦大学）；Center for Control, Dynamical Systems and Computation（控制、动态系统与计算中心）；University of California at Santa Barbara（加州大学圣巴巴拉分校）
Memorization to Generalization: Emergence of Diffusion Models from Associative Memory
Department of Computer Science, Rensselaer Polytechnic Institute ( RPI )（计算机科学系，罗切斯特理工学院（RPI））；Jheronimus Academy of Data Science, Tilburg University（数据科学学院，蒂尔堡大学）；Department of Physics, University of Rome Sapienza（物理系，罗马萨皮恩扎大学）；Donders Institute for Brain, Cognition, and Behaviour, Radboud University（大脑、认知与行为研究所，拉德堡德大学）；IBM Research（IBM研究院）
