The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We analyze the stability of the stored memories: basins of attraction obtained by the Hebbian unlearning technique are found to be comparable in size to those obtained in the symmetric perceptron, while the two algorithms are found to converge in the same region of Gardner's space of interactions, having followed similar learning paths. A geometric interpretation of Hebbian unlearning is proposed to explain its optimal performances. Because the Hopfield model is also a prototypical model of disordered magnetic system, it might be possible to translate our results to other models of interest for memory storage in materials.
Analysis of the Hopfield Model Incorporating the Effects of Unlearning
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（东京大学智能物理学研究所）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
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）
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）
Università del Salento（萨兰托大学）；Istituto Nazionale di Fisica Nucleare（国家核物理研究所）；Sapienza Università di Roma（罗马第一大学）；Istituto Nazionale d’Alta Matematica（国家高等数学研究所）；Bar-Ilan University（巴伊兰大学）
Semi-supervised Hopfield model: Theoretical and Numerical results
Università del Salento（萨伦托大学）；Dipartimento di Matematica e Fisica "Ennio De Giorgi", Università del Salento（萨伦托大学恩尼奥·德乔治数学与物理系）；Istituto Nazionale di Alta Matematica Francesco Severi (INdAM)（弗朗切斯科·塞韦里高等数学国家研究所）；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（罗马大学）；Dipartimento di Scienze di Base e Applicazioni all’Ingegneria, Sapienza Università di Roma（罗马大学基础科学与工程应用系）；Dipartimento di Matematica, Sapienza Università di Roma（罗马大学数学系）
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）
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）
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）
Sapienza Università di Roma（罗马第一大学）；GNFM-INdAM Sezione di Roma（意大利国家数学物理研究所罗马分会）；Università del Salento（萨兰托大学）；GNFM-INdAM Sezione di Lecce（意大利国家数学物理研究所莱切分会）；INFN, Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）
