Statistical mechanics has made significant contributions to the study of biological neural systems by modeling them as recurrent networks of interconnected units with adjustable interactions. Several algorithms have been proposed to optimize the neural connections to enable network tasks such as information storage (i.e. associative memory) and learning probability distributions from data (i.e. generative modeling). Among these methods, the Unlearning algorithm, aligned with emerging theories of synaptic plasticity, was introduced by John Hopfield and collaborators. The primary objective of this thesis is to understand the effectiveness of Unlearning in both associative memory models and generative models. Initially, we demonstrate that the Unlearning algorithm can be simplified to a linear perceptron model which learns from noisy examples featuring specific internal correlations. The selection of structured training data enables an associative memory model to retrieve concepts as attractors of a neural dynamics with considerable basins of attraction. Subsequently, a novel regularization technique for Boltzmann Machines is presented, proving to outperform previously developed methods in learning hidden probability distributions from data-sets. The Unlearning rule is derived from this new regularized algorithm and is showed to be comparable, in terms of inferential performance, to traditional Boltzmann-Machine learning.
Short-term plasticity recalls forgotten memories through a trampoline mechanism
Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）
Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplings
Physics Department, Sapienza University of Rome（罗马大学物理系）；Institute of Nanotechnology, 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，CNR-NANOTEC，罗马分部）
Viscosity, breakdown of Stokes-Einstein relation and dynamical heterogeneity in supercooled liquid Ge$_2$Sb$_2$Te$_5$ from simulations with a neural network potential
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）
