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.

翻译：统计力学通过将生物神经系统建模为具有可调相互作用的递归网络单元，为该领域研究做出了重要贡献。目前已提出多种算法来优化神经连接，使网络能够实现信息存储（即联想记忆）和从数据中学习概率分布（即生成建模）等任务。在这些方法中，由约翰·霍普菲尔德及其合作者提出的"反学习"算法，与新兴的突触可塑性理论相契合。本论文的主要目标是理解反学习在联想记忆模型和生成模型中的有效性。我们首先证明反学习算法可简化为线性感知机模型，该模型能从具有特定内部相关性的含噪样本中学习。结构化训练数据的选择使联想记忆模型能够将概念检索为神经动力学的吸引子，并具有显著的吸引域。随后，我们提出一种针对玻尔兹曼机的新型正则化技术，该技术在从数据集中学习隐藏概率分布方面优于先前开发的方法。从这种新正则化算法推导出的反学习规则，在推理性能方面被证明与传统玻尔兹曼机学习相当。