While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student self-supervised learning problem with Boltzmann machines in terms of a suitable generalization of the Hopfield model with structured patterns, where the spin variables are the machine weights and patterns correspond to the training set's examples. We analyze the learning performance by studying the phase diagram in terms of the training set size, the dataset noise and the inference temperature (i.e. the weight regularization). With a small but informative dataset the machine can learn by memorization. With a noisy dataset, an extensive number of examples above a critical threshold is needed. In this regime the memory storage limits of the system becomes an opportunity for the occurrence of a learning regime in which the system can generalize.

翻译：尽管Hopfield网络作为记忆存储与检索的经典模型而闻名，现代人工智能系统主要基于机器学习范式。我们证明，通过将具有结构化模式的Hopfield模型进行适当推广——其中自旋变量对应机器权重，模式对应训练集样本——可以构建一个基于玻尔兹曼机的师生自监督学习问题。通过研究训练集规模、数据集噪声以及推理温度（即权重正则化）的相图，我们分析了学习性能。当数据集虽小但信息丰富时，机器可通过记忆化完成学习；而面对噪声数据集，则需要超过临界阈值的海量样本。在此机制下，系统的记忆存储限制为泛化学习模式的涌现提供了可能。