Hopfield model with planted patterns: A teacher-student self-supervised learning model

作者：Francesco Alemanno, Luca Camanzi, Gianluca Manzan, Daniele Tantari · 发表于：Applied Mathematics and Computation · 年份：2023 · DOI：10.1016/j.amc.2023.128253 · 被引用次数：11 · 研究领域：Neural Networks and Applications、Generative Adversarial Networks and Image Synthesis、Advanced Memory and Neural Computing

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 become an opportunity for the occurrence of a learning regime in which the system can generalize.