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While Hopfield networks are known as paradigmatic models for memory storageand retrieval, modern artificial intelligence systems mainly stand on themachine learning paradigm. We show that it is possible to formulate ateacher-student self-supervised learning problem with Boltzmann machines interms of a suitable generalization of the Hopfield model with structuredpatterns, where the spin variables are the machine weights and patternscorrespond to the training set's examples. We analyze the learning performanceby studying the phase diagram in terms of the training set size, the datasetnoise and the inference temperature (i.e. the weight regularization). With asmall but informative dataset the machine can learn by memorization. With anoisy dataset, an extensive number of examples above a critical threshold isneeded. In this regime the memory storage limits of the system becomes anopportunity for the occurrence of a learning regime in which the system cangeneralize.

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