A Friendly Tutorial on Mean-Field Spin Glass Techniques for Non-Physicists

Mean-field spin glasses are a class of high-dimensional random cost (energy) function with special exchangeability properties. Random probability measures are defined from these energy functions by the usual Boltzmann formula. Over the last 40 years, an arsenal of sophisticated mathematical techniques (both rigorous and non-rigorous) has been developed to characterize these models. More recently, these techniques have been successfully applied to a number of canonical models in high-dimensional statistics and machine learning, which fit the same framework. This tutorial provides an introduction to such techniques, aimed at non-specialists.