SGD's stationary distribution is Boltzmann-Gibbs with temperature equal to step-size, concentrating exponentially on minimum-energy critical points.
D.Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory, volume 9 ofLecture Notes-Monograph Series
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What is the long-run distribution of stochastic gradient descent? A large deviations analysis
SGD's stationary distribution is Boltzmann-Gibbs with temperature equal to step-size, concentrating exponentially on minimum-energy critical points.