SGD's stationary distribution is Boltzmann-Gibbs with temperature equal to step-size, concentrating exponentially on minimum-energy critical points.
Nonconvergence to unstable points in urn models and stochastic aproximations.Annals of Probability, 18(2):698–712, April 1990
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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.