SGD's stationary distribution is Boltzmann-Gibbs with temperature equal to step-size, concentrating exponentially on minimum-energy critical points.
Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation.Communications in Mathematical Sciences, 18 (1):163–188
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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.