Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent. (arXiv:2207.05705v1 [math.PR])

The convergence of stochastic interacting particle systems in the mean-field
limit to solutions to conservative stochastic partial differential equations is
shown, with optimal rate of convergence. As a second main result, a
quantitative central limit theorem for such SPDEs is derived, again with
optimal rate of convergence.

The results apply in particular to the convergence in the mean-field scaling
of stochastic gradient descent dynamics in overparametrized, shallow neural
networks to solutions to SPDEs. It is shown that the inclusion of …

arxiv gradient math mean pr stochastic