For real-analytic loss functions, Langevin dynamics restricted to the zero set converges, in a Dirichlet-form sense, to a hierarchy of processes that are attracted to more singular strata.
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Langevin dynamics along the zero set of real-analytic potentials
For real-analytic loss functions, Langevin dynamics restricted to the zero set converges, in a Dirichlet-form sense, to a hierarchy of processes that are attracted to more singular strata.