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Diffusion limits provide a framework for the asymptotic analysis ofstochastic gradient descent (SGD) schemes used in machine learning. We consideran alternative framework, the Riemannian Langevin equation (RLE), thatgeneralizes the classical paradigm of equilibration in R^n to a Riemannianmanifold (M^n, g). The most subtle part of this equation is the description ofBrownian motion on (M^n, g). Explicit formulas are presented for somefundamental cones.

The Riemannian Langevin equation and conic programs