Workshop contribution on large deviations and large spikes in stochastic gradient descent, presented in Modern and Emerging Phenomena in Machine Learning (8–13 March 2026).
Published · Stochastic Partial Differential Equations and Related Fields, Springer Proceedings in Mathematics & Statistics 229, pp. 43–67 (2018).
Published · Journal of the European Mathematical Society, 23 (2021) 2, pp. 425-465. We prove optimal regularity for solutions to porous media equations in Sobolev spaces, based on velocity averaging techniques. In particular, the obtained regularity is consistent with the optimal regularity in the linear…
Published · Journal of functional analysis, 263 (2012) 8, pp. 2355-2383. Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies…
Published · Journal of differential equations, 269 (2020) 4, pp. 3414-3455. We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable…
Published · SIAM journal on control and optimization, 62 (2024) 6, pp. 3288-3314. We give quantitative estimates for the rate of convergence of Riemannian stochastic gradient descent (RSGD) to Riemannian gradient flow and to a diffusion process, the so-called Riemannian stochastic modified flow (RSMF). Using…
In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier–Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically strong solutions for the stochastic incompressible Euler equations. In particular, this solves the…
