4 citations · 7 across the 6 of their papers we have counts for
6 papers
Random Quadratic Form on a Sphere: Synchronization by Common Noise
Maximilian Engel, Anna Shalova
We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere. While…
Nonlinear diffusion limit of non-local interactions on a sphere
Mark A. Peletier, Anna Shalova
We study an aggregation PDE with competing attractive and repulsive forces on a sphere of arbitrary dimension. In particular, we consider the limit of strongly localized repulsion…
Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds
Anna Shalova, André Schlichting
We study stationary solutions of McKean-Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem form…
Singular-limit analysis of gradient descent with noise injection
Anna Shalova, André Schlichting, Mark Peletier
We study the limiting dynamics of a large class of noisy gradient descent systems in the overparameterized regime. In this regime the set of global minimizers of the loss is large,…
Tensorized Transformer for Dynamical Systems Modeling
Anna Shalova, Ivan Oseledets
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by t…
Deep Representation Learning for Dynamical Systems Modeling
Anna Shalova, Ivan Oseledets
Proper states' representations are the key to the successful dynamics modeling of chaotic systems. Inspired by recent advances of deep representations in various areas such as natu…