1 citations · 1 across the 2 of their papers we have counts for
7 papers
On the Impact of Stable Ranks in Deep Nets
Bogdan Georgiev, Lukas Franken, Mayukh Mukherjee +1
A recent line of work has established intriguing connections between the generalization/compression properties of a deep neural network (DNN) model and the so-called layer weights'…
Some applications of heat flow to Laplace eigenfunctions
Bogdan Georgiev, Mayukh Mukherjee
We consider mass concentration properties of Laplace eigenfunctions , that is, smooth functions satisfying the equation , on a smooth closed Riemannian manifold.…
Mass non-concentration at the nodal set and a sharp Wasserstein uncertainty principle
Mayukh Mukherjee
We prove -mass concentration properties of Laplace eigenfunctions away from their nodal sets, extending a recent result in \cite{GM3} to all dimensions, and giving a slight re…
Heating up decision boundaries: isocapacitory saturation, adversarial scenarios and generalization bounds
Bogdan Georgiev, Lukas Franken, Mayukh Mukherjee
In the present work we study classifiers' decision boundaries via Brownian motion processes in ambient data space and associated probabilistic techniques. Intuitively, our ideas co…
Nodal sets of Laplace eigenfunctions under small perturbations
Mayukh Mukherjee, Soumyajit Saha
We study the stability properties of nodal sets of Laplace eigenfunctions on compact manifolds under specific small perturbations. We prove that nodal sets are fairly stable if sai…
Polyhedral billiards, eigenfunction concentration and almost periodic control
Mihajlo Cekić, Bogdan Georgiev, Mayukh Mukherjee
We study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non-smooth part of the boundary, called ``pockets''. We prove there are only…