13 citations · 20 across the 15 of their papers we have counts for
6 papers · 1 filter
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.…
Heat profile, level sets and hot spots of Laplace eigenfunctions
Mayukh Mukherjee, Soumyajit Saha
We use probabilistic tools based on Brownian motion and Feynman-Kac formulae to investigate the heat profile for the ground state Dirichlet and second Neumann eigenfunctions. Among…
On the effects of small perturbation on low energy Laplace eigenfunctions
Mayukh Mukherjee, Soumyajit Saha
We investigate several aspects of the nodal geometry and topology of Laplace eigenfunctions, with particular emphasis on the low frequency regime. This includes investigations in a…
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…