11 papers
Approximation Theory for Neural Networks: Old and New
Soumendu Sundar Mukherjee, Himasish Talukdar
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function,…
Elephant random walks on infinite Cayley trees
Soumendu Sundar Mukherjee
We introduce a generalisation of Schütz and Trimper's elephant random walk to finitely generated groups. We focus on the simplest non-abelian setting, i.e. groups whose Cayley gra…
Elephant random walk on the infinite dihedral group
Soumendu Sundar Mukherjee, Himasish Talukdar
Elephant random walks were studied recently in \cite{mukherjee2025elephant} on the groups whose Cayley graphs are infinite -regular tre…
Filtering through a topological lens: homology for point processes on the time-frequency plane
Juan Manuel Miramont, Kin Aun Tan, Soumendu Sundar Mukherjee +2
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a po…
Learning under Latent Group Sparsity via Diffusion on Networks
Subhroshekhar Ghosh, Soumendu Sundar Mukherjee
Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticia…
A new approach to locally adaptive polynomial regression
Sabyasachi Chatterjee, Subhajit Goswami, Soumendu Sundar Mukherjee
Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria f…