Project
Geometric Deep Learning and Kernel Method: Theory and Applications
Within this thesis we will study geometrical aspects of machine learning and kernel methods with an aim to study geometry induced duality principles for machine learning models. In particular we'll focus on the interaction 1) in between equivariance, geometric kernels, and (random) Riemannian manifolds 2) in between discrete convex analysis, kernels and graph networks. Our aim is to get a thorough mathematical understanding of machine learning models used for disentanglement representation learning through understanding the geometric and topological perspective. In the later half we'll also focus on optimal transport theory applicable to both graphs and Riemannian manifold for disentangelement learning and generative modelling even under some uncertainty. In parallel to the mathematical understanding we'll also study the complexity of learning models and mathematical objects like tensors that are widely used in machine learning and signal processing. As applications to our methodological studies we'll study the modelling of dynamical systems, physics inspired deep learning, reinforcement learning and optimization problems. Therefore this thesis provides an excellent platform to connect mathematics with statistical learning theory, geometric machine learning and deep learning.