Projects

This page aims at sharing some of the projects I worked on during my studies.

My Thesis project

• “Convergence and Implicit biases of Deep Residual Networks” (french)

  This PhD Thesis will be supervised by G.Peyré and F-X.Vialard.

Research internship report

• In 2022, I performed a research internship at ETH Zürich under supervision of Pr. A. Bandeira. I studied statistical properties of random “Kikuchi” matrices (details to come).
• “Convergence and Geometric properties of Gradient Descent in the training of Deep Residual Networks”
  This work was carried out as a part of my Master’s research internship, under supervision of G.Peyré and F-X.Vialard. We studied mathematical properties of the optimization methods in the training of deep Neural Networks.

Class projects

• “Sliced Wasserstein Flows: Non-parametric generative modeling via optimal transport and diffusions”
  This report is based on the work of Liutkus et al..

• “Wasserstein projection for texture synthesis”
  We work with T.Naït on an article from Rabin et al..

Bachelor Thesis

• “Mean curvature flow: An introduction to geometrical flows”
  This is a small Bachelor thesis written under supervision of T.Ozuch. We studied the behavior of surfaces evolving under a velocity field that is locally defined by their mean curvature. We took interest in the so-called “level-set” method and studied the well-posedness of the associated PDE in the sense of viscosity solutions.