PhD defense Paul Krzakala: Optimal Transport for Differentiable Graph Prediction and Structured Representation Learning

Jury

• Florence d’Alché-Buc, Professor, Télécom Paris/IP Paris, France (Thesis Supervisor)
• Rémi Flamary, Professor, École Polytechnique, France (Co-Supervisor)
• Pierre Vandergheynst, Professor, EPFL, Switzerland (Reviewer)
• Juho Rousu, Professor, Aalto University, Finland (Reviewer)
• Marco Cuturi, Professor, ENSAE Paris, France (Examiner)
• Stefanie Jegelka, Professor, Technische Universität München, Germany (Examiner)
• Jean-Philippe Vert, Professor, Bioptimus, France (Examiner)
• Pascal Frossard, Professor, EPFL, Switzerland (Guest)
• Charlotte Laclau, Télécom Paris/IP Paris, France (Guest)

Abstract

Many modern machine-learning problems involve structured objects such as graphs, molecules, spectra, sets, or multimodal representations. In this thesis, we study how deep learning can be extended to such data, with a central focus on graph prediction. Throughout the PhD, we use optimal transport as a geometric framework for comparing structured objects, defining permutation-invariant losses, and turning matching problems into differentiable learning objectives.

The core of the presentation will focus on supervised graph prediction, in particular on the optimal-transport relaxation and amortization of the graph matching loss. We will also present contributions on multimodal representation alignment, extending the scope beyond graphs.