The seminar is normally held on Mondays at 14:00 (2:00 PM CET).
The seminar is open; in order to be added to the mailing list, please send an email to Leyla Marzuk (first [dot] last [at] ensae [dot] fr).
Vincent Divol (CREST, ENSAE)
Anna Korba (CREST, ENSAE)
Jaouad Mourtada (CREST, ENSAE)
Monday, September 7, 2:00pm
Kimia Nadjahi (École Normale Supérieure)
Expected Batch Optimal Transport Plans and Consequences for Flow Matching
Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce numerical integration cost. Yet, the population-level coupling induced by repeated minibatch OT remains only partially understood. We formalize this coupling as the expected batch OT plan, obtained by averaging empirical OT plans over independent minibatches. We then establish its large-batch consistency and, in the semidiscrete case relevant to generative modeling, derive rates for both the transport-cost bias and the convergence of the expected batch OT plan to the OT plan. For FM, this yields a population coupling whose induced velocity field is regular enough to define a unique flow from the source to the discrete target. We finally quantify how OT batch size interacts with numerical integration in a tractable two-atom model and in synthetic and image experiments.
Monday, September 14, 2:00pm
Richard Nickl (University of Cambridge)
TBA
Monday, September 28, 2:00pm
Michael Jordan (UC Berkeley)
TBA
Monday, November 9, 2:00pm
Tim Van Erven (Korteweg-de Vries Institute for Mathematics)
TBA
See other tabs for previous editions of the seminar.