Maxime Nicaise

MVA student at ENS Paris-Saclay and engineering student at CentraleSupélec. Interested in optimal transport, optimization, and machine learning.

Publications and Preprints

  • M. Nicaise, Y. Bermudez, and S. M. Perlaza. “A Gauge-Fixed Sinkhorn Algorithm for Semi-Relaxed Optimal Transport”. Inria Research Report, 2026. [HAL] [GitHub]

  • M. Nicaise, Y. Bermudez, and S. M. Perlaza. “Equivalence of optimal transport problems to regularization on the family of f-divergences”. IEEE International Symposium on Information Theory (ISIT), Guangzhou, China, 2026. [arXiv] [IEEE]

  • M. Nicaise, Y. Bermudez, and S. M. Perlaza. “On optimal transport with f-divergence regularization”. Inria Research Report, 2026. [HAL]

Feature-Map Resolution Continuation in CNN Training

CentraleSupélec, France

Joint work with CentraleSupélec students Idriss El khamlichi, Aubin Charley, Alexandre Corrard under the supervision of Joseph Gabet, a PhD student at L2S. We study a simple training intervention for convolutional image classifiers. The feature maps are processed at a lower spatial resolution early in training, and the native resolution is restored step by step before the end, so the final network is unchanged. The report measures the effect across different datasets, architectures, optimizers and training budgets, compares it with feature-map smoothing and with two methods from the literature, and examines whether loss-geometry diagnostics account for the gains.

Report Repository

Internship at INRIA

Sophia-Antipolis, France

I pursued a research internship at INRIA, at the intersection of Applied Mathematics, Machine Learning, and Optimal Transport. More precisely, my work focused on entropic optimal transport as well as the broader class of f-divergence–regularized frameworks, establishing theoretical correspondances between these problems. My focus then shifted to the computational aspects of semi-relaxed optimal transport.

Three-semester PDE research project

MICS laboratory, CentraleSupélec, France

Research project focusing on the generalization of PDE and Functional Analysis theories to rough boundary domains. Explored the Stokes system for fluids with fractal boundaries to establish well-posedness with Dirichlet conditions, and expanded Hodge decomposition results to rough boundary domains.

Last semester (EN) Last semester slides Second semester report First semester report