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math.OC2026
On the global convergence of gradient flow for wide shallow models beyond homogeneous nonlinearities
Romain Petit, Clarice Poon, Gabriel Peyré
A surprising phenomenon in the training of neural networks is the ability of gradient descent to find global minimizers of the training loss despite its non-convexity. Following ea…
math.OC2026
Second-order geometry of optimal transport: cost identifiability and stability
Gabriel Peyré, Clarice Poon, Oscar Tron
We study the optimal transport value as a functional of the ground cost. Although this functional is an infimum of linear functionals and is therefore polyhedral for finitely suppo…