Learning from data via overparameterization

par Cesare Molinari

mardi 27 janv. 2026, 14:00 → 15:00 Europe/Paris

Solving data driven problems requires defining complex models and fitting them on data, neural networks being a motivating example. The fitting procedure can be seen as an optimization problem which is often non convex, and hence optimization guarantees hard to derive. An opportunity is provided by viewing the model of interest as a redundant re-parameterization - an overparametrization - of some simpler model for which optimization results are easier to achieve.  

In this paper, after formalizing the above idea, we review some recent results and derive new ones. In particular, we consider the gradient flow of some classes of linear overparametrization and show they correspond to suitable mirror flow on the original parameters. Our main contribution relates to the study of the latter, for which we establish well posedness and convergence. The  results yields insight on the role of overparametrization for implicit regularization and constrained optimization.