6 citations · 27 across the 19 of their papers we have counts for
22 papers
Minimax-Optimal Early Stopping for Continuous-Time SGD via the Discrepancy Principle
Tim Jahn, Loucas Pillaud-Vivien, Adrien Schertzer
We study early stopping for a continuous-time model of stochastic gradient descent (SGD) in ill-posed linear inverse problems. We consider an a posteriori stopping rule based on th…
Incremental Learning in Mirror Flows
Raphaël Berthier, Loucas Pillaud-Vivien
We study mirror flows generated by a convex quadratic loss and a general convex lower semicontinuous mirror potential. We show that, when initialized near the boundary of the domai…
Oscillating solutions to the mean-field Langevin descent-ascent flow
Jean-Christophe Mourrat, Loucas Pillaud-Vivien
We present a counterexample to the statement of convergence of the mean-field Langevin descent-ascent flow on . We consider payoff functions that are shaped as a doub…
Joint Learning in the Gaussian Single Index Model
Loucas Pillaud-Vivien, Adrien Schertzer
We consider the problem of jointly learning a one-dimensional projection and a univariate function in high-dimensional Gaussian models. Specifically, we study predictors of the for…
Convergence of Shallow ReLU Networks on Weakly Interacting Data
Léo Dana, Francis Bach, Loucas Pillaud-Vivien
We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on data points. Our main contribution leverages the high dimensionality of the ambient spa…
Stochastic Differential Equations models for Least-Squares Stochastic Gradient Descent
Adrien Schertzer, Loucas Pillaud-Vivien
We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze St…