14 papers
Singular perturbations and hierarchical learning in two-layer neural networks
Cédric Gerbelot, Jean-Christophe Mourrat
We study the population gradient flow of an infinitely wide two-layer neural network learning a misspecified single-index model in high dimension. The two layers are optimized join…
Free energy of non-convex multi-species spin glasses with centered Ising spins
Hong-Bin Chen, Victor Issa, Jean-Christophe Mourrat
We identify the limit free energy of all multi-species spin glasses with centered spins. The result was previously known only under a convexity assumption on the covariance…
PL conditions do not guarantee convergence of gradient descent-ascent dynamics
Jean-Christophe Mourrat
We give an example of a function satisfying a two-sided Polyak-Lojasiewicz condition but for which a gradient descent-ascent flow line fails to converge to the saddle point, circli…
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…
One-sided large deviations for the ground-state energy of spin glasses
Hong-Bin Chen, Alice Guionnet, Justin Ko +2
We describe the large deviations above its typical value of the maximal energy of a spin glass with +/-1 spins. Thanks to the relatively explicit description of the rate function w…
Critical point representation of the mutual information in the sparse stochastic block model
Tomas Dominguez, Jean-Christophe Mourrat
We consider the problem of recovering the community structure in the stochastic block model. We aim to describe the mutual information between the observed network and the actual c…