4 papers
Symmetry-Aware Feature Learning: A Polynomial Separation for Multi-Index Models
Jivan Waber, Vanessa Piccolo, Yatin Dandi +1
We establish a polynomial sample complexity separation between symmetry-aware and symmetry-agnostic feature learning. We study growing-rank multi-index models with high-dimensional…
Spectral phase transitions in Gaussian multi-index models
Florent Krzakala, Pierre Mergny, Vanessa Piccolo
Recovering a low-dimensional latent subspace from nonlinear observations of Gaussian covariates in high dimensions is a fundamental problem in feature learning. Here, we consider G…
Global law of conjugate kernel random matrices with heavy-tailed weights
Alice Guionnet, Vanessa Piccolo
We study the asymptotic spectral distribution of the conjugate kernel random matrix , where arises from a two-layer neural network model. We consider the settin…
Topological complexity of spiked random polynomials and finite-rank spherical integrals
Vanessa Piccolo
We study the annealed complexity of Gaussian random homogeneous polynomials on the -dimensional unit sphere in the presence of deterministic perturbations depending on fixed…