no code implementations • 25 Feb 2025 • Alice Guionnet, Vanessa Piccolo
We study the asymptotic spectral behavior of the conjugate kernel random matrix $YY^\top$, where $Y= f(WX)$ arises from a two-layer neural network model.
no code implementations • 19 Dec 2024 • Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
We determine the sample complexity required for gradient flow to efficiently recover all spikes, without imposing any assumptions on the separation of the signal-to-noise ratios (SNRs).
no code implementations • 23 Oct 2024 • Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
The order in which correlations become macroscopic depends on their initial values and the corresponding SNRs, leading to either exact recovery or recovery of a permutation of the spikes.
no code implementations • 12 Aug 2024 • Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem.
no code implementations • 19 Dec 2023 • Vanessa Piccolo
More precisely, the determinant analysis is based on recent advances on finite-rank spherical integrals by [Guionnet, Husson 2022] to study the large deviations of multi-rank spiked Gaussian Wigner matrices.
1 code implementation • NeurIPS 2021 • Vanessa Piccolo, Dominik Schröder
We extend the previous results to the case of additive bias $Y=f(WX+B)$ with $B$ being an independent rank-one Gaussian random matrix, closer modelling the neural network infrastructures encountered in practice.
