Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks - Université de Paris - Faculté des Sciences Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks

Résumé

This paper is concerned with the asymptotic distribution of the largest eigenvalues for some nonlinear random matrix ensemble stemming from the study of neural networks. More precisely we consider M = 1 m Y Y with Y = f (W X) where W and X are random rectangular matrices with i.i.d. centered entries. This models the data covariance matrix or the Conjugate Kernel of a single layered random Feed-Forward Neural Network. The function f is applied entrywise and can be seen as the activation function of the neural network. We show that the largest eigenvalue has the same limit (in probability) as that of some well-known linear random matrix ensembles. In particular, we relate the asymptotic limit of the largest eigenvalue for the nonlinear model to that of an information plus noise random matrix, establishing a possible phase transition depending on the function f and the distribution of W and X. This may be of interest for applications to machine learning.
Fichier principal
Vignette du fichier
2201.04753.pdf (1.89 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04033305 , version 1 (17-03-2023)

Identifiants

Citer

L Benigni, S Péché. Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks. 2023. ⟨hal-04033305⟩
10 Consultations
17 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More