Lucas Benigni

collaborators

6 papers

math.OC2026

Phases of Muon: When Muon Eclipses SignSGD

Elliot Paquette, Noah Marshall, Lucas Benigni +3

Recently, Muon and related spectral optimizers have demonstrated strong empirical performance as scalable stochastic methods, often outperforming Adam. Yet their behaviour remains…

math.PR2026

The delocalization of eigenvectors of real elliptic matrices

Lucas Benigni, Simon Coste, Guillaume Dubach

We investigate delocalization phenomena for eigenvectors of real random matrices that are invariant by orthogonal transformations. A specific phenomenon with these ensembles is tha…

math.PR2026

Hadamard product of independent random sample covariance matrices with correlation structure

Lucas Benigni, Ziyad Zaklani

We compute the asymptotic empirical eigenvalue distribution of the matrix $M = ⨀_{i = 1}^{k} \frac{1}{d _{i}} X^{(i)} X^{(i)}^{⊤}$ where $X^{(i)} \in R^{n \times d_{i}}$ are i…

math.PR2025

Convergence of local eigenvector processes of generalized Wigner matrices

Lucas Benigni, Mohammadreza Rezaei Feyzabady

We prove convergence of eigenvector processes of the form $(N ⟨ u_{k}, A_{t} u_{k} ⟩)_{t \in [0, 1]}$ where $u_{k}$ is a bulk eigenvector of generali…

math.PR2025

Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling

Lucas Benigni, Elliot Paquette

We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\in\mathbb{R}^{n\ti…

math.PR2025

Eigenvalue distribution of the Hadamard product of sample covariance matrices in a quadratic regime

Sebastien Abou Assaly, Lucas Benigni

In this note, we prove that if $X \in R^{n \times d}$ and $Y \in R^{n \times p}$ are two independent matrices with i.i.d entries then the empirical spectral distributio…