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math.ST2026
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…
math.ST2025
Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares
Pierre Mergny, Lenka Zdeborová
We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These model…