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stat.ML2025
Computational Thresholds in Multi-Modal Learning via the Spiked Matrix-Tensor Model
Hugo Tabanelli, Pierre Mergny, Lenka Zdeborova +1
We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This sett…
stat.ML2024
Fundamental limits of Non-Linear Low-Rank Matrix Estimation
Pierre Mergny, Justin Ko, Florent Krzakala +1
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are chara…
stat.ML2024
Spectral Phase Transition and Optimal PCA in Block-Structured Spiked models
Pierre Mergny, Justin Ko, Florent Krzakala
We discuss the inhomogeneous spiked Wigner model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random m…