6 papers
Optimal scaling laws in learning hierarchical multi-index models
Leonardo Defilippis, Florent Krzakala, Bruno Loureiro +1
In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited…
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…
Fundamental Limits of Matrix Sensing: Exact Asymptotics, Universality, and Applications
Yizhou Xu, Antoine Maillard, Lenka Zdeborová +1
In the matrix sensing problem, one wishes to reconstruct a matrix from (possibly noisy) observations of its linear projections along given directions. We consider this model in the…
Fundamental limits of learning in sequence multi-index models and deep attention networks: High-dimensional asymptotics and sharp thresholds
Emanuele Troiani, Hugo Cui, Yatin Dandi +2
In this manuscript, we study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. We first…
Asymptotics of Non-Convex Generalized Linear Models in High-Dimensions: A proof of the replica formula
Matteo Vilucchio, Yatin Dandi, Matéo Pirio Rossignol +2
The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and pr…
Optimal Spectral Transitions in High-Dimensional Multi-Index Models
Leonardo Defilippis, Yatin Dandi, Pierre Mergny +2
We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a…