113 citations · 392 across the 22 of their papers we have counts for
23 papers
Efficient computation of the asymptotics of extensive-rank HCIZ integrals
Antoine Maillard, Jean-Christophe Mourrat
We study the high-dimensional asymptotics of Harish-Chandra-Itzykson-Zuber (HCIZ) integrals in the extensive-rank regime. The limit of these integrals is governed by a one-dimensio…
Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval
Antoine Maillard, Tony Bonnaire, Giulio Biroli
We consider the landscape of empirical risk minimization for high-dimensional Gaussian single-index models (generalized linear models). The objective is to recover an unknown signa…
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…
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…
Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokens
Vittorio Erba, Emanuele Troiani, Luca Biggio +2
Current progress in artificial intelligence is centered around so-called large language models that consist of neural networks processing long sequences of high-dimensional vectors…
Bayes-optimal learning of an extensive-width neural network from quadratically many samples
Antoine Maillard, Emanuele Troiani, Simon Martin +2
We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random…