2 citations · 5 across the 27 of their papers we have counts for
11 papers · 1 filter
Single-Head Attention in High Dimensions: A Theory of Generalization, Weights Spectra, and Scaling Laws
Fabrizio Boncoraglio, Vittorio Erba, Emanuele Troiani +3
Trained attention layers exhibit striking and reproducible spectral structure of the weights, including low-rank collapse, bulk deformation, and isolated spectral outliers, yet the…
Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime
Leonardo Defilippis, Yizhou Xu, Julius Girardin +5
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a…
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…
Asymptotics of SGD in Sequence-Single Index Models and Single-Layer Attention Networks
Luca Arnaboldi, Bruno Loureiro, Ludovic Stephan +2
We study the dynamics of stochastic gradient descent (SGD) for a class of sequence models termed Sequence Single-Index (SSI) models, where the target depends on a single direction…
Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensions
Yizhou Xu, Florent Krzakala, Lenka Zdeborová
The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its perfor…
The Nuclear Route: Sharp Asymptotics of ERM in Overparameterized Quadratic Networks
Vittorio Erba, Emanuele Troiani, Lenka Zdeborová +1
We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data.…
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…
The Computational Advantage of Depth: Learning High-Dimensional Hierarchical Functions with Gradient Descent
Yatin Dandi, Luca Pesce, Lenka Zdeborová +1
Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce…
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…