Publications by Vittorio Erba | EPFL Graph Search

Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-Dimensional Tokens

Lenka Zdeborová, Emanuele Troiani, Vittorio Erba, Luca Biggio

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 called tokens. Statistical physics provides powerful tools to study the fun ...

American Physical Society2025

Les Houches lectures on deep learning at large and infinite width

Vittorio Erba

These lectures, presented at the 2022 Les Houches Summer School on Statistical Physics and Machine Learning, focus on the infinite-width limit and large-width regime of deep neural networks. Topics covered include the various statistical and dynamical prop ...

2024

Statistical mechanics of the maximum-average submatrix problem

Florent Gérard Krzakala, Lenka Zdeborová, Vittorio Erba

We study the maximum-average submatrix problem, wherein given an N x N matrix J, one needs to find the k x k submatrix with the largest average number of entries. We investigate the problem for random matrices J, whose entries are i.i.d. random variables, ...

Iop Publishing Ltd2024

Asymptotic Characterisation of the Performance of Robust Linear Regression in the Presence of Outliers

Florent Gérard Krzakala, Emanuele Troiani, Vittorio Erba

We study robust linear regression in highdimension, when both the dimension d and the number of data points n diverge with a fixed ratio α = n/d, and study a data model that includes outliers. We provide exact asymptotics for the performances of the empiri ...

2024

Quenches in the Sherrington-Kirkpatrick model

Freya Behrens, Florent Gérard Krzakala, Lenka Zdeborová, Vittorio Erba

The Sherrington-Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that local ...

2024

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022