Publications by Vittorio Erba | EPFL Graph Search

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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, ...

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 ...

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 ...

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 ...

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 ...

Vittorio Erba

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Statistical mechanics of the maximum-average submatrix problem

Quenches in the Sherrington-Kirkpatrick model

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

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

Optimal denoising of rotationally invariant rectangular matrices