Publications by Alessandro Favero

Probing the latent hierarchical structure of data via diffusion models

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce. Likewise, accessin ...

2025

A phase transition in diffusion models reveals the hierarchical nature of data

Matthieu Wyart, Alessandro Favero, Antonio Sclocchi

Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural networks capture d ...

National Academy of Sciences2025

How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model

Matthieu Wyart, Umberto Maria Tomasini, Francesco Cagnetta, Alessandro Favero, Leonardo Petrini

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representatio ...

American Physical Society2024

Computational complexity of deep learning: fundamental limitations and empirical phenomena

Alessandro Favero, Ludovic Théo Stephan

This manuscript is the lecture notes of B. Barak’s course in the Les Houches ‘Statistical Physics and Machine Learning’ summer school in 2022. It surveys various proxies for computational hardness in random planted problems, from the low-degree likelihood ...

2024

What can be learnt with wide convolutional neural networks?

Matthieu Wyart, Francesco Cagnetta, Alessandro Favero

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, ...

2024

Relative stability toward diffeomorphisms indicates performance in deep nets

Matthieu Wyart, Alessandro Favero, Mario Geiger, Leonardo Petrini

Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We revisit this qu ...

IOP Publishing Ltd2022

Locality defeats the curse of dimensionality in convolutional teacher-student scenarios*

Matthieu Wyart, Francesco Cagnetta, Alessandro Favero

Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher-student framework for kernel r ...

IOP Publishing Ltd2022

Relative stability toward diffeomorphisms indicates performance in deep nets

Matthieu Wyart, Alessandro Favero, Mario Geiger, Leonardo Petrini

Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We revisit this qu ...

2021