Publications by Francesco Cagnetta

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

Kernels, data & physics

Francesco Cagnetta

Lecture notes from the course given by Professor Julia Kempe at the summer school ‘Statistical physics of Machine Learning’ in Les Houches. The notes discuss the so-called NTK approach to problems in machine learning, which consists of gaining an understan ...

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

Learning sparse features can lead to overfitting in neural networks

Matthieu Wyart, Francesco Cagnetta, Leonardo Petrini

It is widely believed that the success of deep networks lies in their ability to learn a meaningful representation of the features of the data. Yet, understanding when and how this feature learning improves performance remains a challenge. For example, it ...

Iop Publishing Ltd2023

How deep convolutional neural networks lose spatial information with training

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

A central question of machine learning is how deep nets manage to learn tasks in high dimensions. An appealing hypothesis is that they achieve this feat by building a representation of the data where information irrelevant to the task is lost. For image da ...

Iop Publishing Ltd2023

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

Work fluctuations in the active Ornstein-Uhlenbeck particle model

Francesco Cagnetta

We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle- ...

IOP Publishing Ltd2021