Publications by Alessandro Favero

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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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...

Alessandro Favero

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

What can be learnt with wide convolutional neural networks?

Relative stability toward diffeomorphisms indicates performance in deep nets

Probing the latent hierarchical structure of data via diffusion models

Relative stability toward diffeomorphisms indicates performance in deep nets

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

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

Computational complexity of deep learning: fundamental limitations and empirical phenomena