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Antonio Sclocchi

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Related publications (5)

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Probing the latent hierarchical structure of data via diffusion models

Noam Itzhak Levi, Alessandro Favero, Antonio Sclocchi

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

High-dimensional optimization under nonconvex excluded volume constraints

Antonio Sclocchi

We consider high-dimensional random optimization problems where the dynamical variables are subjected to nonconvex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints a ...

AMER PHYSICAL SOC2022

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Matthieu Wyart, Antonio Sclocchi, Umberto Maria Tomasini

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

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

On the different regimes of stochastic gradient descent

Matthieu Wyart, Antonio Sclocchi

Modern deep networks are trained with stochastic gradient descent (SGD) whose key hyperparameters are the number of data considered at each step or batch size B, and the step size or learning rate n. For small B and large n, SGD corresponds to a stochastic ...

National Academy of Sciences2024