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Elisabetta Cornacchia

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Related publications (4)

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Fundamental Limits in Statistical Learning Problems: Block Models and Neural Networks

Elisabetta Cornacchia

This thesis focuses on two selected learning problems: 1) statistical inference on graphs models, and, 2) gradient descent on neural networks, with the common objective of defining and analysing the measures that characterize the fundamental limits. In th ...

EPFL2023

Theory and applications of the sum-of-squares technique

Luca Pesce, Giovanni Piccioli, Elisabetta Cornacchia

The sum-of-squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method t ...

2024

An Initial Alignment between Neural Network and Target is Needed for Gradient Descent to Learn

Emmanuel Abbé, Jan Hazla, Elisabetta Cornacchia

This paper introduces the notion of "Initial Alignment" (INAL) between a neural network at initialization and a target function. It is proved that if a network and a Boolean target function do not have a noticeable INAL, then noisy gradient descent on a fu ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Learning curves for the multi-class teacher-student perceptron

Lenka Zdeborová, Bruno Loureiro, Elisabetta Cornacchia, Rodrigo Soares Veiga

One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

IOP Publishing Ltd2023