Publications by Luca Pesce | EPFL Graph Search

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For high-dimensional Gaussian data, we investigate theoretically how the features of a two-layer neural network adapt to the structure of the target function through a few large batch gradient descent steps, leading to an improvement in the approximation c ...

We investigate the training dynamics of two-layer neural networks when learning multi-index target functions. We focus on multi-pass gradient descent (GD) that reuses the batches multiple times and show that it significantly changes the conclusion about wh ...

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 ...

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regim ...

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging the insight from (Ba et al., 2022), we model t ...

A simple model to study subspace clustering is the high-dimensional k -Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction error in this model i ...

We study the impact of the batch

n_b

on the iteration time

T

of training two-layer neural networks with one-pass stochastic gradient descent (SGD) on multi-index target functions of isotropic covariates. We characterize the optimal batch size minimizin ...

Luca Pesce

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How Two-Layer Neural Networks Learn, One (Giant) Step at a Time

The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents

Theory and applications of the sum-of-squares technique

Are Gaussian data all you need? the extents and limits of universality in high-dimensional generalized linear estimation

Asymptotics of feature learning in two-layer networks after one gradient-step

Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap

Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs