Graph neural network (GNN) is a formidable deep learning framework that enables the
analysis and modeling of intricate relationships present in data structured as graphs. In …

The uncanny ability of over-parameterised neural networks to generalise well has been
explained using various" simplicity biases". These theories postulate that neural networks …

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 …

A recent line of work in high-dimensional statistics working under the Gaussian mixture
hypothesis has led to a number of results in the context of empirical risk minimization …

Approximate message passing (AMP) algorithms have become an important element of high-
dimensional statistical inference, mostly due to their adaptability and concentration …

We address the problem of denoising data from a Gaussian mixture using a two-layer non-
linear autoencoder with tied weights and a skip connection. We consider the high …

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in
modern Machine Learning practice. Understanding the statistical fluctuations engendered …

Uncertainty quantification is a central challenge in reliable and trustworthy machine
learning. Naive measures such as last-layer scores are well-known to yield overconfident …

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 …

This paper investigates the asymptotic distribution of the maximum-likelihood estimate
(MLE) in multinomial logistic models in the high-dimensional regime where dimension and …