Understanding deep learning is increasingly emergent as it penetrates more and more into
industry and science. In recent years, a research line from Fourier analysis sheds light on …

Over the last decade or so, Approximate Message Passing (AMP) algorithms have become
extremely popular in various structured high-dimensional statistical problems. Although the …

We study generalised linear regression and classification for a synthetically generated
dataset encompassing different problems of interest, such as learning with random features …

Understanding the reasons for the success of deep neural networks trained using stochastic
gradient-based methods is a key open problem for the nascent theory of deep learning. The …

In these Lecture Notes, we provide a comprehensive introduction to the most recent
advances in the application of machine learning methods in quantum sciences. We cover …

Understanding the impact of data structure on the computational tractability of learning is a
key challenge for the theory of neural networks. Many theoretical works do not explicitly …

We consider the problem of learning a target function corresponding to a deep, extensive-
width, non-linear neural network with random Gaussian weights. We consider the asymptotic …

Continual learning {—} the ability to learn many tasks in sequence {—} is critical for artificial
learning systems. Yet standard training methods for deep networks often suffer from …

Deep neural networks achieve stellar generalisation even when they have enough
parameters to easily fit all their training data. We study this phenomenon by analysing the …

Generalised linear models for multi-class classification problems are one of the fundamental
building blocks of modern machine learning tasks. In this manuscript, we characterise the …