The purpose of this article is to review the achievements made in the last few years towards
the understanding of the reasons behind the success and subtleties of neural network …

One of the key issues in the analysis of machine learning models is to identify the
appropriate function space and norm for the model. This is the set of functions endowed with …

We study the variation space corresponding to a dictionary of functions in L 2 (Ω) for a
bounded domain Ω⊂ R d. Specifically, we compare the variation space, which is defined in …

Controlling the parameters' norm often yields good generalisation when training neural
networks. Beyond simple intuitions, the relation between regularising parameters' norm and …

This paper proposes a flexible probabilistic activation function that enhances the training
and operation of artificial neural networks by intentionally injecting noise to gain additional …

Large language models based on the Transformer architecture have demonstrated
impressive capabilities to learn in context. However, existing theoretical studies on how this …

We investigate how shallow ReLU networks interpolate between known regions. Our
analysis shows that empirical risk minimizers converge to a minimum norm interpolant as …

Generalization error bounds for deep neural networks trained by stochastic gradient descent
(SGD) are derived by combining a dynamical control of an appropriate parameter norm and …

The approximation properties of infinitely wide shallow neural networks heavily depend on
the choice of the activation function. To understand this influence, we study embeddings …

We use explicit representation formulas to show that solutions to certain partial differential
equa-tions lie in Barron spaces or multilayer spaces if the PDE data lie in such function …