Today, I had the opportunity to present my research on random neural networks and their approximation via Gaussian processes at the Analysis and Applied Mathematics seminar, Bocconi University. It was a great pleasure to share my findings with the audience and I really thank them for valuable feedback and interesting questions. In particular I warmly acknowledge Giuseppe Savaré for the invitation!
Slides can be dowloaded here (.pdf).
The seminar was largely based on my joint work with Andrea Basteri (arXiv:2203.07379), where we discuss the relationship between the output distribution of randomly initialized fully connected neural networks and suitable Gaussian distributions. We derived explicit inequalities that provide bounds using the quadratic Wasserstein distance and offering a quantitative understanding of the Gaussian-like behavior observed in wide random neural networks.
Additionally, I extended the bounds to the Gaussian approximation of the exact Bayesian posterior distribution of the network, if the likelihood is sufficiently regular. Although very much theoretical, this step opens up possibilities for modeling and performing similar analyses on neural networks trained via gradient descent algorithms, thus closer to machine learning applications.
