Martedì 24 giugno 2025 alle 14.30 Dario Trevisan, professore ordinario in probabilità e statistica matematica, presso l’Università di Pisa, Dipartimento di Matematica, sarà lo speaker del prossimo appuntamento con i Seminari Generali dell'IAC 2025.
Il talk, dal titolo Quantitative Convergence of Deep Neural Networks to Gaussian Processes, si svolge in modalità mista, in presenza presso il CNR IAC di Roma, via dei Taurini 19 e in streaming (vedi link in calce), trasmesso sul canale YT dell'istituto.
Di seguito l'abstract.
In this seminar, we explore the quantitative convergence of wide deep neural networks with Gaussian weights to Gaussian processes, establishing novel rates for their Gaussian approximation. We show that the Wasserstein distance between the network output and its Gaussian counterpart scales inversely with network width, with bounds apply for any finite input set under specific non-degeneracy conditions of the covariances. Additionally, we extend our analysis to the Bayesian framework, by studying exact posteriors for neural networks, when endowed with Gaussian priors and regular Likelihood functions, but we also provide recent advancements in quantitative approximation of trained networks via gradient descent in the NTK regime. Based on joint works with A. Basteri, and A. Agazzi and E. Mosig.
