Buongiorno, Martedì 3 Novembre alla Sapienza Simmaco di Lillo terrà il seminario descritto sotto. Tutti gli interessati sono invitati a partecipare. Cordialmente, Alessandra Faggionato %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Where: Sala di Consiglio, Dipartimento di Matematica G. Castelnuovo, Sapienza. When: November 3 2026, at 14:00. Speaker: Simmaco Di Lillo (Roma Tor Vergata - University of Luxembourg) Title: Geometry and Spectra of Deep Neural Networks Abstract: In this talk we show how tools from spherical harmonic analysis, stochastic geometry and random fields can be used to study deep neural networks. In the infinite-width limit, a deep network induces an isotropic Gaussian field on the sphere, and we investigate its behaviour as the depth increases. At the spectral level, a single parameter, easily computed from the activation, splits networks into three regimes. Depending on the regime, the fields converge to a constant, converge in L^2 while their Sobolev norms diverge, or have their angular power spectrum drift towards arbitrarily high frequencies. At the geometric level, we study the boundary volumes of excursion sets. For irregular activations (e.g., Heaviside) they exhibit fractal behaviour, with Hausdorff dimension increasing with depth. For more regular ones (e.g., ReLU, logistic, tanh) the same spectral parameter determines whether the expected boundary volumes vanish, stay constant or diverge exponentially. Based on joint works with Domenico Marinucci, Michele Salvi, Stefano Vigogna -- ****************************************************************************** Prof. Alessandra Faggionato https://sites.google.com/mat.uniroma1.it/alessandrafaggionato/home Department of Mathematics University "La Sapienza" Piazzale Aldo Moro, 5 00185 - Rome Office 123, first floor ******************************************************************************