Dear Colleagues, We would like to invite you to the following two**SPASS seminars, by Claudio Macci and Giovanni Torrisi, on Wednesday December 10th 2025, starting at 4PM. A link for online participants will be shared on the website https://sites.google.com/unipi.it/spass Titles and abstract are below. With best regards, Dario Trevisan ---- Wednesday December 10th 2025 at 17:00 CET - Aula Fib N1 (Polo Fibonacci B, Università di Pisa) Speaker:/Claudio Macci/ (Università di Roma Tor Vergata) Title:*Some recent large deviation results on random neural networks * Abstract: In this talk, I consider random neural networks with Gaussian weights and biases. A well-known result (proved under various assumptions in several references) concerns the convergence in distribution of the network output, in the infinite-width limit, to a centered Gaussian process with i.i.d. components (with the depth $L$ kept fixed). I will present some large deviation results describing a collapse of the network output (which, as expected, converges to the zero vector) with a multiplicative scaling tending to zero; see [1], where moderate deviations are also studied. In the final part, I will outline some results (currently in preparation, see [2]) on the deep limit (that is, as $L\to\infty$) for a generic component of the Gaussian process mentioned above. REFERENCES [1] C. Macci, B. Pacchiarotti, G.L. Torrisi. Journal of Applied Probability (2026), in press. [2] S. Di Lillo, C. Macci, B. Pacchiarotti. In preparation. Wednesday December 10th 2025 at 17:00 CET - Aula Fib N1 (Polo Fibonacci B, Università di Pisa) Speaker: /Giovanni Luca Torrisi /(CNR - IAC) Title:*Posterior Bayesian Neural Networks with Dependent and Heavy-Tailed Weights* Abstract: We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights. These networks have been introduced to alleviate the drawbacks due to a Gaussian initialization. In a Bayesian framework, when the likelihood is Gaussian, we identify the posterior distribution of the output in the sequential wide-width limit and, in the shallow case, we compute explicitly the posterior distribution of these models. The talk is based on a joint work with Nicola Apollonio and Giovanni Franzina. -- Professor of Probability and Statistics Coordinator for Internationalization Dipartimento di Matematica Università di Pisa https://web.dm.unipi.it/trevisan/