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

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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/