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/