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Settimana 06/10/2025 - 10/10/2025
Seminari
Nel link sottostante trovate la Newsletter n.5 del progetto di Dipartimento MatMod@TOV, con l'invito di leggerla ed a darne massima diffusione:
Click below for PDF file Download:
NEWSLETTER n.5
Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
Ro.Ma.D.S. - Rome Centre on Mathematics for Modelling and Data ScienceS Seminar
Date: 06 October 2025
Schedule: 14:00 Rome Time
Where: ROOM 1201 "R. Dal Passo"
Title: "Scaling Limits of Bayesian Neural Networks: Gaussian Processes and Mixtures "
Speaker: Emanuele Natale - Université Côte d'Azur
Abstract:
In large neural networks, key theoretical insights emerge in the infinite-width limit, where the number of neurons per layer grows while depth stays fixed. In this regime, networks with Gaussian-initialized weights define a mixture of Gaussian processes with random covariance, which converges in the infinite-width limit to a pure Gaussian process with deterministic covariance. However, this Gaussian limit sacrifices descriptive power, as it lacks the ability to learn dependent features and produce output correlations that reflect observed labels. Motivated by these limitations, we explore deep linear networks in the proportional limit, where both depth and width diverge at a fixed ratio. In this setting, the network converges to a nontrivial Gaussian mixture, both at the prior and posterior level. This structure allows the network to capture dependencies in the outputs—an ability lost in the infinite-width limit but retained in finite networks. Our contribution extends previous works by explicitly characterizing, for linear activation functions, the limiting distribution as a nontrivial mixture of Gaussians.
The talk is based on
F. Bassetti, L. Ladelli, P. Rotondo. Proportional infinite-width infinite-depth limit for deep linear neural networks (2024+) Click here for arxiv document
Bassetti,F. Gherardi, M. Ingrosso, A. Pastore, M. Rotondo, P. Feature learning in finite-width Bayesian deep linear networks with multiple outputs and convolutional layers. Journal of Machine Learning Research 26 (2025) 1-35.
Nota: Questo seminari
o fa parte delle attività finanziate dal progetto MIUR Dipartimento d'eccellenza MatMod@TOV (2023-27) CUP E83C23000330006
Note: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (2023-27) CUP E83C23000330006
Organizing Committee:
Domenico Marinucci contact Mail
Michele Salvi contact Mail
Stefano Vigogna contact Mail
Further Info and Program: Click here for RoMaDS event Page
Streaming Link (MS Teams): Link TEAMS Click here for Link
Further Info and Program: Click here for RoMaDS event Page
Streaming Link (MS Teams): Link TEAMS Click here for Link
Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
Algebra and Representation Theory Seminar
Date: Friday 10th October 2025
Schedule:
FIRST SEMINAR 14:30 Rome Time
SECOND SEMINAR 16:00 Rome Time
Where: Conference 1201 - Room Dal Passo
FIRST SEMINAR 14:30 Rome Time
Speaker: Luca Casarin - "Sapienza" Università di Roma
Title: " The factorizable Feigin-Frenkel center "
Abstract:
Given a simple finite Lie algebra over the complex numbers, we can consider two other Lie algebras attached to it:
its Langlands dual Lie algebra and the affine algebra at the critical level. It is a theorem of the nineties,
by Feigin and Frenkel, that the center of the completed enveloping algebra of the affine algebra at the critical
level is canonically isomorphic to the algebra of functions on the space of Opers on the pointed disk for the Langlands
dual Lie algebra. These objects are actually pointwise instances of a more general picture: the space of opers for example
enhances to a space which lives over an arbitrary smooth curve that is equipped with a natural factorization structure.
This structure is fundamental for the Geometric Langlands community: factorization patterns allow for local to global arguments.
In this talk I will explain the construction of the objects mentioned above and elaborate on a joint work with Andrea Maffei in
which we prove the factorizable version of the Feigin-Frenkel theorem.
Note: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
SECOND SEMINAR 16:00 Rome Time
Speaker: Jiefeng LIU - Northeast Normal University, Changchun
Title: " Cohomology of restricted Poisson algebras in characteristic 2 "
Abstract:
In this talk, I will introduce restricted Poisson algebras in characteristic 2 and explore their connection with restricted Lie-Rinehart algebras. For the latter, a cohomology theory is developed and abelian extensions are investigated. I will also construct a cohomology complex for restricted Poisson algebras in characteristic 2 that controls formal deformations. This complex is shown to be isomorphic to the cohomology complex of a suitable restricted Lie-Rinehart algebra. Several examples are provided to illustrate the constructions.
This is a joint work with Sofiane Bouarroudj and Quentin Ehret
Note: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
Organizing Committee:
Fabio Gavarini (mail to)
Niels Kowalzig (mail to)
Martina Lanini (mail to)
Further Info: Click here for A.R.T.S. Webpage
Streaming Link (MS Teams): This seminar will be held in person
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