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Settimana 19/02/2024 - 23/02/2024
Seminari
Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
Rome Centre on Mathematics for Modelling and Data ScienceS (RoMaDS) Mini-course seminar
Date: 19-22th February 2024
Schedule:
Mon 14h00-17h00
Wed 09h30-12h30
Thu 09:30-12:30
Where: Conference Room 1201 "R. Dal Passo"
Title: " An introduction to Score-based Generative Models "
Speaker:
Alain Durmus - École Polytechnique, Paris
Giovanni Conforti - École Polytechnique, Paris
Abstract:
In simple words, generative modeling consists in learning a map capable of generating
new data instances that resemble a given set of observations, starting from a simple
prior distribution, most often a standard Gaussian distribution.
This course aims at providing a mathematical introduction to generative models
and in particular to Score-based Generative Models (SGM).
SGMs have gained prominence for their ability to generate realistic data across
diverse domains, making them a popular tool for researchers and practitioners
in machine learning. Participants will learn about the methodological and theoretical
foundations, as well as some practical applications associated with these models.
The first two lectures motivate the use of generative models, introduce their
formalism and present two simple though relevant examples: energy-based models
and Generative Adversarial Networks. In the third and fourth lecture we present
score-based diffusion models and explain how they provide an algorithmical framework
to the basic idea that sampling from the time-reversal of a diffusion process converts
noise into new data instances. We shall do so following two different approaches:
a first elementary one that only relies on discrete transition probabilities,
and a second one based on stochastic calculus. After this introduction, we derive
sharp theoretical guarantees of convergence for score-based diffusion models assembling
together ideas coming from stochastic control, functional inequalities and regularity
theory for Hamilton- Jacobi-Bellman equations. The course ends with an overview of some
of the most recent and sophisticated algorithms such as flow matching and
diffusion Sch¨odinger bridges (DSB), which bring an (entropic) optimal
transport insight into generative modeling. .
Organizing Committee:
Domenico Marinucci - Coordinator - (mail to contact)
Michele Salvi (mail to contact)
Stefano Vigogna (mail to contact)
Further Info: Click here for RoMaDS events Page
Streaming Link (MS Teams): This seminar will be held in mix mode: in person and video streaming: -> MS TEAMS LINK for streaming
Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
Geometry Seminar
Date: 20th February 2024
Schedule: 14:30 - Rome Time
Where: Conference Room 1101 "C. D'Antoni"
Title: " CM-minimizers and standard models of Fano fibrations over curves "
Speaker: Maksym Fedorchuk - Boston College
Abstract:
A recent achievement in K-stability of Fano varieties is an
algebro-geometric construction of a projective moduli space of
K-polystable Fanos. The ample line bundle on this moduli space is the
CM line bundle of Tian. One of the consequences of the general theory
is that given a family of K-stable Fanos over a punctured curve, the
polystable filling is the one that minimizes the degree of the CM line
bundle after every finite base change. A natural question is to
ask what are the CM-minimizers without base change. In
answering this question, we arrive at a theory of Kollár stability
for fibrations over one-dimensional bases, and standard models of Fano
fibrations. After explaining the general theory, I will sketch work in
progress on standard models of quartic threefold hypersurfaces. This
talk is based on joint work with Hamid Abban and Igor Krylov.
This talk is part of the activity of the MIUR Excellence Department Projects MatMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry
Organizing Committee:
Giulio Codogni (mail to contact)
Guido Maria Lido (mail to contact)
Further Info: Click here for Geometry events Page
Streaming Link (MS Teams): This seminar will be held in person
Eventi