# Chairmen Welcome

**Welcome to “Geometric Science of Information” 2019 Conference in Toulouse**

On behalf of both the organizing and the scientific committees, it is our great pleasure to welcome all delegates, representatives and participants from around the world to the fourth International SEE conference on “Geometric Science of Information” (GSI’19), hosted at ENAC in Toulouse, 27^{th} to 29^{th} August 2019.

GSI’19 benefits from scientific sponsor and financial sponsors.

The 3-day conference is also organized in the frame of the relations set up between SEE and scientific institutions or academic laboratories: ENAC, Institut Mathématique de Bordeaux, Ecole Polytechnique, Ecole des Mines ParisTech, INRIA, CentraleSupélec, Institut Mathématique de Bordeaux, Sony Computer Science Laboratories.

We would like to express all our thanks to the local organizers (ENAC, IMT and CIMI Labex) for hosting this event at the interface between Geometry, Probability and Information Geometry.

The GSI conference cycle has been initiated by the Brillouin Seminar Team as soon as 2009. The GSI’19 event has been motivated in the continuity of first initiatives launched in 2013 (https://www.see.asso.fr/gsi2013) at Mines PatisTech, consolidated in 2015 (https://www.see.asso.fr/gsi2015) at Ecole Polytechnique and opened to new communities in 2017 (https://www.see.asso.fr/gsi2017) at Mines ParisTech. We mention that in 2011, we organized an indo-french workshop on “Matrix Information Geometry” that yielded an edited book in 2013, and in 2017, collaborate to CIRM seminar in Luminy TGSI’17 “Topoplogical & Geometrical Structures of Information” (http://forum.cs-dc.org/category/94/tgsi2017). Last GSI’17 Proceedings have been edited by SPRINGER in Lecture Notes (https://www.springer.com/fr/book/9783319684444) and the most important contributions to the conference GSI’2017 have been collected in SPRINGER Book “Geometric Structures of Information” (https://www.springer.com/us/book/9783030025199).

The technical program of GSI’19 covers all the main topics and highlights in the domain of “Geometric Science of Information” including Information Geometry Manifolds of structured data/information and their advanced applications. This proceedings consists solely of original research papers that have been carefully peer-reviewed by two or three experts before, and revised before acceptance.

The GSI19 program includes a renown honorary speaker, one guest honorary speaker and three (3) keynote distinguished speakers, and an History session with a talk on “Fermat, Pascal & the Geometry of Chance” and a “Tribute to Jean-Louis Koszul (who passed away in January 2018)”.

**Historical background**

As for the GSI’13, GSI’15, and GSI’17, GSI’19 addresses inter-relations between different mathematical domains like shape spaces (geometric statistics on manifolds and Lie groups, deformations in shape space, ...), probability/optimization & algorithms on manifolds (structured matrix manifold, structured data/Information, ...), relational and discrete metric spaces (graph metrics, distance geometry, relational analysis,...), computational and Hessian information geometry, geometric structures in thermodynamics and statistical physics, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, ... and applications like geometries of audio-processing, inverse problems and signal/image processing. GSI’19 topics were enriched with contributions from Lie Group Machine Learning, Harmonic Analysis on Lie Groups, Geometric Deep Learning, Geometry of Hamiltonian Monte Carlo, Geometric & (Poly)Symplectic Integrators, Contact Geometry & Hamiltonian Control, Geometric and structure preserving discretizations, Probability Density Estimation & Sampling in High Dimension, Geometry of Graphs and Networks and Geometry in Neuroscience & Cognitive Sciences.

At the turn of the century, new and fruitful interactions were discovered between several branches of science: Information Science (information theory, digital communications, statistical signal processing,), Mathematics (group theory, geometry and topology, probability, statistics, sheaves theory,...) and Physics (geometric mechanics, thermodynamics, statistical physics, quantum mechanics, ...). GSI conference cycle is a tentative to discover joint mathematical structures to all these disciplines by elaboration of a “General Theory of Information” embracing physics science, information science, and cognitive science in a global scheme.

**Frank Nielsen**, co-chair

Ecole Polytechnique, Palaiseau, France

Sony Computer Science Laboratories, Tokyo, Japan

**Frédéric Barbaresco**, co-chair

President of SEE ISIC Club (Ingénierie des Systèmes d'Information et de Communications)

Representative of KTD PCC (Key Technology Domain / Processing, Computing & Cognition ) Board, THALES LAND & AIR SYSTEMS, France