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 sixth International SEE conference on “Geometric Science of Information” (GSI’23), scheduled at the end of August 2023.

**GSI’23 benefits from scientific sponsors 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 such as Ecole Polytechnique, Ecole des Mines ParisTech, INRIA, CentraleSupélec, Institut Mathématique de Bordeaux, Sony Computer Science Laboratories.

The GSI conference cycle has been initiated by the Brillouin Seminar Team as soon as 2009. The GSI’23 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 in 2019 (https://www.see.asso.fr/gsi2019) at ENAC Toulouse and in 2023 at Paris Sorbonne. 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’21 Proceedings have been edited by SPRINGER in Lecture Notes (https://link.springer.com/book/10.1007/978-3-030-80209-7 )

GSI satellites event have been organized in 2019 and 2020 as, FGSI’19 “Foundation of Geometric Science of Information” in Montpellier and Les Houches Seminar SPIGL’20 “Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning” or MaxEnt’22.

The technical program of GSI’23 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.

As for the GSI’13, GSI’15, GSI’17, GSI’19 and GSI’21, GSI’23 addresses inter-relations between different mathematical domains like shape spaces (geometric statistics on manifolds and Lie groups, deformations in shape space etc.), probability/optimization & algorithms on manifolds (structured matrix manifold, structured data/Information etc.), relational and discrete metric spaces (graph metrics, distance geometry, relational analysis etc.), 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 etc., and applications like geometries of audio-processing, inverse problems and signal/image processing. GSI’21 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 etc.) and Physics (geometric mechanics, thermodynamics, statistical physics, quantum mechanics etc.). The 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.

More in Frank Nielsen’s GSI pages : https://franknielsen.github.io/GSI/

**Frédéric Barbaresco, Frank Nielsen**