BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Frédéric Barbaresco (Thales Land and Air Systems\, France) DTSTART:20230828T153000Z DTEND:20230828T163000Z DTSTAMP:20260423T005712Z UID:Wisla23/7 DESCRIPTION:Title: Symplectic Foliation Structures of Information Geometry for Lie Groups Mac hine Learning\nby Frédéric Barbaresco (Thales Land and Air Systems\, France) as part of Mapping the Interdisciplinary Horizons of AI: Safety\, Functional Programming\, Information Geometry\n\n\nAbstract\nWe present a new symplectic model of Information Geometry based on Jean-Marie Souriau 's Lie Groups Thermodynamics. Souriau model was initially described in cha pter IV “Statistical Mechanics” of his book “Structure of dynamical systems” published in 1969. This model gives a purely geometric charact erization of Entropy\, which appears as an invariant Casimir function in c oadjoint representation\, characterized by Poisson cohomology. Souriau has proved that we can associate a symplectic manifold to coadjoint orbits of a Lie group by the KKS 2-form (Kirillov\, Kostant\, Souriau 2-form) in th e affine case (affine model of coadjoint operator equivariance via Souriau 's cocycle)\, that we have identified with Koszul-Fisher metric from Infor mation Geometry. Souriau established the generalized Gibbs density covaria nt under the action of the Lie group. The dual space of the Lie algebra fo liates into coadjoint orbits that are also the Entropy level sets that cou ld be interpreted in the framework of Thermodynamics by the fact that dyna mics on these symplectic leaves are non-dissipative\, whereas transversal dynamics\, given by Poisson transverse structure\, are dissipative. We wil l finally introduce Gaussian distribution on the space of Symmetric Positi ve Definite (SPD) matrices\, through Souriau's covariant Gibbs density by considering this space as the pure imaginary axis of the homogeneous Siege l upper half space where Sp(2n\,R)/U(n) acts transitively. We will also co nsider Gibbs density for Siegel Disk where SU(n\,n)/S(U(n)xU(n)) acts tran sitively. Gauss density of SPD matrices is then computed through Souriau's moment map and coadjoint orbits. Souriau’s Lie Groups Thermodynamics mo del will be further explored in European COST network CaLISTA and European HORIZON-MSCA project CaLIGOLA.\n LOCATION:https://researchseminars.org/talk/Wisla23/7/ END:VEVENT END:VCALENDAR