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CATEGORIES:Signal Processing and Communications Lab Seminars
SUMMARY: Lie Group Machine Learning and Natural Gradient f
rom Information Geometry - Dr Frederic Barbaresco\
, THALES Land and Air Systems
DTSTART;TZID=Europe/London:20191204T140000
DTEND;TZID=Europe/London:20191204T150000
UID:TALK135115AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/135115
DESCRIPTION:The classical simple gradient descent used in Deep
Learning has two drawbacks: the use of the same n
on-adaptive learning rate for all parameter compon
ents\, and a non-invariance with respect to parame
ter re-encoding inducing different learning rates.
As the parameter space of multilayer networks for
ms a Riemannian space equipped with Fisher informa
tion metric\, instead of the usual gradient descen
t method\, the natural gradient or Riemannian grad
ient method\, which takes account of the geometric
structure of the Riemannian space\, is more effec
tive for learning. The natural gradient preserves
this invariance to be insensitive to the character
istic scale of each parameter direction. The Fishe
r metric defines a Riemannian metric as the Hessia
n of two dual potential functions (the Entropy and
the Massieu Characteristic Function).\n\nIn Souri
au’s Lie groups thermodynamics\, the invariance by
re-parameterization in information geometry has b
een replaced by invariance with respect to the act
ion of the group. In Souriau model\, under the act
ion of the group\, the entropy and the Fisher metr
ic are invariant. Souriau defined a Gibbs density
that is covariant under the action of the group. T
he study of exponential densities invariant by a g
roup goes back to the work of Muriel Casalis in he
r 1990 thesis. The general problem was solved for
Lie groups by Jean-Marie Souriau in Geometric Mech
anics in 1969\, by defining a "Lie groups Thermody
namics" in Statistical Mechanics. These new tools
are bedrocks for Lie Group Machine Learning. Souri
au introduced a Riemannian metric\, linked to a ge
neralization of the Fisher metric for homogeneous
Symplectic manifolds. This model considers the KKS
2-form (Kostant-Kirillov-Souriau) defined on the
coadjoint orbits of the Lie group in the non-null
cohomology case\, with the introduction of a Sympl
ectic cocycle\, called "Souriau's cocycle"\, chara
cterizing the non-equivariance of the coadjoint ac
tion (action of the Lie group on the moment map).\
n\nWe will introduce the link between Souriau "Lie
Groups Thermodynamics"\, Information Geometry and
Kirillov representation theory to define probabil
ity densities as Souriau covariant Gibbs densities
(density of Maximum of Entropy). We will illustra
te this case for the matrix Lie group SU (1\,1) (c
ase with null cohomology)\, and the one for the ma
trix Lie group SE(3) (case with non-null cohomolog
y)\, through the computation of Souriau’s moment m
ap\, and Kirillov's orbit method.\n\n\n*BIO*: F. B
arbaresco received his State Engineering degree fr
om the French Grand Ecole CENTRALE-SUPELEC\, Paris
\, France\, in 1991. Since then\, he has worked fo
r the THALES Group where he is now SENSING Segment
Leader of Key Technology Domain PCC (Processing\,
Control & Cognition). He has been an Emeritus Mem
ber of SEE since 2011 and he was awarded the Aymé
Poirson Prize (for application of sciences to indu
stry) by the French Academy of Sciences in 2014\,
the SEE Ampere Medal in 2007\, the Thévenin Prize
in 2014 and the NATO SET Lecture Award in 2012. He
is President of SEE Technical Club ISIC “Engineer
ing of Information and Communications Systems” and
a member of the SEE administrative board. He is m
ember of the administrative board of SMAI and GRET
SI. He was an invited lecturer for UNESCO on “Adva
nced School and Workshop on Matrix Geometries and
Applications” in Trieste at the ITCP in June 2013.
He is the General Co-chairman of the new internat
ional conference GSI “Geometric Sciences of Inform
ation”. He was co-editor of MDPI Entropy Books “In
formation\, Entropy and Their Geometric Structures
” and "Joseph Fourier 250th Birthday: Modern Fouri
er Analysis and Fourier Heat Equation in Informati
on Sciences for the XXIst century". He has co-orga
nized the CIRM seminar TGSI’17 “Topological and Ge
ometrical Structures of Information” and “FGSI’19
Cartan-Koszul-Souriau” in 2019. He was keynote spe
aker at SOURIAU’19 event.
LOCATION:LT6\, Baker Building\, CUED
CONTACT:Dr Ramji Venkataramanan
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