In the middle of the last century, Léon Brillouin in "The Science and The Theory of
Information" or André Blanc-Lapierre in "Statistical Mechanics" forged the first links
between the Theory of Information and Statistical Physics as precursors.
In the context of Artificial Intelligence, machine learning algorithms use more and
more methodological tools coming from the Physics or the Statistical Mechanics. The
laws and principles that underpin this Physics can shed new light on the conceptual
basis of Artificial Intelligence. Thus, the principles of Maximum Entropy, Minimum of
Free Energy, Gibbs-Duhem's Thermodynamic Potentials and the generalization of
François Massieu's notions of characteristic functions enrich the variational
formalism of machine learning. Conversely, the pitfalls encountered by Artificial
Intelligence to extend its application domains, question the foundations of Statistical
Physics, such as the construction of stochastic gradient in large dimension, the
generalization of the notions of Gibbs densities in spaces of more elaborate
representation like data on homogeneous differential or symplectic manifolds, Lie
groups, graphs, tensors, ....
Sophisticated statistical models were introduced very early to deal with
unsupervised learning tasks related to Ising-Potts models (the Ising-Potts model
defines the interaction of spins arranged on a graph) of Statistical Physics. and
more generally the Markov fields. The Ising models are associated with the theory
of Mean Fields (study of systems with complex interactions through simplified
models in which the action of the complete network on an actor is summarized by a
single mean interaction in the sense of the mean field).
The porosity between the two disciplines has been established since the birth of
Artificial Intelligence with the use of Boltzmann machines and the problem of robust
methods for calculating partition function. More recently, gradient algorithms for
neural network learning use large-scale robust extensions of the natural gradient of
Fisher-based Information Geometry (to ensure reparameterization invariance), and
stochastic gradient based on the Langevin equation (to ensure regularization), or
their coupling called "Natural Langevin Dynamics".
Concomitantly, during the last fifty years, Statistical Physics has been the object
of new geometrical formalizations (contact or symplectic geometry, ...) to try to
give a new covariant formalization to the thermodynamics of dynamic systems. We
can mention the extension of the symplectic models of Geometric Mechanics to
Statistical Mechanics, or other developments such as Random Mechanics, Geometric
Mechanics in its Stochastic version, Lie Groups Thermodynamic, and geometric
modeling of phase transition phenomena.
Finally, we refer to Computational Statistical Physics, which uses efficient
numerical methods for large-scale sampling and multimodal probability
measurements (sampling of Boltzmann-Gibbs measurements and calculations of
free energy, metastable dynamics and rare events, ...) and the study of geometric
integrators (Hamiltonian dynamics, symplectic integrators, ...) with good properties
of covariances and stability (use of symmetries, preservation of invariants, ...).
Machine learning inference processes are just beginning to adapt these new
integration schemes and their remarkable stability properties to increasingly
abstract data representation spaces.
Artificial Intelligence currently uses only a very limited portion of the conceptual
and methodological tools of Statistical Physics. The purpose of this conference is to
encourage constructive dialogue around a common foundation, to allow the
establishment of new principles and laws governing the two disciplines in a unified
approach. But, it is also about exploring new « chemins de traverse ».
Frédéric Barbaresco, THALES, KTD PCC, Palaiseau, France
Silvère Bonnabel, Mines ParisTech, CAOR, Paris, France
Gery de Saxcé, Université de Lille, LAM3, Lille, France
François Gay-Balmaz, Ecole Normale Supérieure Ulm, CNRS & LMD, Paris, France
Bernhard Maschke, Université Claude Bernard, LAGEPP, Lyon, France
Eric Moulines, Ecole Polytechnique, CMAP, Palaiseau, France
Registration fees for Summer Week is 450 euros, including catering (bedroom and 3 meals a dayon 5 days) and all accommodation on site: https://www.houches-school-physics.com/practical-information/facilities/ https://www.houches-school-physics.com/practical-information/your-stay/
Registration will be paid at Les Houches reception desk at your arrival by credit card (or VAD payment of your lab).
Any registration canceled less than two weeks before the arrival date will be due.
Please fill this form 2020_SPIG'20 Attendees list.xlsx
The arrival is Sunday July 26th starting from 3:00 pm. On the day of arrival, only the evening meal is planned.
On Sunday, the secretariat is open from 6:00 pm to 7:30 pm.
Summer Week will be closed Friday July 31st at 4 pm.
Access to Les Houches:
Ecole de Physique des Houches, 149 Chemin de la Côte, F-74310 Les Houches, France
Les Houches is a village located in Chamonix valley, in the French Alps.
Established in 1951, the Physics School is situated at 1150 m above sea level in natural surroundings, with breathtaking views on the Mont-Blanc mountain range.
Mornings will be dedicated to 3 hours courses. Afternoons will be dedicated to long keynotes.
Poster session will be organized Wednesday morning.
CONNECTING STOCHASTIC OPTIMIZATION
WITH SCHRÖDINGER EVOLUTION WITH
RESPECT TO NON HERMITIAN HAMILTONIANS - C. Couto, J. Mourão, J.P. Nunes and P. Ribeiro
A Python Package for Geometry in Machine Learning
and Information Geometry - Nina Miolane, Nicolas Guigui1, Alice Le Brigant, Hadi Zaatiti, Christian Shewmake, Hatem Hajri, Johan Mathe, Benjamin Hou, Yann Thanwerdas,
Stefan Heyder, Olivier Peltre, Niklas Koep, Yann Cabanes, Thomas Gerald, Paul Chauchat, Daniel Brooks, Bernhard Kainz, Claire Donnat, Susan
Holmes, Xavier Pennec
Wrapped statistical models on SE(n): motivation
challenges and generalization to symmetric spaces - Emmanuel Chevallier and Nicolas Guigui
Fast High-order Tensor Learning Based on
Grassmann Manifold - O.KARMOUDA, R.BOYER and J.BOULANGER
A Geometric Interpretation of Stochastic Gradient
Descent in Deep Learning and Bolzmann Machines -
Calibrating Bayesian Neural Networks with
Alpha-divergences and Normalizing Flows -
Hector J. Hortua, Luigi Malago and Riccardo Volpi
Lagrangian and Hamiltonian Dynamics on the Simplex ---
Goffredo Chirco, Luigi Malago, Giovanni Pistone
The conference will deal with the following topics:
Geometric Structures of Statistical Physics and Information
Statistical Mechanics and Geometric Mechanics
Thermodynamics, Symplectic and Contact Geometries
Lie groups Thermodynamics
Relativistic and continuous media Thermodynamics
Physical structures of inference and learning
Stochastic gradient of Langevin's dynamics
Information geometry, Fisher metric and natural gradient
Monte-Carlo Hamiltonian methods
Varational inference and Hamiltonian controls
Wednesday afternoon is free. Excursion could be organized to