Joint Structures and Common Foundations of
Statistical Physics, Information Geometry and Inference for Learning (SPIGL'20)

Thank you for your participation: The event was held both onsite and online.

We are looking forward to welcoming you at Geometric Science of Information (GSI) 2021 in Paris! Details to come soon...

Date: 26th July to 31st July 2020
(The workshop started on the morning of 27th July and closed on 31st July 4pm)

Location: Ecole de Physique des Houches
Ecole de Physique des Houches
149 Chemin de la Côte, F-74310 Les Houches, France
(+33/0) 4 57 04 10 40

All recorded keynote talks can be watched from the playlist below:
Playlist of all videos presented at SPIGL'20
Les Houches youtube channel:

Suggestion: Play the music while browsing!
Music (c) Sonata for Violin and Keyboard No. 5 in F Minor by Renaud Capuçon and David Fray

Workshop event poster (pdf)

Workshop overview, programme with abstracts

Documentation/information (pdf)

Practical information (pdf)

View in a new tab the video presentation: Video of Les Houches
Opening session (pdf)
[Registration] [registration fee] [Arrival/Departure] [Programme] [Excursion]

Scientific rationale:

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 ».



Registration fees for Summer Week is 450 euros, including catering (bedroom and 3 meals a dayon 5 days) and all accommodation on site: 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

Registration payment:

Information for the payment of the registration fee (pdf)

Registration fees for Summer Week is 450 euros, including catering (bedroom and 3 meals a day) and all accommodation on site:
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.
The school has 5 double rooms only for accompanying persons. Accompanying persons should pay same registration fees.


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.

Scientific Programme:

Lectures (90 min)

  1. Langevin Dynamics: Old and News (x 2) – Eric Moulines
  2. Computational Information Geometry
    1. [slides] On statistical distances and information geometry for ML – Frank Nielsen [video]
    2. Information Manifold modeled with Orlicz Spaces – Giovanni Pistone [video]
  3. Non-Equilibrium Thermodynamic Geometry
    1. A variational perspective of closed and open systems - François Gay-Balmaz
    2. [slides] Geometry of non-equilibrium thermodynamics: a homogeneous symplectic approach - Arjan van der Schaft, Bernhard Maschke
  4. Geometric Mechanics:
  5. « Structure des Systèmes Dynamiques » (SSD) Jean-Marie Souriau’s book 50th Birthday [Wikipedia page]

17 Keynotes (60 min)

  1. [slides] Learning with Few Labeled Data - Pratik Chaudhari
  2. [slides] Sampling and statistical physics via symmetry - Steve Huntsman
  3. [slides] Geometry of Measure-Preserving Flows and Hamiltonian Monte Carlo - Alessandro Barp (with Girolami, Betancourt, Kennedy, Lelievre...)
  4. [slides] Exponential Family by Representation Theory - Koichi Tojo
  5. [slides] Learning Physics from Data - Francisco Chinesta
  6. [slides] Information Geometry and Integrable Systems - Jean-Pierre Françoise
  7. [slides] Information Geometry and Quantum Fields - Kevin Grosvenor
  8. [slides] Thermodynamic efficiency implies predictive inference- Susanne Still
  9. [slides] Diffeological Fisher Metric - Hông Vân Lê
  10. [slides] Deep Learning as Optimal Control - Elena Celledoni
  11. [slides] Schroedinger's problem, Hamilton-Jacobi-Bellman equations and regularized Mass Transportation - Jean-Claude Zambrini
  12. [slides] Mechanics of the probability simplex - Luigi Malagò
  13. [slides] Dirac structures in nonequilibrium thermodynamics - Hiroaki Yoshimura
  14. [slides] Port-thermodynamic systems’ control - Arjan van der Schaft
  15. [slides] Covariant Momentum Map Thermodynamics - Goffredo Chirco
  16. [slides] Contact geometry and thermodynamical systems - Manuel de León
  17. [slides] Computational dynamics of reduced coupled multibodyfluid system in Lie group setting - Zdravko Terze


A poster session will take place July 29th with 18 Posters

PDF of posters:


The conference will deal with the following topics:


Wednesday afternoon is free. Excursion could be organized to
  1. The Mer de Glace (Sea of Ice): It is the largest glacier in France, 7 km long and 200m deep and is one of the biggest attractions in the Chamonix Valley:
  2. L’Aiguille du midi: From its height of 3,777m, the Aiguille du Midi and its laid-out terraces offer a 360° view of all the French, Swiss and Italian Alps. A lift brings you to the summit terrace at 3,842m, where you will have a clear view of Mont Blanc:,80,en.html

contribute to the post-workshop proceedings
Last updated, July 20th 2020 by Frank Nielsen.