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Accueil du site > Seminars > Séminaires théorie > Theory Club Thursday June 25 2020 at 11am (Zoom). Olivier Peltre: "Cluster Variational Methods, Message-Passing Algorithms and Homology..

Theory Club Thursday June 25 2020 at 11am (Zoom). Olivier Peltre: "Cluster Variational Methods, Message-Passing Algorithms and Homology.

Unless otherwise stated, seminars and defences take place at 11:30 in room 454A of Condorcet building.


Cluster Variational Methods, Message-Passing Algorithms and Homology

Olivier Peltre

I will present the combinatorics behind a localised approximation of free energy first introduced by Bethe (1935) and later generalised by Kikuchi (1951), who suggested to solve a variational problem on the localised functional to numerically estimate the Gibbs state’s marginals.

I will then sketch the proof of a correspondence theorem between critical points of the Bethe-Kikuchi free energy and stationary points of message-passing algorithms. They are a class of parallel computations where a collection of local units communicate until they eventually reach a consensual state. The "belief propagation" or "sum-product” algorithm and its variants now have a wide area of applications, from telecommunications (5G decoding) to computational thermodynamics, computer vision and artificial intelligence.

Understanding this correspondence motivates to consider a local description of statistical systems, where potentials ( scalar fields) and heat fluxes ( vector fields) are related by algebraic analogs of the gradient and divergence operators. The hamiltonian is a global observable defined as a sum of local interaction potentials ( integration): two potentials define the same hamiltonian iff they only differ by a divergence ( Gauss theorem). Message-passing algorithms derive from analogs of diffusion equations, where potentials evolve up to a conservative flux term, until some form of effective constistency is attained.


Contact : Équipe séminaires / Seminar team - Published on / Publié le 12 December 2020


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