Learning multiscale invariants from big data for physics - Stéphane Mallat

Conférence de Stéphane Mallat organisée par le département de Physique.

Machine learning requires to find low-dimensional models governing the properties of high dimensional functionals. This could almost be called physics. Algorithms have considerably improved in the last 10 years through the processing of massive amounts of data. In particular, deep neural network have spectacular applications, to image classification, medical, industrial and physical data analysis.

We show that the approximation capabilities of deep convolution networks come from their ability to compute invariant and continuous representations over complex groups, including diffeomorphisms. High dimensional structures are represented by multiscale interference terms, with wavelets on appropriate groups. It yields new representations of stochastic processes, which will be illustrated on Ising models and fluid turbulences, for statistical physics. We also show applications to the regressions of quantum molecular energies from chemical data bases, which are compared to density functional theory approximations.

[Stéphane Mallat, est mathématicien, professeur à l’École Polytechnique jusqu’en 2012, et depuis Professeur d’informatique à l’École normale supérieure. Ses recherches touchent à la théorie des ondelettes, à la géométrie, à la représentation de l’information. Il a également créé une start-up au début des années 2000, "Let It Wave".

Médaille de l’innovation du CNRS 2013.]