Research Seminar on AI: Mean-field and kinetic descriptions of residual neural networks with infinite layers

 

Dienstag, 02.11.2021, 16.00 Uhr

Kinetic and mean-field theory are useful mathematical tools for hierarchical scale modeling of a variety of physical and sociological processes. It in particular allows to study emergent behavior as consequence of particle–to–particle dynamics. Modern artificial intelligence methods can be also mathematically reformulated such that a particle interaction structure emerges. For instance, this is the case of a class of residual neural networks in the limit of infinitely many layers: an interacting ’particle’ system of ordinary differential equations can be obtained, where the state of each particle corresponds to the activation state of a neuron at a certain point in time. Giuseppe Visconti and his team aim to study this class of artificial intelligence models within the kinetic and mean-field theory to provide a mathematical framework in order to gain insight on properties and mechanisms, and to reduce the complexity. Results on experimental engineering data are presented.

Giuseppe Visconti is Assistant Professor at the Department of Mathematics of the University of Roma "La Sapienza" since December 2020. Prior to that, from 2017 to 2020, he was Post-Doc Researcher at the Institute of Geometry and Applied Mathematics of the RWTH Aachen University in the research group of Prof. Michael Herty, and he was involved in the DFG Excellence Cluster. He was awarded Ph.D. in Computer Science and Computational Mathematics from the University of Insubria in Como (Italy) in 2016. He is active in the area of mathematical modeling at the kinetic scale and in the area of numerical analysis. In particular, his current research concerns study of kinetic models for vehicular traffic flow, AI and learning methods, as well as the study of high-order numerical schemes for hyperbolic equations.