Expertise: Adaptive system learning on differentiable manifolds
A classical learning paradigm is based on criterion optimization over an Euclidean space by a first-order learning algorithm. A more advanced instance of parameter learning is by constrained optimization with smooth equality constraints. In such a context, the constraints on parameters' values reflect the natural constraints presented by the learning problem. In this case, differential geometry is an appropriate mathematical instrument to formulate and to implement a learning theory. The current research aims at introducing a general framework to develop a theory of learning on differentiable manifolds which leads to a second-order learning paradigm. Such a research effort is based on dynamical system theory on manifolds. The formulation of the second-order learning equations on manifolds requires instruments from differential geometry. Likewise, the numerical implementation of second-order learning systems on a computation platform requires instruments from geometric numerical integration. Such a research activity has led to cooperation with the University of Bari (Italy), the Trondheim Technical University (Norway) and the Tokyo University of Agriculture and Technology (Japan).
Simone Fiori received the Italian Laurea (Dr. Eng.) cum laude in Electronic Engineering in July 1996 from the University of Ancona (Italy) and the Ph.D. degree in Electrical Engineering (circuit theory) in March 2000 from the University of Bologna (Italy). His research interests include learning theory for artificial neural networks, linear and non-linear adaptive discrete-time filter theory, image processing by neural networks, differential geometrical methods for machine learning and signal processing. He is author of more than 150 refereed scientific contributions. Dr. Fiori was the recipient of the 2001 “E.R. Caianiello Award” for the best Ph.D. dissertation in the artificial neural network field and the 2010 “Rector Award” as a proficient researcher. He is currently serving as Associate Editor for Neurocomputing (Elsevier), Computational Intelligence and Neuroscience and Cognitive Computation (Springer). Dr. Fiori was awarded several scholarships to visit the RIKEN research institute (Japan), the Tokyo University of Agriculture and Technology (Japan), the Trondheim Technical University (Norway), the University of Bari (Italy) and the Bioinformatics Institute (Singapore).