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cs.LG2026
Neural Legendre-Fenchel transform with Hessian Preconditioning
Basile Plus-Gourdon, Frank Nielsen
The Legendre-Fenchel (LF) transform is a fundamental tool in convex analysis and machine learning that maps lower semi-continuous functions to their convex conjugates. In practice,…
cs.LG2026
Generalising maximum mean discrepancy: kernelised functional Bregman divergences
Russell Tsuchida, Frank Nielsen
Bregman divergences play a pivotal role in statistics, machine learning and computational information geometry. Particularly in the context of machine learning, they are central to…
cs.LG2025
Mirror Descent and Novel Exponentiated Gradient Algorithms Using Trace-Form Entropies and Deformed Logarithms
Andrzej Cichocki, Toshihisa Tanaka, Frank Nielsen +1
This paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms…