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cs.IT2025
A note on the Artstein-Avidan-Milman's generalized Legendre transforms
Frank Nielsen
Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661-674] characterized invertible reverse-ordering transforms on the space of lower semi-continuous extended real-va…
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…