Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning
We introduce a comprehensive theoretical and algorithmic framework that bridges formal group theory and group entropies with modern machine learning, paving the way for an infinite, flexible family of Mirror Descent (MD) optimization algorithms. Our approach exploits the rich structure of group entropies, which are generalized entropic functionals governed by group composition laws, encompassing and significantly extending all trace-form entropies such as the Shannon, Tsallis, and Kaniadakis families. By leveraging group-theoretical mirror maps (or link functions) in MD, expressed via multi-parametric generalized logarithms and their inverses (group exponentials), we achieve highly flexib...
| Authors | Andrzej Cichocki, Piergiulio Tempesta |
|---|---|
| Primary category | cs.LG |
| Published | 9 March 2026 |
| Last updated at source | 29 May 2026 |
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