The gradient-flow equations of information geometry are rewritten as Weyl-symmetric geodesic equations, relating the alpha = plus or minus 1 connections to the Levi-Civita connection of a conformally rescaled Fisher metric.
Wada, Weyl geometric approach to the gradient-flow equations in information geometry
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Weyl symmetry of the gradient-flow in information geometry
The gradient-flow equations of information geometry are rewritten as Weyl-symmetric geodesic equations, relating the alpha = plus or minus 1 connections to the Levi-Civita connection of a conformally rescaled Fisher metric.