The Dual Structure of Information Geometry
FrnkNlsn · x · 2026-07-13
This post outlines the fundamental construction of information geometry in an "a la carte" manner: selecting a manifold \(M\), a metric \(g\), and a torsion-free affine connection \(\nabla\), then deriving the dual connection \(\nabla^ = 2\nabla^g - \nabla\) via the Levi-Civita connection \(\nabla^g\).
The author emphasizes that the core of information geometry lies in its "dual geometry" perspective—building a customized system through various combinations of metrics and connections.
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