Information Geometry a la carte: build your own dual geometry in three steps
FrnkNlsn · x · 2026-10-22
A concise visual explainer on building your own Information Geometry: IG is about dual geometry, and you can construct one by choosing (1) a manifold M (Gaussians, SPD cone, probability simplex...), (2) a metric g (Fisher information metric, divergence-induced metrics...), and (3) a torsion-free affine connection ∇ (exponential, mixture, α-connections...).
The dual connection follows as ∇ = 2∇^g − ∇ using the Levi-Civita connection. Full tutorial linked in the author's pinned tweet.
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