Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc

Levent Ali Mengütürk

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arXiv · 2602.17159

Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc

Levent Ali Mengütürk

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Abstract

The paper presents a statistical geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group. Motivated by the geometric connection, we propose the usage of the L2-embedded hyperbolic isometric invariant as an alternative way to quantify statistical divergence between Gaussian measures as a contribution to information theory and machine learning.

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Levent Ali Mengütürk. 2026-02-19. Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc. https://arxiv.org/abs/2602.17159

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