Two IGO flows on spheres are designed with natural gradients from Poincaré and Bergman hyperbolic geometries, realized via Kuramoto oscillator ensembles, with a noted link to quantum decision making.
Huang and S.-Y
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Introduces a statistical model on complex domains via probability measures, derives a covariance-based curvature formula for the Bergman metric, proves a biholomorphism criterion from metric preservation, and establishes consistency plus CLT for the Fréchet mean of Calabi's diastasis.
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Information-Geometric Optimization on Spheres
Two IGO flows on spheres are designed with natural gradients from Poincaré and Bergman hyperbolic geometries, realized via Kuramoto oscillator ensembles, with a noted link to quantum decision making.
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Statistical Bergman geometry
Introduces a statistical model on complex domains via probability measures, derives a covariance-based curvature formula for the Bergman metric, proves a biholomorphism criterion from metric preservation, and establishes consistency plus CLT for the Fréchet mean of Calabi's diastasis.