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This œuvre, Standard Divergence in Manifold of Dual Affine Connections, by Shun-ichi Amari is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

Standard Divergence in Manifold of Dual Affine Connections


Standard Divergence in Manifold of Dual Affine Connections
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A divergence function defines a Riemannian metric G and dually coupled affine connections (∇, ∇  ∗ ) with respect to it in a manifold M. When M is dually flat, a canonical divergence is known, which is uniquely determined from {G, ∇, ∇  ∗ }. We search for a standard divergence for a general non-flat M. It is introduced by the magnitude of the inverse exponential map, where α = -(1/3) connection plays a fundamental role. The standard divergence is different from the canonical divergence.
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Standard Divergence in Manifold of Dual Affine Connections
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