An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.
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A fully hyperbolic attention model using Busemann energy in Poincaré discs produces emotion predictions from text that generalize well even at low embedding dimensions.
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Cauchy's Surface Area Formula in the Funk Geometry
An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.
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Busemann energy-based attention for emotion analysis in Poincar\'e discs
A fully hyperbolic attention model using Busemann energy in Poincaré discs produces emotion predictions from text that generalize well even at low embedding dimensions.