New arXiv paper recasts Legendre-Fenchel transform as quadratic polarity in projective geometry
FrnkNlsn · x · 2026-09-09
A new arXiv paper by Frank Nielsen, Basile Plus-Gourdon and Mahito Sugiyama shows generic polarities from quadratic polarity functionals reduce to (deformed) Legendre polarity, computable via (n+2)×(n+2) homogeneous-coordinate linear algebra (GPU-friendly inner products). They define polar divergences generalizing Fenchel-Young/Bregman divergences and reinterpret total Bregman divergences via dual polar conformal factors.
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