AI RESEARCH
Yau's Affine Normal Descent: Algorithmic Framework and Convergence Analysis
arXiv CS.LG
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ArXi:2603.28448v1 Announce Type: cross We propose Yau's Affine Normal Descent (YAND), a geometric framework for smooth unconstrained optimization in which search directions are defined by the equi-affine normal of level-set hypersurfaces. The resulting directions are invariant under volume-preserving affine transformations and intrinsically adapt to anisotropic curvature. Using the analytic representation of the affine normal from affine differential geometry, we establish its equivalence with the classical slice-centroid construction under convexity.