Diffeological Riemannian orbifolds

What the math gives to ML

The paper supplies a principled way to represent geometry on quotient spaces with singularities, where multiple local coordinate descriptions are identified by a Lie groupoid. The transferable asset is the distinction between ambient tangent directions and orbit directions, together with the requirement that metrics and differential quantities descend through the quotient map. This suggests neural modules that canonicalize or regularize representations modulo continuous or discrete symmetries while remaining well behaved near points with changing stabilizers. The most practical first experiment is a quotient-aware encoder with an explicit orbit-tangent consistency loss.