Spherical Regression Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres

regression methods on continuous problems are not popular

• classification based approaches being more reliable
  • contained in a probability n-simplex geometry defined by softmax
  • gradients being constrained
• continuous output also contained in closed geometrical manifolds
  • introducing n-spheres
• e.g. nn can be viewed as x -> o -> p
  • where o being latent embedding and p being activated o
  • explicit activation function serves as a constraint
    • and partial L / o is bounded
    • not true in regression case
• n-spheres constraint
  • we need a. activation function s.t.
    • output p lieves on a n-sphere
    • gradient w.r.t. o also depends only on p
  • and seperate sign and magnitute