Review for NeurIPS paper: CircleGAN: Generative Adversarial Learning across Spherical Circles

Correctness: I like the ideas and concepts of'diversity' and'realness' on the sphere (which is projected by simple L2-normalization), but it is non-trivial to say that proposed objective function actually minimizes some'distance' between real and fake probability distribution. SphereGAN implements IPMs as their objective function and shows the equivalence relation between minimizing Wasserstein distance in hyper-sphere and minimizing objective functions, but this kind of analysis is not dealt in proposed method even if SphereGAN is main baseline method. Thus authors needs to clarify what to minimize. The proposed method uses L2-normalization as a projection onto hyper-sphere which induces information loss as it is not one-to-one (All the conventional features lying in same lay started at origin is projected to same point in hyper-sphere). The stereo-graphic projection not only admits single fixed point where north pole ('center' in the paper) can be rotated transitively on the hyper-sphere.