CircleGAN: Generative Adversarial Learning across Spherical Circles

We present a novel discriminator for GANs that improves realness and diversity of generated samples by learning a structured hypersphere embedding space using spherical circles. The proposed discriminator learns to populate realistic samples around the longest spherical circle, i.e., a great circle, while pushing unrealistic samples toward the poles perpendicular to the great circle. Since longer circles occupy larger area on the hypersphere, they encourage more diversity in representation learning, and vice versa. Discriminating samples based on their corresponding spherical circles can thus naturally induce diversity to generated samples. We also extend the proposed method for conditional settings with class labels by creating a hypersphere for each category and performing class-wise discrimination and update. In experiments, we validate the effectiveness for both unconditional and conditional generation on standard benchmarks, achieving the state of the art. We provide the architectural details for the unconditional and the conditional CircleGANs, where we borrow some expressions from [29] . We denote the ResNet blocks (see Fig. s.1) with 1) R S d , R D d