Title: On Noise Injection in Generative Adversarial Networks. Abstract: Noise injection is an effective way of circumventing overfitting  and enhancing generalization in machine learning, the rationale of which has been validated in deep learning as well.  Recently, noise injection exhibits surprising performance when
  generating high-fidelity images in Generative Adversarial Networks (GANs). Despite its successful applications in GANs, the mechanism of its validity is still unclear. In this paper, we propose a geometric framework to theoretically analyze the role of noise injection in GANs. Based on Riemannian geometry, we successfully model the noise injection framework as fuzzy equivalence on geodesic normal coordinates. Guided by our theories, we find that existing methods are incomplete and a new strategy for noise injection is devised. Experiments on image generation and GAN inversion demonstrate the superiority of our method.