Domain adaptation of GANs is a problem of fine-tuning GAN models pretrained on a large dataset (e.g. StyleGAN) to a specific domain with few samples (e.g. painting faces, sketches, etc.). While there are many methods that tackle this problem in different ways, there are still many important questions that remain unanswered. In this paper, we provide a systematic and in-depth analysis of the domain adaptation problem of GANs, focusing on the StyleGAN model. We perform a detailed exploration of the most important parts of StyleGAN that are responsible for adapting the generator to a new domain depending on the similarity between the source and target domains. As a result of this study, we propose new efficient and lightweight parameterizations of StyleGAN for domain adaptation. Particularly, we show that there exist directions in StyleSpace (StyleDomain directions) that are sufficient for adapting to similar domains. For dissimilar domains, we propose Affine+ and AffineLight+ parameterizations that allows us to outperform existing baselines in few-shot adaptation while having significantly less training parameters. Finally, we examine StyleDomain directions and discover their many sur prising properties that we apply for domain mixing and cross-domain image morphing. Source code can be found at https://github.com/AIRI-Institute/StyleDomain.

A fundamental property of deep learning normalization techniques, such as batch normalization, is making the pre-normalization parameters scale invariant. The intrinsic domain of such parameters is the unit sphere, and therefore their gradient optimization dynamics can be represented via spherical optimization with varying effective learning rate (ELR), which was studied previously. However, the varying ELR may obscure certain characteristics of the intrinsic loss landscape structure. In this work, we investigate the properties of training scale-invariant neural networks directly on the sphere using a fixed ELR. We discover three regimes of such training depending on the ELR value: convergence, chaotic equilibrium, and divergence. We study these regimes in detail both on a theoretical examination of a toy example and on a thorough empirical analysis of real scale-invariant deep learning models. Each regime has unique features and reflects specific properties of the intrinsic loss landscape, some of which have strong parallels with previous research on both regular and scale-invariant neural networks training. Finally, we demonstrate how the discovered regimes are reflected in conventional training of normalized networks and how they can be leveraged to achieve better optima.