The latent space of a Generative Adversarial Network (GAN) has been shown to encode rich semantics within some subspaces. To identify these subspaces, researchers typically analyze the statistical information from a collection of synthesized data, and the identified subspaces tend to control image attributes globally (i.e., manipulating an attribute causes the change of an entire image). By contrast, this work introduces low-rank subspaces that enable more precise control of GAN generation. Concretely, given an arbitrary image and a region of interest (e.g., eyes of face images), we manage to relate the latent space to the image region with the Jacobian matrix and then use low-rank factorization to discover steerable latent subspaces. There are three distinguishable strengths of our approach that can be aptly called LowRankGAN. First, compared to analytic algorithms in prior work, our low-rank factorization of Jacobians is able to find the low-dimensional representation of attribute manifold, making image editing more precise and controllable. Second, low-rank factorization naturally yields a null space of attributes such that moving the latent code within it only affects the outer region of interest. Therefore, local image editing can be simply achieved by projecting an attribute vector into the null space without relying on a spatial mask as existing methods do. Third, our method can robustly work with a local region from one image for analysis yet well generalize to other images, making it much easy to use in practice. Extensive experiments on state-of-the-art GAN models (including StyleGAN2 and BigGAN) trained on various datasets demonstrate the effectiveness of our LowRankGAN.

使用低秩矩阵分解的方法可以更好地控制GAN生成的图像特征，同时局部的图像编辑控制可以通过该方法实现。

GAN中的低秩子空间