In StyleGAN, convolution kernels are shaped by both static parameters shared across images and dynamic modulation factors $w^+\in\mathcal{W}^+$ specific to each image. Therefore, $\mathcal{W}^+$ space is often used for image inversion and editing. However, pre-trained model struggles with synthesizing out-of-domain images due to the limited capabilities of $\mathcal{W}^+$ and its resultant kernels, necessitating full fine-tuning or adaptation through a complex hypernetwork. This paper proposes an efficient refining strategy for dynamic kernels. The key idea is to modify kernels by low-rank residuals, learned from input image or domain guidance. These residuals are generated by matrix multiplication between two sets of tokens with the same number, which controls the complexity. We validate the refining scheme in image inversion and domain adaptation. In the former task, we design grouped transformer blocks to learn these token sets by one- or two-stage training. In the latter task, token sets are directly optimized to support synthesis in the target domain while preserving original content. Extensive experiments show that our method achieves low distortions for image inversion and high quality for out-of-domain editing.