Despite recent progress in 3D head avatar generation, balancing identity preservation, i.e., reconstruction, with novel poses and expressions, i.e., animation, remains a challenge. Existing methods struggle to adapt Gaussians to varying geometrical deviations across facial regions, resulting in suboptimal quality. To address this, we propose GeoAvatar, a framework for adaptive geometrical Gaussian Splatting. GeoAvatar leverages Adaptive Pre-allocation Stage (APS), an unsupervised method that segments Gaussians into rigid and flexible sets for adaptive offset regularization. Then, based on mouth anatomy and dynamics, we introduce a novel mouth structure and the part-wise deformation strategy to enhance the animation fidelity of the mouth. Finally, we propose a regularization loss for precise rigging between Gaussians and 3DMM faces. Moreover, we release DynamicFace, a video dataset with highly expressive facial motions. Extensive experiments show the superiority of GeoAvatar compared to state-of-the-art methods in reconstruction and novel animation scenarios.

We address a challenging lifelong few-shot image generation task for the first time. In this situation, a generative model learns a sequence of tasks using only a few samples per task. Consequently, the learned model encounters both catastrophic forgetting and overfitting problems at a time. Existing studies on lifelong GANs have proposed modulation-based methods to prevent catastrophic forgetting. However, they require considerable additional parameters and cannot generate high-fidelity and diverse images from limited data. On the other hand, the existing few-shot GANs suffer from severe catastrophic forgetting when learning multiple tasks. To alleviate these issues, we propose a framework called Lifelong Few-Shot GAN (LFS-GAN) that can generate high-quality and diverse images in lifelong few-shot image generation task. Our proposed framework learns each task using an efficient task-specific modulator - Learnable Factorized Tensor (LeFT). LeFT is rank-constrained and has a rich representation ability due to its unique reconstruction technique. Furthermore, we propose a novel mode seeking loss to improve the diversity of our model in low-data circumstances. Extensive experiments demonstrate that the proposed LFS-GAN can generate high-fidelity and diverse images without any forgetting and mode collapse in various domains, achieving state-of-the-art in lifelong few-shot image generation task. Surprisingly, we find that our LFS-GAN even outperforms the existing few-shot GANs in the few-shot image generation task. The code is available at Github.