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We introduce a novel method for low-rank personalization of a generic model for head avatar generation. Prior work proposes generic models that achieve high-quality face animation by leveraging large-scale datasets of multiple identities. However, such generic models usually fail to synthesize unique identity-specific details, since they learn a general domain prior. To adapt to specific subjects, we find that it is still challenging to capture high-frequency facial details via popular solutions like low-rank adaptation (LoRA). This motivates us to propose a specific architecture, a Register Module, that enhances the performance of LoRA, while requiring only a small number of parameters to adapt to an unseen identity. Our module is applied to intermediate features of a pre-trained model, storing and re-purposing information in a learnable 3D feature space. To demonstrate the efficacy of our personalization method, we collect a dataset of talking videos of individuals with distinctive facial details, such as wrinkles and tattoos. Our approach faithfully captures unseen faces, outperforming existing methods quantitatively and qualitatively.