3D Gaussian avatars support fast rendering, however, their real-time animation is often challenged by the costly neural inference. We address this bottleneck and show that the animation of pretrained avatar models can be closely approximated by a linear combination of identity-independent blendshapes. Building on this finding, we introduce GALA (Gaussian Animation via Linear Approximation), a distillation method that replaces per-frame heavy neural decoding with a shallow coefficient predictor and a linear blend. To improve fidelity and reduce memory requirements, we propose to construct the basis using block-local PCA under a rendering-aware metric and a memory budget. Our method learns a shallow MLP network to predict blendshape coefficients and applies to various animation architectures without retraining original models. We validate GALA by accelerating the inference of three distinct avatar models for 3D animation of facial expressions and full-bodies with clothing dynamics. Across these models, our distillation generalizes to held-out identities and reduces CPU animation cost by up to three orders of magnitude while preserving most of the rendering quality. Excellent results of our method confirm the shared linear structure of learned avatar representations and enable highly efficient and accurate animation at frame rates reaching up to 60fps on mobile devices. Project page: https://ramazan793.github.io/gala/
