A Geometric Algebra-Informed 3D Gaussian Splatting Framework for Wireless Scene Representation

In this paper, we introduce Geometric Algebra-Informed 3D Gaussian Splatting (GAI-GS), a framework for wireless modeling that couples 3D Gaussian splatting with a geometric algebra-based attention mechanism to explicitly model ray-object interactions in complex propagation environments. GAI-GS encodes joint spatial-electromagnetic (EM) relations into token representations, enabling scene-level aggregation within a unified, end-to-end neural architecture. This design grounds wireless ray propagation in electromagnetic principles, allowing token interactions to model key effects such as multipath, attenuation, and reflection/diffraction. Through extensive evaluations on multiple real-world indoor datasets, GAI-GS consistently surpasses current baselines across various wireless tasks.