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.

翻译：本文提出基于几何代数的三维高斯泼溅框架（GAI-GS），该框架将三维高斯泼溅与基于几何代数的注意力机制相结合，显式建模复杂传播环境中的射线-物体相互作用。GAI-GS将联合空间-电磁关系编码为令牌表示，在统一的端到端神经架构中实现场景级聚合。该设计将无线射线传播建立在电磁原理基础上，使令牌交互能够模拟多径、衰减、反射/绕射等关键效应。通过在多个真实室内数据集上的广泛评估，GAI-GS在各种无线任务中持续超越现有基准方法。