Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels
This work addresses spatial modeling for domains like trajectory analysis, but it appears incremental as it bridges existing concepts from kernel methods and attention mechanisms.
The paper tackles spatial modeling by introducing Adaptive Density Fields (ADF), a geometric attention framework that formulates spatial aggregation as a query-conditioned attention operator in continuous space, achieving scalability with FAISS-accelerated kernels and demonstrating it on aircraft trajectory analysis to extract Zones of Influence (ZOI) in the Chengdu region.
This work introduces Adaptive Density Fields (ADF), a geometric attention framework that formulates spatial aggregation as a query-conditioned, metric-induced attention operator in continuous space. By reinterpreting spatial influence as geometry-preserving attention grounded in physical distance, ADF bridges concepts from adaptive kernel methods and attention mechanisms. Scalability is achieved via FAISS-accelerated inverted file indices, treating approximate nearest-neighbor search as an intrinsic component of the attention mechanism. We demonstrate the framework through a case study on aircraft trajectory analysis in the Chengdu region, extracting trajectory-conditioned Zones of Influence (ZOI) to reveal recurrent airspace structures and localized deviations.