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.

翻译：本研究提出自适应密度场（ADF）——一种将空间聚合建模为连续空间中查询条件化、度量诱导的注意力算子的几何注意力框架。通过将空间影响重新阐释为基于物理距离的几何保持注意力机制，ADF融合了自适应核方法与注意力机制的核心概念。该框架借助FAISS加速的倒排文件索引实现可扩展性，将近似最近邻搜索处理为注意力机制的内在组成部分。我们以成都地区航空轨迹分析为案例，通过提取轨迹条件化的影响区域（ZOI），揭示了重复出现的空域结构与局部航迹偏移模式。