Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910008253349888 |
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| author | Fan, Zhaowen |
| author_facet | Fan, Zhaowen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels Fan, Zhaowen Machine Learning Computer Vision and Pattern Recognition Graphics 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. |
| title | Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels |
| topic | Machine Learning Computer Vision and Pattern Recognition Graphics |
| url | https://arxiv.org/abs/2601.06135 |