{
  "annotation_id": "1b25dcbe-bb18-41c4-9767-e09cad7220b5",
  "date_created": "2026-02-17T05:53:05.099000Z",
  "date_modified": "2026-02-17T05:53:05.099000Z",
  "file_hash": "34d9af9e979d7743347c29c2567bacf4cc12b997e435a02b438854446e0ebc13",
  "private": false,
  "record": {
    "abstract": "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.",
    "arxiv_id": "2601.06135",
    "authors": [
      "Zhaowen Fan"
    ],
    "categories": [
      "cs.LG",
      "cs.CV",
      "cs.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels",
    "url": "https://arxiv.org/abs/2601.06135",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5894e85e-e805-4f96-85b0-8ff410fa2b25",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}