Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels

• URL: http://arxiv.org/abs/2601.06135v1
• Date: Mon, 05 Jan 2026 05:42:40 GMT
• Title: Attention in Geometry: Scalable Spatial Modeling via Adaptive Density Fields and FAISS-Accelerated Kernels
• Authors: Zhaowen Fan,
• Abstract summary: 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.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Bridging Diffusion Guidance and Anderson Acceleration via Hopfield Dynamics [8.46069844016289]
  We establish a framework for attention-space extrapolation by modeling attention dynamics as fixed-point iterations within Modern Hopfield Networks.<n>We propose Geometry Aware Attention Guidance (GAG) to stabilize the acceleration process and maximize guidance efficiency.
  arXiv  Detail & Related papers  (2026-03-03T02:44:21Z)
• SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework [2.070436148502153]
  SENDAI is a hierarchical Sparse-measurement framework that reconstructs full spatial states from sparse sensor observations.<n>S SENDAI achieves a maximum SSIM improvement of 185% over traditional baselines and a 36% improvement over recent high-frequency-based methods.
  arXiv  Detail & Related papers  (2026-01-29T12:58:54Z)
• Fluxamba: Topology-Aware Anisotropic State Space Models for Geological Lineament Segmentation in Multi-Source Remote Sensing [6.815807403335458]
  We propose a lightweight architecture that introduces a topology-aware feature rectification framework.<n>F Fluxamba achieves a real-time inference speed of over 24 FPS with only 3.4M parameters and 6.3G FLOPs.
  arXiv  Detail & Related papers  (2026-01-24T03:55:21Z)
• Foggy Crowd Counting: Combining Physical Priors and KAN-Graph [19.690003059392893]
  This paper proposes a crowd-counting method with a physical a priori of atmospheric scattering.<n>It achieves a 12.2%-27.5% reduction in MAE metrics compared to mainstream algorithms in dense fog scenarios.
  arXiv  Detail & Related papers  (2025-09-29T09:59:36Z)
• Geometry-Editable and Appearance-Preserving Object Compositon [67.98806888489385]
  General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties.<n>Recent approaches derive semantic embeddings and integrate them into advanced diffusion models to enable geometry-editable generation.<n>We introduce a Disentangled Geometry-editable and Appearance-preserving Diffusion model that first leverages semantic embeddings to implicitly capture desired geometric transformations.
  arXiv  Detail & Related papers  (2025-05-27T09:05:28Z)
• DA-STGCN: 4D Trajectory Prediction Based on Spatiotemporal Feature Extraction [6.781509470656284]
  We propose DA-STGCN, an innovative graph convolutional network that integrates a dual attention mechanism.<n>Our model reconstructs adjacency matrix through a self-attention approach, enhancing the capture of node correlations.<n>Results demonstrate a notable improvement over current 4D trajectory prediction methods, achieving a 20% and 30% reduction in the Average Displacement Error (Attention) and Final Displacement Error (FDE)
  arXiv  Detail & Related papers  (2025-03-05T03:42:49Z)
• SFANet: Spatial-Frequency Attention Network for Weather Forecasting [54.470205739015434]
  Weather forecasting plays a critical role in various sectors, driving decision-making and risk management. Traditional methods often struggle to capture the complex dynamics of meteorological systems. We propose a novel framework designed to address these challenges and enhance the accuracy of weather prediction.
  arXiv  Detail & Related papers  (2024-05-29T08:00:15Z)
• Data-Driven Target Localization Using Adaptive Radar Processing and Convolutional Neural Networks [18.50309014013637]
  This paper presents a data-driven approach to improve radar target localization post adaptive radar detection. We produce heatmap tensors from the radar returns, in range, azimuth [and Doppler], of the normalized adaptive matched filter (NAMF) test statistic. We then train a regression convolutional neural network (CNN) to estimate target locations from these heatmap tensors.
  arXiv  Detail & Related papers  (2022-09-07T02:23:40Z)
• Fuzzy Attention Neural Network to Tackle Discontinuity in Airway Segmentation [67.19443246236048]
  Airway segmentation is crucial for the examination, diagnosis, and prognosis of lung diseases. Some small-sized airway branches (e.g., bronchus and terminaloles) significantly aggravate the difficulty of automatic segmentation. This paper presents an efficient method for airway segmentation, comprising a novel fuzzy attention neural network and a comprehensive loss function.
  arXiv  Detail & Related papers  (2022-09-05T16:38:13Z)
• Relation Matters: Foreground-aware Graph-based Relational Reasoning for Domain Adaptive Object Detection [81.07378219410182]
  We propose a new and general framework for DomainD, named Foreground-aware Graph-based Reasoning (FGRR) FGRR incorporates graph structures into the detection pipeline to explicitly model the intra- and inter-domain foreground object relations. Empirical results demonstrate that the proposed FGRR exceeds the state-of-the-art on four DomainD benchmarks.
  arXiv  Detail & Related papers  (2022-06-06T05:12:48Z)
• Transforming Feature Space to Interpret Machine Learning Models [91.62936410696409]
  This contribution proposes a novel approach that interprets machine-learning models through the lens of feature space transformations. It can be used to enhance unconditional as well as conditional post-hoc diagnostic tools. A case study on remote-sensing landcover classification with 46 features is used to demonstrate the potential of the proposed approach.
  arXiv  Detail & Related papers  (2021-04-09T10:48:11Z)
• Bi-Dimensional Feature Alignment for Cross-Domain Object Detection [71.85594342357815]
  We propose a novel unsupervised cross-domain detection model. It exploits the annotated data in a source domain to train an object detector for a different target domain. The proposed model mitigates the cross-domain representation divergence for object detection.
  arXiv  Detail & Related papers  (2020-11-14T03:03:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.