# Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells

arXiv: https://arxiv.org/abs/2003.00824 · HTML: https://mlsanity.com/paper/2003.00824/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2020.

## Built on by (most cited first, 30 of 90)

- [SatCLIP: Global, General-Purpose Location Embeddings with Satellite Imagery](https://mlsanity.com/paper/2311.17179/) (2023)
- [On the Opportunities and Challenges of Foundation Models for Geospatial Artificial Intelligence](https://mlsanity.com/paper/2304.06798/) (2023)
- [Mission Critical -- Satellite Data is a Distinct Modality in Machine Learning](https://mlsanity.com/paper/2402.01444/) (2024)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks](https://mlsanity.com/paper/2310.06743/) (2023)
- [Spatial Implicit Neural Representations for Global-Scale Species Mapping](https://mlsanity.com/paper/2306.02564/) (2023)
- [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021)
- [Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions](https://mlsanity.com/paper/2306.17624/) (2023)
- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [Geographic Question Answering: Challenges, Uniqueness, Classification, and Future Directions](https://mlsanity.com/paper/2105.09392/) (2021)
- [Towards Urban General Intelligence: A Review and Outlook of Urban Foundation Models](https://mlsanity.com/paper/2402.01749/) (2024)
- [Towards General-Purpose Representation Learning of Polygonal Geometries](https://mlsanity.com/paper/2209.15458/) (2022)
- [City Foundation Models for Learning General Purpose Representations from OpenStreetMap](https://mlsanity.com/paper/2310.00583/) (2023)
- [Positional Encoder Graph Neural Networks for Geographic Data](https://mlsanity.com/paper/2111.10144/) (2021)
- [Vision-Language Modeling Meets Remote Sensing: Models, Datasets and Perspectives](https://mlsanity.com/paper/2505.14361/) (2025)
- [Dynamic MLP for Fine-Grained Image Classification by Leveraging Geographical and Temporal Information](https://mlsanity.com/paper/2203.03253/) (2022)
- [Towards Artificial General Intelligence (AGI) in the Internet of Things (IoT): Opportunities and Challenges](https://mlsanity.com/paper/2309.07438/) (2023)
- [SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss](https://mlsanity.com/paper/2109.15044/) (2021)
- [Poly2Vec: Polymorphic Fourier-Based Encoding of Geospatial Objects for GeoAI Applications](https://mlsanity.com/paper/2408.14806/) (2024)
- [TrajGPT: Controlled Synthetic Trajectory Generation Using a Multitask Transformer-Based Spatiotemporal Model](https://mlsanity.com/paper/2411.04381/) (2024)
- [Mapping oil palm density at country scale: An active learning approach](https://mlsanity.com/paper/2105.11207/) (2021)
- [Road Network Representation Learning: A Dual Graph based Approach](https://mlsanity.com/paper/2304.07298/) (2023)
- [GeoMultiTaskNet: remote sensing unsupervised domain adaptation using geographical coordinates](https://mlsanity.com/paper/2304.07750/) (2023)
- [GAIR: Location-Aware Self-Supervised Contrastive Pre-Training with Geo-Aligned Implicit Representations](https://mlsanity.com/paper/2503.16683/) (2025)
- [Measuring the Intrinsic Dimension of Earth Representations](https://mlsanity.com/paper/2511.02101/) (2025)
- [Transformation vs Tradition: Artificial General Intelligence (AGI) for Arts and Humanities](https://mlsanity.com/paper/2310.19626/) (2023)
- [Bird Distribution Modelling using Remote Sensing and Citizen Science data](https://mlsanity.com/paper/2305.01079/) (2023)
- [DeeprETA: An ETA Post-processing System at Scale](https://mlsanity.com/paper/2206.02127/) (2022)
- [Geo2Vec: Shape- and Distance-Aware Neural Representation of Geospatial Entities](https://mlsanity.com/paper/2508.19305/) (2025)
- [Joint Estimation and Prediction of City-wide Delivery Demand: A Large Language Model Empowered Graph-based Learning Approach](https://mlsanity.com/paper/2408.17258/) (2024)

## Abstract (arXiv)

Unsupervised text encoding models have recently fueled substantial progress in NLP. The key idea is to use neural networks to convert words in texts to vector space representations based on word positions in a sentence and their contexts, which are suitable for end-to-end training of downstream tasks. We see a strikingly similar situation in spatial analysis, which focuses on incorporating both absolute positions and spatial contexts of geographic objects such as POIs into models. A general-purpose representation model for space is valuable for a multitude of tasks. However, no such general model exists to date beyond simply applying discretization or feed-forward nets to coordinates, and little effort has been put into jointly modeling distributions with vastly different characteristics, which commonly emerges from GIS data. Meanwhile, Nobel Prize-winning Neuroscience research shows that grid cells in mammals provide a multi-scale periodic representation that functions as a metric for location encoding and is critical for recognizing places and for path-integration. Therefore, we propose a representation learning model called Space2Vec to encode the absolute positions and spatial relationships of places. We conduct experiments on two real-world geographic data for two different tasks: 1) predicting types of POIs given their positions and context, 2) image classification leveraging their geo-locations. Results show that because of its multi-scale representations, Space2Vec outperforms well-established ML approaches such as RBF kernels, multi-layer feed-forward nets, and tile embedding approaches for location modeling and image classification tasks. Detailed analysis shows that all baselines can at most well handle distribution at one scale but show poor performances in other scales. In contrast, Space2Vec's multi-scale representation can handle distributions at different scales.