# Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions

arXiv: https://arxiv.org/abs/2306.17624 · HTML: https://mlsanity.com/paper/2306.17624/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 97 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering](https://mlsanity.com/paper/2112.05504/) (2021)
- [Geography-Aware Self-Supervised Learning](https://mlsanity.com/paper/2011.09980/) (2020)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [PlaNet - Photo Geolocation with Convolutional Neural Networks](https://mlsanity.com/paper/1602.05314/) (2016)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [Image Generators with Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2011.13775/) (2020)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [On the Opportunities and Challenges of Foundation Models for Geospatial Artificial Intelligence](https://mlsanity.com/paper/2304.06798/) (2023)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [Hypernetwork functional image representation](https://mlsanity.com/paper/1902.10404/) (2019)
- [Sat-NeRF: Learning Multi-View Satellite Photogrammetry With Transient Objects and Shadow Modeling Using RPC Cameras](https://mlsanity.com/paper/2203.08896/) (2022)
- [LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection](https://mlsanity.com/paper/2006.10521/) (2020)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)

## Built on by (most cited first, 30 of 39)

- [GeoLLM: Extracting Geospatial Knowledge from Large Language Models](https://mlsanity.com/paper/2310.06213/) (2023)
- [Img2Loc: Revisiting Image Geolocalization using Multi-modality Foundation Models and Image-based Retrieval-Augmented Generation](https://mlsanity.com/paper/2403.19584/) (2024)
- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [RANGE: Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings](https://mlsanity.com/paper/2502.19781/) (2025)
- [Towards Artificial General Intelligence (AGI) in the Internet of Things (IoT): Opportunities and Challenges](https://mlsanity.com/paper/2309.07438/) (2023)
- [A Survey of Large Language Model-Powered Spatial Intelligence Across Scales: Advances in Embodied Agents, Smart Cities, and Earth Science](https://mlsanity.com/paper/2504.09848/) (2025)
- [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)
- [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)
- [LocDiff: Identifying Locations on Earth by Diffusing in the Hilbert Space](https://mlsanity.com/paper/2503.18142/) (2025)
- [Enriching Location Representation with Detailed Semantic Information](https://mlsanity.com/paper/2506.02744/) (2025)
- [CITYREP: A Unified Benchmark for Urban Representations Across Cities, Tasks, and Modalities](https://mlsanity.com/paper/2605.26036/) (2026)
- [Spatioformer: A Geo-encoded Transformer for Large-Scale Plant Species Richness Prediction](https://mlsanity.com/paper/2410.19256/) (2024)
- [S2Vec: Self-Supervised Geospatial Embeddings for the Built Environment](https://mlsanity.com/paper/2504.16942/) (2025)
- [MoRA: Mobility as the Backbone for Geospatial Representation Learning at Scale](https://mlsanity.com/paper/2506.01297/) (2025)
- [Into the Unknown: Applying Inductive Spatial-Semantic Location Embeddings for Predicting Individuals' Mobility Beyond Visited Places](https://mlsanity.com/paper/2506.14070/) (2025)
- [Probing the Information Theoretical Roots of Spatial Dependence Measures](https://mlsanity.com/paper/2405.18459/) (2024)
- [GeoBS: Information-Theoretic Quantification of Geographic Bias in AI Models](https://mlsanity.com/paper/2509.23482/) (2025)
- [Localized, High-resolution Geographic Representations with Slepian Functions](https://mlsanity.com/paper/2602.00392/) (2026)
- [SSIF: Learning Continuous Image Representation for Spatial-Spectral Super-Resolution](https://mlsanity.com/paper/2310.00413/) (2023)
- [MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations](https://mlsanity.com/paper/2405.18395/) (2024)
- [MiTREE: Multi-input Transformer Ecoregion Encoder for Species Distribution Modelling](https://mlsanity.com/paper/2412.18995/) (2024)
- [Beyond AlphaEarth: Toward Human-Centered Geospatial Foundation Models via POI-Guided Contrastive Learning](https://mlsanity.com/paper/2510.09894/) (2025)
- [Tessellating The Earth](https://mlsanity.com/paper/2606.27514/) (2026)
- [Latent Domain Modeling Improves Robustness to Geographic Shifts](https://mlsanity.com/paper/2503.02036/) (2025)
- [Physics-Assisted and Topology-Informed Deep Learning for Weather Prediction](https://mlsanity.com/paper/2505.04918/) (2025)
- [ZooplanktonBench: A Geo-Aware Zooplankton Recognition and Classification Dataset from Marine Observations](https://mlsanity.com/paper/2505.18477/) (2025)
- [ProM3E: Probabilistic Masked MultiModal Embedding Model for Ecology](https://mlsanity.com/paper/2511.02946/) (2025)
- [HierLoc: Hyperbolic Entity Embeddings for Hierarchical Visual Geolocation](https://mlsanity.com/paper/2601.23064/) (2026)

## Abstract (arXiv)

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in ML. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D/3D Euclidean space as a high-dimensional vector, and has been successfully applied to various geospatial prediction and generative tasks. However, all current 2D and 3D location encoders are designed to model point distances in Euclidean space. So when applied to large-scale real-world GPS coordinate datasets, which require distance metric learning on the spherical surface, both types of models can fail due to the map projection distortion problem (2D) and the spherical-to-Euclidean distance approximation error (3D). To solve these problems, we propose a multi-scale location encoder called Sphere2Vec which can preserve spherical distances when encoding point coordinates on a spherical surface. We developed a unified view of distance-reserving encoding on spheres based on the DFS. We also provide theoretical proof that the Sphere2Vec preserves the spherical surface distance between any two points, while existing encoding schemes do not. Experiments on 20 synthetic datasets show that Sphere2Vec can outperform all baseline models on all these datasets with up to 30.8% error rate reduction. We then apply Sphere2Vec to three geo-aware image classification tasks - fine-grained species recognition, Flickr image recognition, and remote sensing image classification. Results on 7 real-world datasets show the superiority of Sphere2Vec over multiple location encoders on all three tasks. Further analysis shows that Sphere2Vec outperforms other location encoder models, especially in the polar regions and data-sparse areas because of its nature for spherical surface distance preservation. Code and data are available at https://gengchenmai.github.io/sphere2vec-website/.