# Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks

arXiv: https://arxiv.org/abs/2310.06743 · HTML: https://mlsanity.com/paper/2310.06743/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A simple yet effective baseline for 3d human pose estimation](https://mlsanity.com/paper/1705.03098/) (2017)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [Lightweight, Pre-trained Transformers for Remote Sensing Timeseries](https://mlsanity.com/paper/2304.14065/) (2023)
- [A high-resolution canopy height model of the Earth](https://mlsanity.com/paper/2204.08322/) (2022)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (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)
- [Geo-Aware Networks for Fine-Grained Recognition](https://mlsanity.com/paper/1906.01737/) (2019)
- [Improving Image Classification with Location Context](https://mlsanity.com/paper/1505.03873/) (2015)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [SE-KGE: A Location-Aware Knowledge Graph Embedding Model for Geographic Question Answering and Spatial Semantic Lifting](https://mlsanity.com/paper/2004.14171/) (2020)
- [Positional Encoder Graph Neural Networks for Geographic Data](https://mlsanity.com/paper/2111.10144/) (2021)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [TIML: Task-Informed Meta-Learning for Agriculture](https://mlsanity.com/paper/2202.02124/) (2022)

## Built on by (most cited first, 30 of 61)

- [SatCLIP: Global, General-Purpose Location Embeddings with Satellite Imagery](https://mlsanity.com/paper/2311.17179/) (2023)
- [Mission Critical -- Satellite Data is a Distinct Modality in Machine Learning](https://mlsanity.com/paper/2402.01444/) (2024)
- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025)
- [RANGE: Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings](https://mlsanity.com/paper/2502.19781/) (2025)
- [Vision-Language Modeling Meets Remote Sensing: Models, Datasets and Perspectives](https://mlsanity.com/paper/2505.14361/) (2025)
- [Active Learning-Based Species Range Estimation](https://mlsanity.com/paper/2311.02061/) (2023)
- [Combining Observational Data and Language for Species Range Estimation](https://mlsanity.com/paper/2410.10931/) (2024)
- [A2-MAE: A spatial-temporal-spectral unified remote sensing pre-training method based on anchor-aware masked autoencoder](https://mlsanity.com/paper/2406.08079/) (2024)
- [Fast Training of Sinusoidal Neural Fields via Scaling Initialization](https://mlsanity.com/paper/2410.04779/) (2024)
- [Attention on the Sphere](https://mlsanity.com/paper/2505.11157/) (2025)
- [Measuring the Intrinsic Dimension of Earth Representations](https://mlsanity.com/paper/2511.02101/) (2025)
- [CaFA: Global Weather Forecasting with Factorized Attention on Sphere](https://mlsanity.com/paper/2405.07395/) (2024)
- [Paving the way toward foundation models for irregular and unaligned Satellite Image Time Series](https://mlsanity.com/paper/2407.08448/) (2024)
- [LocDiff: Identifying Locations on Earth by Diffusing in the Hilbert Space](https://mlsanity.com/paper/2503.18142/) (2025)
- [GPS as a Control Signal for Image Generation](https://mlsanity.com/paper/2501.12390/) (2025)
- [Earth Embeddings as Products: Taxonomy, Ecosystem, and Standardized Access](https://mlsanity.com/paper/2601.13134/) (2026)
- [LD-SDM: Language-Driven Hierarchical Species Distribution Modeling](https://mlsanity.com/paper/2312.08334/) (2023)
- [Imbalance-aware Presence-only Loss Function for Species Distribution Modeling](https://mlsanity.com/paper/2403.07472/) (2024)
- [Gridded Transformer Neural Processes for Large Unstructured Spatio-Temporal Data](https://mlsanity.com/paper/2410.06731/) (2024)
- [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)
- [A Genealogy of Foundation Models in Remote Sensing](https://mlsanity.com/paper/2504.17177/) (2025)
- [MoRA: Mobility as the Backbone for Geospatial Representation Learning at Scale](https://mlsanity.com/paper/2506.01297/) (2025)
- [Probing the Information Theoretical Roots of Spatial Dependence Measures](https://mlsanity.com/paper/2405.18459/) (2024)
- [Earth System Data Cubes: Avenues for advancing Earth system research](https://mlsanity.com/paper/2408.02348/) (2024)
- [Feedforward Few-shot Species Range Estimation](https://mlsanity.com/paper/2502.14977/) (2025)
- [MaskSDM with Shapley values to improve flexibility, robustness, and explainability in species distribution modeling](https://mlsanity.com/paper/2503.13057/) (2025)
- [Mobility-Embedded POIs: Learning What A Place Is and How It Is Used from Human Movement](https://mlsanity.com/paper/2601.21149/) (2026)
- [Localized, High-resolution Geographic Representations with Slepian Functions](https://mlsanity.com/paper/2602.00392/) (2026)

## Abstract (arXiv)

Learning representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features. These embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, little attention has been paid to the exact design of the neural network architectures with which these functional embeddings are combined. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate positional embeddings and neural network architectures across various benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. The model code and experiments are available at https://github.com/marccoru/locationencoder.