# Localized, High-resolution Geographic Representations with Slepian Functions

arXiv: https://arxiv.org/abs/2602.00392 · HTML: https://mlsanity.com/paper/2602.00392/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 62 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 33)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [GeoCLIP: Clip-Inspired Alignment between Locations and Images for Effective Worldwide Geo-localization](https://mlsanity.com/paper/2309.16020/) (2023)
- [SatCLIP: Global, General-Purpose Location Embeddings with Satellite Imagery](https://mlsanity.com/paper/2311.17179/) (2023)
- [AlphaEarth Foundations: An embedding field model for accurate and efficient global mapping from sparse label data](https://mlsanity.com/paper/2507.22291/) (2025)
- [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)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [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)
- [ACE: A fast, skillful learned global atmospheric model for climate prediction](https://mlsanity.com/paper/2310.02074/) (2023)
- [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021)
- [Continental-Scale Building Detection from High Resolution Satellite Imagery](https://mlsanity.com/paper/2107.12283/) (2021)
- [Galileo: Learning Global & Local Features of Many Remote Sensing Modalities](https://mlsanity.com/paper/2502.09356/) (2025)
- [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)
- [Artificial intelligence to advance Earth observation: : A review of models, recent trends, and pathways forward](https://mlsanity.com/paper/2305.08413/) (2023)
- [Species Distribution Modeling for Machine Learning Practitioners: A Review](https://mlsanity.com/paper/2107.10400/) (2021)
- [RANGE: Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings](https://mlsanity.com/paper/2502.19781/) (2025)
- [Measuring the Intrinsic Dimension of Earth Representations](https://mlsanity.com/paper/2511.02101/) (2025)
- [Contrasting local and global modeling with machine learning and satellite data: A case study estimating tree canopy height in African savannas](https://mlsanity.com/paper/2411.14354/) (2024)
- [Deep Random Features for Scalable Interpolation of Spatiotemporal Data](https://mlsanity.com/paper/2412.11350/) (2024)
- [LocDiff: Identifying Locations on Earth by Diffusing in the Hilbert Space](https://mlsanity.com/paper/2503.18142/) (2025)
- [No Location Left Behind: Measuring and Improving the Fairness of Implicit Representations for Earth Data](https://mlsanity.com/paper/2502.06831/) (2025)

## Built on by (most cited first, 3 of 3)

- [Tessellating The Earth](https://mlsanity.com/paper/2606.27514/) (2026)
- [Chronosphere: Space-Time Tessellation of Local Climate Experts](https://mlsanity.com/paper/2609.21872/) (2026)
- [Planetary Feature Fields are Scalable Earth Representations](https://mlsanity.com/paper/2609.37784/) (2026)

## Abstract (arXiv)

Geographic data is fundamentally local. Disease outbreaks cluster in population centers, ecological patterns emerge along coastlines, and economic activity concentrates within country borders. Machine learning models that encode geographic location, however, distribute representational capacity uniformly across the globe, struggling at the fine-grained resolutions that localized applications require. We propose a geographic location encoder built from spherical Slepian functions that concentrate representational capacity inside a region-of-interest and scale to high resolutions without extensive computational demands. For settings requiring global context, we present a hybrid Slepian-Spherical Harmonic encoder that efficiently bridges the tradeoff between local-global performance, while retaining desirable properties such as pole-safety and spherical-surface-distance preservation. Across five tasks spanning classification, regression, and image-augmented prediction, Slepian encodings outperform baselines and retain performance advantages across a wide range of neural network architectures.