# MIND the Gap: A Geographic Implicit Neural Representation with Adjustable Spatial Scale

arXiv: https://arxiv.org/abs/2609.25454 · HTML: https://mlsanity.com/paper/2609.25454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [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)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularization](https://mlsanity.com/paper/2303.07418/) (2023)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [SatCLIP: Global, General-Purpose Location Embeddings with Satellite Imagery](https://mlsanity.com/paper/2311.17179/) (2023)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [AlphaEarth Foundations: An embedding field model for accurate and efficient global mapping from sparse label data](https://mlsanity.com/paper/2507.22291/) (2025)
- [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)
- [SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning](https://mlsanity.com/paper/2111.04724/) (2021)
- [TaxaBind: A Unified Embedding Space for Ecological Applications](https://mlsanity.com/paper/2411.00683/) (2024)
- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [PHI-S: Distribution Balancing for Label-Free Multi-Teacher Distillation](https://mlsanity.com/paper/2410.01680/) (2024)
- [RANGE: Retrieval Augmented Neural Fields for Multi-Resolution Geo-Embeddings](https://mlsanity.com/paper/2502.19781/) (2025)
- [General Geospatial Inference with a Population Dynamics Foundation Model](https://mlsanity.com/paper/2411.07207/) (2024)
- [SMEC: Rethinking Matryoshka Representation Learning for Retrieval Embedding Compression](https://mlsanity.com/paper/2510.12474/) (2025)
- [Evaluation Challenges for Geospatial ML](https://mlsanity.com/paper/2303.18087/) (2023)
- [GAIR: Location-Aware Self-Supervised Contrastive Pre-Training with Geo-Aligned Implicit Representations](https://mlsanity.com/paper/2503.16683/) (2025)
- [Climplicit: Climatic Implicit Embeddings for Global Ecological Tasks](https://mlsanity.com/paper/2504.05089/) (2025)
- [TESSERA v2: Scaling Pixel-wise Earth Foundation Models](https://mlsanity.com/paper/2607.03949/) (2026)
- [UNIGEOCLIP: Unified Geospatial Contrastive Learning](https://mlsanity.com/paper/2604.11668/) (2026)
- [Tessellating The Earth](https://mlsanity.com/paper/2606.27514/) (2026)
- [SLED: Scalable Location Encoding via Distillation](https://mlsanity.com/paper/2608.06612/) (2026)

## Abstract (arXiv)

Geographic measurements are often sparse, leaving large areas without labels for the quantities we want to map. Geographic implicit neural representations (INRs) provide coordinate-based embeddings that can be combined with sparse labels to predict at unsampled locations without satellite imagery at inference. Yet existing INRs are largely evaluated with random holdouts, leaving their ability to generalize across larger geographic gaps unclear. We introduce Matryoshka Implicit Neural Distillation (MIND), a geographic INR whose spatial granularity can be adjusted after training. MIND distills several pretrained geospatial models using nested supervision at increasing embedding dimensions, dividing the representation into contiguous chunks. Early chunks capture broad spatial patterns, while later chunks add increasingly local variation. Downstream models can retain only the leading chunks or use our Chunked Penalty to reduce reliance on later chunks without retraining the INR. We also introduce CoordBench, comprising 52 datasets and 78 targets with both random and regional holdouts at multiple spatial scales. Across CoordBench, fine-scale features help most when labels are nearby, while smoother representations generalize better across larger geographic gaps. MIND with the Chunked Penalty achieves the highest aggregate regression and classification performance among tested INRs and the highest overall performance under regional holdout. These results show that geographic representations should be evaluated and adapted according to the spatial separation between labeled and prediction locations.