# Measuring the Intrinsic Dimension of Earth Representations arXiv: https://arxiv.org/abs/2511.02101 ยท HTML: https://mlsanity.com/paper/2511.02101/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Builds on 47 of its 60 references that are in the map. - First posted on arXiv 3 Nov 2025. ## Builds on (most cited first, 30 of 47) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020) - [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) - [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025) - [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018) - [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018) - [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018) - [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017) - [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021) - [Scale-MAE: A Scale-Aware Masked Autoencoder for Multiscale Geospatial Representation Learning](https://mlsanity.com/paper/2212.14532/) (2022) - [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018) - [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019) - [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018) - [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020) - [GeoCLIP: Clip-Inspired Alignment between Locations and Images for Effective Worldwide Geo-localization](https://mlsanity.com/paper/2309.16020/) (2023) - [CROMA: Remote Sensing Representations with Contrastive Radar-Optical Masked Autoencoders](https://mlsanity.com/paper/2311.00566/) (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) - [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023) - [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019) - [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020) - [A Generalizable and Accessible Approach to Machine Learning with Global Satellite Imagery](https://mlsanity.com/paper/2010.08168/) (2020) - [MMEarth: Exploring Multi-Modal Pretext Tasks For Geospatial Representation Learning](https://mlsanity.com/paper/2405.02771/) (2024) - [TorchGeo: Deep Learning With Geospatial Data](https://mlsanity.com/paper/2111.08872/) (2021) - [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) - [On the Intrinsic Dimensionality of Image Representations](https://mlsanity.com/paper/1803.09672/) (2018) - [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021) ## Built on by (most cited first, 10 of 10) - [Earth Embeddings as Products: Taxonomy, Ecosystem, and Standardized Access](https://mlsanity.com/paper/2601.13134/) (2026) - [Characterizing AlphaEarth Embedding Geometry for Agentic Environmental Reasoning](https://mlsanity.com/paper/2604.18715/) (2026) - [Localized, High-resolution Geographic Representations with Slepian Functions](https://mlsanity.com/paper/2602.00392/) (2026) - [Automatic Layer Selection for Hallucination Detection](https://mlsanity.com/paper/2605.26366/) (2026) - [What's in an Earth Embedding? An Explainability Analysis of Location Encoders](https://mlsanity.com/paper/2606.24997/) (2026) - [Multi-Modal Contrastive Learning for Implicit Earth Embeddings via Location Tying](https://mlsanity.com/paper/2606.20167/) (2026) - [Do Location Encoders Capture Spatial Effects? A GeoShapley Benchmark Across Scales](https://mlsanity.com/paper/2606.23453/) (2026) - [Curated retrieval versus open web search in public AI information services: a coverage-trust trade-off](https://mlsanity.com/paper/2607.05217/) (2026) - [TerraNova: A Foundation Model for the Anthropocene](https://mlsanity.com/paper/2607.29527/) (2026) - [Earth Embeddings](https://mlsanity.com/paper/2608.03410/) (2026) ## Abstract (arXiv) Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on geo-referenced satellite, image or text data. Despite the common aim of geographic INRs to distill Earth's data into compact, learning-friendly representations, we lack an understanding of how much information is contained in these Earth representations, and where that information is concentrated. The intrinsic dimension of a dataset measures the number of degrees of freedom required to capture its local variability, regardless of the ambient high-dimensional space in which it is embedded. This work provides the first study of the intrinsic dimensionality of geographic INRs. Analyzing INRs with ambient dimension between 256 and 512, we find that their intrinsic dimensions fall roughly between 2 and 10 and are sensitive to changing spatial resolution and input modalities during INR pre-training. Furthermore, we show that the intrinsic dimension of a geographic INR correlates with downstream task performance and can capture spatial artifacts, facilitating model evaluation and diagnostics. More broadly, our work offers an architecture-agnostic, label-free metric of information content that can enable unsupervised evaluation, model selection, and pre-training design across INRs.