[2511.02101] Measuring the Intrinsic Dimension of Earth Representations

Computer Science > Machine Learning arXiv:2511.02101 (cs) [Submitted on 3 Nov 2025 (v1), last revised 1 Mar 2026 (this version, v3)] Title:Measuring the Intrinsic Dimension of Earth Representations Authors:Arjun Rao, Marc Rußwurm, Konstantin Klemmer, Esther Rolf View a PDF of the paper titled Measuring the Intrinsic Dimension of Earth Representations, by Arjun Rao and 3 other authors View PDF Abstract: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 dimensi...