LEPA: Learning Geometric Equivariance in Satellite Remote Sensing Data with a Predictive Architecture

Geospatial foundation models increasingly expose pixel-level embedding products that can be downloaded and reused without access to the underlying encoder. In this setting, downstream tasks with patch- or region-level labels require a post-hoc aggregation step that maps dense pixel embeddings to a single representation. The default choice, mean pooling, discards within-patch variability and can underperform under spatial distribution shift. To study this setting, we introduce EuroSAT-Embed: 81,000 embedding GeoTIFFs derived from three foundation models: AlphaEarth, OlmoEarth, and Tessera. Using these fixed embedding products, we benchmark 11 training-free pooling methods and 2 train-set-fitted baselines under both random and geographically disjoint test splits. Richer pooling schemes reduce the geographic generalization gap by over 50% relative to mean pooling and improve accuracy by up to 6% on spatial splits. We recommend a three-tier strategy: (1) mean as a baseline, (2) stats pooling (min/max/mean/std) as the default at 4x the embedding dimension, and (3) covariance pooling for peak accuracy. Across all three embedding products, simple distributional statistics improve spatial-split performance over mean pooling.

Earth-observation (EO) foundation models provide reusable embeddings, yet downstream task accuracy does not reveal whether these representations encode geographic information, which may be beneficial for location-aware applications but potentially detrimental when representations invariant to geographic location are desired. We therefore evaluate the geographic coordinate robustness of Tessera v1, Tessera v1.1, and AlphaEarth by testing whether coordinates can be predicted from the embedding representations using 284 quality-verified European solar farms from 2024. We assessed geographic information content information through the association between cosine and geodesic distances and through prediction of projected coordinates in EPSG:3035. Embeddings from all three EO foundation models contain recoverable geographic information. All prediction models significantly outperform training-range uniform random sampling baselines, with AlphaEarth exhibiting the strongest distance association and lowest mean geodesic error. Both Tessera variants also yielded higher geographic distance correlations than the Sentinel-2 controls. These findings motivate geographic information content as an additional criterion for auditing EO foundation models.

In this work, we present LIANet (Location Is All You Need Network), a coordinate-based neural representation that models multi-temporal spaceborne Earth observation (EO) data for a given region of interest as a continuous spatiotemporal neural field. Given only spatial and temporal coordinates, LIANet reconstructs the corresponding satellite imagery. Once pretrained, this neural representation can be adapted to various EO downstream tasks, such as semantic segmentation or pixel-wise regression, importantly, without requiring access to the original satellite data. LIANet intends to serve as a user-friendly alternative to Geospatial Foundation Models (GFMs) by eliminating the overhead of data access and preprocessing for end-users and enabling fine-tuning solely based on labels. We demonstrate the pretraining of LIANet across target areas of varying sizes and show that fine-tuning it for downstream tasks achieves competitive performance compared to training from scratch or using established GFMs. The source code and datasets are publicly available at https://github.com/mojganmadadi/LIANet/tree/v1.0.1.