ICL Characterization of Geo-Foundation Models

Geo-foundation models (GeoFMs) have emerged as powerful tools for remote sensing, yet there exists no theoretical framework characterizing which downstream tasks admit efficient few-shot adaptation. We address this gap by applying the in-context learning (ICL) complexity framework to classify remote sensing tasks as either ICL-Easy or ICL-Hard. We formalize six core remote sensing function classes—spectral classification, semantic segmentation, object localization, dense change detection, sparse change localization, and spatial interpolation—with explicit sufficient statistic structure. For ICL-Easy tasks (classification, segmentation, dense change detection, spatial interpolation), we prove that additive sufficient statistics enable attention-based aggregation with optimal sample complexity nICL = Θ(CB2/ε), matching empirical risk minimization. For ICL-Hard tasks (object localization, sparse change detection, instance segmentation), we establish that combinatorial sufficient statistics require super-polynomial transformer size or super-constant depth, via reduction to sparse parity and Håstad's circuit lower bounds. Our main result, the Remote Sensing Dichotomy Theorem, proves that every natural remote sensing task falls into exactly one category with no intermediate cases: pixel-wise prediction tasks are ICL-Easy while instance-level localization tasks are ICL-Hard for J = ω(log log n) objects. This dichotomy explains empirical observations that GeoFMs excel at land cover classification but struggle with object detection, and yields testable predictions including threshold behavior at J* ≈ 2–4 objects for typical context sizes. We provide deployment guidelines distinguishing when few-shot ICL suffices versus when fine-tuning or hybrid approaches are required.