HyperRS: Hyperbolic Embeddings for Hierarchical Remote Sensing Understanding

Remote sensing scenes are inherently hierarchical—the coarse category "transportation land" entails "airport", which further entails "apron" as a fine-grained subcategory. Yet existing remote sensing foundation models produce Euclidean embeddings that treat all semantic levels uniformly, discarding this rich taxonomic structure despite it being formally defined and consistently adopted across the remote sensing community. We propose HyperRS, a remote sensing foundation model that learns multi-level hyperbolic representations by mapping CLIP representations to the Lorentz hyperboloid through a lightweight exponential map, introducing no additional trainable parameters while naturally accommodating tree-like hierarchical structure through the exponentially expanding volume of hyperbolic space—coarse categories reside near the origin, and fine-grained instances are positioned progressively further away. Unlike CLIP-style contrastive pretraining that operates on flat image–text pairs, HyperRS explicitly exploits the known class taxonomy of multi-level remote sensing datasets through two complementary objectives: a hierarchical contrastive loss that mines hard negatives across semantic levels, and a stacked entailment loss that enforces partial-order relationships at every level of the hierarchy simultaneously, ensuring that fine-grained embeddings are geometrically entailed by their parent categories. We further demonstrate that the resulting representation space supports interpretable image traversal from specific instances towards generic concepts, and enables zero-shot generalisation to unseen fine-grained categories via hyperbolic interpolation along the taxonomy tree. Experiments on hierarchical remote sensing classification benchmarks including Million-AID and CB-RSI-256 demonstrate that HyperRS improves the overall three-level classification accuracy on Million-AID by 2.1% over the original CLIP baseline, while also improving cross-level prediction consistency and providing a geometrically structured embedding space that reflects the semantic organisation of real-world remote sensing taxonomies.