Beyond Flat Spaces: Hyperbolic Manifolds for Unexploded Ordnance Identification

Unexploded Ordnance (UXO) identification is a safety-critical visual recognition problem characterized by extreme data scarcity and substantial visual similarity across ordnance categories. We analyse UXO embeddings using complementary geometric diagnostics and find evidence of low effective dimensionality and stronger tree-like structure relative to a calibrated null model. Motivated by this evidence, we introduce LorentzTIM, a transductive information-maximization method formulated directly on the Lorentz hyperboloid. LorentzTIM represents samples and class prototypes in hyperbolic space and performs transductive prototype adaptation using geodesic distances and Riemannian optimization. On the CTX-UXO benchmark, LorentzTIM consistently improves F1 over the evaluated Euclidean and hyperbolic baselines, with consistent gains across all shots regime. The improvements persist across different feature extractors and extend to CUB-200-2011, FGVC-Aircraft, and tieredImageNet, supporting the broader applicability of the proposed approach beyond UXO identification.