Lorentz Evidential Deep learning for Out-of-distribution Detection

Evidential Deep Learning (EDL) provides an efficient paradigm for open‑set recognition by quantifying uncertainty in a single forward pass. However, existing Euclidean‑based EDL methods struggle to directly adapt to hyperbolic representation learning, lacking standardized and interpretable rules for evidence construction and valid correlations between Dirichlet parameters and manifold geometric confidence, which leads to inherent limitations in hyperbolic evidence modeling. To address these issues, we present the Lorentz Evidential Deep Learning (LEDL) framework to refine evidence modeling in hyperbolic space. Specifically, we first formulate the Lorentz‑decoupling constraint to screen valid Lorentz embedding components from the perspective of semantic reliability and provide geometric rationale for reliable hyperbolic evidence construction. Second, we build a dedicated hyperbolic evidence inference pipeline based on the proposed constraint to achieve stable and standardized Dirichlet parameter generation. Finally, we develop Lorentz Prototype‑Guided Evidence Alignment to establish explicit mappings between evidence and manifold geometric confidence, enabling close alignment between evidential modeling and hyperbolic geometric properties. Extensive experiments demonstrate that the proposed LEDL achieves competitive open‑set detection performance and robustness compared to existing baseline methods.