Hyperbolic Live-Manifold Learning for Generalizable Face Anti-Spoofing

Generalizable face anti-spoofing (FAS) aims to learn liveness representations that remain discriminative across unseen domains. Most methods optimize live and spoof samples symmetrically in Euclidean space, overlooking their structural asymmetry: live samples tend to share coherent liveness properties, whereas spoof samples vary substantially across attack types and domains. Such symmetric modeling makes it difficult to preserve a stable live structure while accommodating diverse spoof patterns. To address this issue, we propose HypLive-FAS, which organizes live representations into a compact manifold in hyperbolic space and identifies spoof samples through their deviations from this manifold. The expanding capacity of hyperbolic space away from the live region allows heterogeneous spoof patterns to be accommodated without forcing them into a unified cluster. Specifically, Hyperbolic Live-Manifold Learning (HLM) constructs a live-centered manifold primarily from live samples while encouraging spoof samples to remain separated from it, thereby reducing their interference with the intrinsic live structure. While HLM captures this asymmetric class structure, the learned manifold may still drift under domain-specific appearance variations. We therefore introduce Liveness-Preserving Augmentation (LPA), which perturbs domain-dependent appearance while enforcing representation- and prediction-level consistency between original and augmented samples, improving the stability of the learned liveness structure. Extensive experiments on multiple benchmarks demonstrate that HypLive-FAS achieves competitive cross-domain generalization and consistently outperforms existing methods.