Face recognition technology has become an integral part of modern security systems and user authentication processes. However, these systems are vulnerable to spoofing attacks, where malicious actors attempt to circumvent the security measures by presenting fake or manipulated facial data. Most prior research in face anti-spoofing (FAS) approaches this challenge as a two-class classification task, where models are trained on real samples and known spoof attacks, and then tested for their ability to detect unknown spoof attacks. However, in practical scenarios, FAS should be treated as a one-class classification task, where the system cannot assume any prior knowledge regarding the nature of potential spoof samples during the training phase.

To address this challenge, the authors propose a novel hyperbolic one-class classification framework for face anti-spoofing. The key idea is to train the network using a pseudo-negative class sampled from a Gaussian distribution with a weighted running mean. This approach eliminates the need for explicit knowledge of spoof samples during training, making the system more robust and adaptable to real-world scenarios.

The authors introduce two novel loss functions specifically designed for this task: (1) Hyp-PC: Hyperbolic Pairwise Confusion loss, and (2) Hyp-CE: Hyperbolic Cross Entropy loss, which operate in the hyperbolic space. Additionally, they employ Euclidean feature clipping and gradient clipping techniques to stabilize the training process in the hyperbolic space.

Through extensive experiments on five benchmark datasets: Rose-Youtu, MSU-MFSD, CASIA-MFSD, Idiap Replay-Attack, and OULU-NPU, the authors demonstrate that their method significantly outperforms state-of-the-art approaches, achieving superior spoof detection performance. This work represents a significant advancement in the field of face anti-spoofing, as it is the first to extend hyperbolic embeddings for this task in a one-class manner.