# Group-wise Scaling and Orthogonal Decomposition for Domain-Invariant Feature Extraction in Face Anti-Spoofing

arXiv: https://arxiv.org/abs/2507.04006 · HTML: https://mlsanity.com/paper/2507.04006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 5 Jul 2025.

## Builds on (most cited first, 30 of 32)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Joint Face Detection and Alignment using Multi-task Cascaded Convolutional Networks](https://mlsanity.com/paper/1604.02878/) (2016)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [DLOW: Domain Flow for Adaptation and Generalization](https://mlsanity.com/paper/1812.05418/) (2018)
- [Searching Central Difference Convolutional Networks for Face Anti-Spoofing](https://mlsanity.com/paper/2003.04092/) (2020)
- [Learning Deep Models for Face Anti-Spoofing: Binary or Auxiliary Supervision](https://mlsanity.com/paper/1803.11097/) (2018)
- [Single-Side Domain Generalization for Face Anti-Spoofing](https://mlsanity.com/paper/2004.14043/) (2020)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [Cross-domain Face Presentation Attack Detection via Multi-domain Disentangled Representation Learning](https://mlsanity.com/paper/2004.01959/) (2020)
- [Biometric Face Presentation Attack Detection with Multi-Channel Convolutional Neural Network](https://mlsanity.com/paper/1909.08848/) (2019)
- [Domain Generalization via Shuffled Style Assembly for Face Anti-Spoofing](https://mlsanity.com/paper/2203.05340/) (2022)
- [PatchNet: A Simple Face Anti-Spoofing Framework via Fine-Grained Patch Recognition](https://mlsanity.com/paper/2203.14325/) (2022)
- [CASIA-SURF CeFA: A Benchmark for Multi-modal Cross-ethnicity Face Anti-spoofing](https://mlsanity.com/paper/2003.05136/) (2020)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [CASIA-SURF: A Large-scale Multi-modal Benchmark for Face Anti-spoofing](https://mlsanity.com/paper/1908.10654/) (2019)
- [Self-Domain Adaptation for Face Anti-Spoofing](https://mlsanity.com/paper/2102.12129/) (2021)
- [Adaptive Normalized Representation Learning for Generalizable Face Anti-Spoofing](https://mlsanity.com/paper/2108.02667/) (2021)
- [Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment](https://mlsanity.com/paper/2303.13662/) (2023)
- [Dual Reweighting Domain Generalization for Face Presentation Attack Detection](https://mlsanity.com/paper/2106.16128/) (2021)
- [FLIP: Cross-domain Face Anti-spoofing with Language Guidance](https://mlsanity.com/paper/2309.16649/) (2023)
- [Instance-Aware Domain Generalization for Face Anti-Spoofing](https://mlsanity.com/paper/2304.05640/) (2023)
- [Multi-domain Learning for Updating Face Anti-spoofing Models](https://mlsanity.com/paper/2208.11148/) (2022)
- [CFPL-FAS: Class Free Prompt Learning for Generalizable Face Anti-spoofing](https://mlsanity.com/paper/2403.14333/) (2024)
- [Multi-Modal Face Anti-Spoofing Based on Central Difference Networks](https://mlsanity.com/paper/2004.08388/) (2020)
- [Generative Domain Adaptation for Face Anti-Spoofing](https://mlsanity.com/paper/2207.10015/) (2022)
- [Towards Effective Adversarial Textured 3D Meshes on Physical Face Recognition](https://mlsanity.com/paper/2303.15818/) (2023)
- [Feature Alignment and Restoration for Domain Generalization and Adaptation](https://mlsanity.com/paper/2006.12009/) (2020)
- [DomainMix: Learning Generalizable Person Re-Identification Without Human Annotations](https://mlsanity.com/paper/2011.11953/) (2020)

## Built on by (most cited first, 1 of 1)

- [Primitive-Driven Compositional Forensic Visual Prompting for Open-World Face Anti-Spoofing](https://mlsanity.com/paper/2608.17351/) (2026)

## Abstract (arXiv)

Domain Generalizable Face Anti-Spoofing (DGFAS) methods effectively capture domain-invariant features by aligning the directions (weights) of local decision boundaries across domains. However, the bias terms associated with these boundaries remain misaligned, leading to inconsistent classification thresholds and degraded performance on unseen target domains. To address this issue, we propose a novel DGFAS framework that jointly aligns weights and biases through Feature Orthogonal Decomposition (FOD) and Group-wise Scaling Risk Minimization (GS-RM). Specifically, GS-RM facilitates bias alignment by balancing group-wise losses across multiple domains. FOD employs the Gram-Schmidt orthogonalization process to decompose the feature space explicitly into domain-invariant and domain-specific subspaces. By enforcing orthogonality between domain-specific and domain-invariant features during training using domain labels, FOD ensures effective weight alignment across domains without negatively impacting bias alignment. Additionally, we introduce Expected Calibration Error (ECE) as a novel evaluation metric for quantitatively assessing the effectiveness of our method in aligning bias terms across domains. Extensive experiments on benchmark datasets demonstrate that our approach achieves state-of-the-art performance, consistently improving accuracy, reducing bias misalignment, and enhancing generalization stability on unseen target domains.