Abstract
Face recognition is an open-set problem requiring high discriminative power to ensure that intra-class distances remain smaller than inter-class distances. Margin-based softmax losses, such as SphereFace, CosFace, and ArcFace, have been widely adopted to enhance intra-class compactness and inter-class separability, yet they overlook the impact of noisy samples. By examining the distribution of samples in the angular space, we observe that clean samples predominantly cluster in the center region, whereas noisy samples tend to shift toward the peripheral region. Motivated by this observation, we propose the Exponential Angular Margin Loss (ExpFace), which introduces an angular exponential term as the margin. This design applies a larger penalty in the center region and a smaller penalty in the peripheral region within the angular space, thereby emphasizing clean samples while suppressing noisy samples. We present a unified analysis of ExpFace and classical margin-based softmax losses in terms of margin embedding forms, similarity curves, and gradient curves, showing that ExpFace not only avoids the training instability of SphereFace and the non-monotonicity of ArcFace, but also exhibits a similarity curve that applies penalties in the same manner as the decision boundary in the angular space. Extensive experiments demonstrate that ExpFace achieves state-of-the-art performance. To facilitate future research, we have released the source code at: this https URL.
Abstract (translated)
人脸识别是一个开放集问题，需要强大的判别能力以确保同类样本之间的距离小于不同类样本之间的距离。为了提高这一性能，基于余弦softmax损失的方法（如SphereFace、CosFace和ArcFace）已经被广泛采用来增强同类紧凑性和异类可分离性。然而，这些方法在处理噪声样本时表现不佳。 通过对角空间中样本分布的分析发现，干净样本主要聚集在中心区域，而噪声样本则倾向于移向边缘区域。基于这一观察，我们提出了一种指数角度余量损失（ExpFace），它引入了一个角度指数项作为余量。这种设计在角空间中的中心区域施加更大的惩罚，在边缘区域施加较小的惩罚，从而强调干净样本的同时抑制噪声样本。 我们在余量嵌入形式、相似性曲线和梯度曲线上对ExpFace与传统基于边际的softmax损失进行了统一分析。结果显示，ExpFace不仅避免了SphereFace训练时的不稳定性和ArcFace非单调性的缺点，还展示出一种与其角空间决策边界施加惩罚方式一致的相似性曲线。 广泛的实验表明，ExpFace在性能上达到了最先进的水平。为了促进未来的研究工作，我们已经发布了源代码：[请参考原文献或该领域的研究论文获取准确链接]。
URL
https://arxiv.org/abs/2509.19753
