用切比雪夫多项式替代角度计算，解决说话人验证中的训练不稳问题。
The Achilles' Heel of Angular Margins: A Chebyshev Polynomial Fix for Speaker Verification
- 用切比雪夫多项式近似arccos，避免梯度爆炸
- 在VoxCeleb/SITW/CN-Celeb上均提升性能
- 适合追求稳定训练的度量学习研究者
角度边界损失（如AAM-Softmax）已成为说话人与人脸验证的标配，其核心是直接操纵特征与类别原型间的夹角。然而，该方法依赖arccos函数恢复角度，导致训练不稳定：arccos导数在边界处发散，引发优化过程中的梯度峰值；同时对难分类样本的梯度不够尖锐。本文提出ChebyAAM，用arccos的切比雪夫多项式近似替代显式计算，有效消除梯度爆炸，并对难例施加更强修正信号，实现更优优化。在VoxCeleb、SITW和CN-Celeb三个基准上实验表明，该方法显著缓解了不稳定性并持续提升性能。结果表明，近似角度操作而非精确计算，是未来度量学习损失设计更稳健的路径。代码已开源。
原文摘要 · Abstract (English)
Angular margin losses, such as AAM-Softmax, have become the de facto in speaker and face verification. Their success hinges on directly manipulating the angle between features and class prototypes. However, this manipulation relies on the arccos function to recover the angle, introducing a significant yet overlooked source of training instability. The derivative of arccos explodes at its boundaries, causing gradient peaks during optimisation. Furthermore, the formulation fails to generate a sufficiently sharp gradient for hard-to-classify examples. We address these issues by proposing ChebyAAM, a loss that replaces the arccos operation with its Chebyshev polynomial approximation. This substitution eliminates gradient explosion and applies a stronger corrective signal to hard examples, leading to more effective optimisation. Experiments on three benchmarks (VoxCeleb, SITW, and CN-Celeb) demonstrate that our method resolves the instability and consistently improves performance. Our work suggests that approximating angular operations, rather than calculating them explicitly, offers a more robust path for designing future metric learning losses. Code is available at https://github.com/ExtraOrdinaryLab/vibe.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。