The Achilles'Heel of Angular Margins: A Chebyshev Polynomial Fix for Speaker Verification

2026-01-19

AI Summary

This work addresses the instability in speaker verification training caused by the exploding gradients of the arccos function in Angular Margin loss, which also hinders effective optimization on hard samples. To mitigate this issue, the authors propose ChebyAAM, a novel loss function that, for the first time, incorporates Chebyshev polynomials into angular margin design to accurately approximate the arccos operation. This approximation effectively alleviates gradient explosion and enhances discriminative learning for challenging samples. Extensive experiments on three benchmark datasets—VoxCeleb, SITW, and CN-Celeb—demonstrate significant performance improvements, confirming the superiority and stability of the proposed approximation strategy.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Learning & Optimization for NLP
• Cognitive Modeling & Cognitive Systems: Affective Computing

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• angular margin
• arccos instability
• gradient explosion
• speaker verification
• hard examples

Innovation

• angular margin
• Chebyshev polynomial
• gradient stability
• speaker verification
• metric learning