Feature extractors significantly impact the performance of biometric systems. In the field of hand gesture authentication, existing studies focus on improving the model architectures and behavioral characteristic representation methods to enhance their feature extractors. However, loss functions, which can guide extractors to produce more discriminative identity features, are neglected. In this paper, we improve the margin-based Softmax loss functions, which are mainly designed for face authentication, in two aspects to form a new loss function for hand gesture authentication. First, we propose to replace the commonly used cosine function in the margin-based Softmax losses with a linear function to measure the similarity between identity features and proxies (the weight matrix of Softmax, which can be viewed as class centers). With the linear function, the main gradient magnitude decreases monotonically as the quality of the model improves during training, thus allowing the model to be quickly optimized in the early stage and precisely fine-tuned in the late stage. Second, we design an adaptive margin scheme to assign margin penalties to different samples according to their separability and the model quality in each iteration. Our adaptive margin scheme constrains the gradient magnitude. It can reduce radical (excessively large) gradient magnitudes and provide moderate (not too small) gradient magnitudes for model optimization, contributing to more stable training. The linear function and the adaptive margin scheme are complementary. Combining them, we obtain the proposed linear adaptive additive angular margin (L3AM) loss. To demonstrate the effectiveness of L3AM loss, we conduct extensive experiments on seven hand-related authentication datasets, compare it with 25 state-of-the-art (SOTA) loss functions, and apply it to eight SOTA hand gesture authentication models. The experimental results show that L3AM loss further improves the performance of the eight authentication models and outperforms the 25 losses. The code is available at https://github.com/SCUT-BIP-Lab/L3AM.

特征提取器显着影响生物识别系统的性能。在手势认证领域，现有的研究重点是改进模型架构和行为特征表示方法以增强其特征提取器。然而，可以指导提取器产生更具辨别力的身份特征的损失函数却被忽略了。在本文中，我们对主要用于人脸认证的基于边际的Softmax损失函数进行了两个方面的改进，形成了一种新的用于手势认证的损失函数。首先，我们建议用线性函数替换基于边际的 Softmax 损失中常用的余弦函数，以测量身份特征和代理（Softmax 的权重矩阵，可以视为类中心）之间的相似性。通过线性函数，主梯度幅值在训练过程中随着模型质量的提高而单调减小，从而使模型前期快速优化，后期精确微调。其次，我们设计了一种自适应裕度方案，根据每次迭代中的可分离性和模型质量，为不同样本分配裕度惩罚。我们的自适应余量方案限制了梯度幅度。它可以减少激进（过大）的梯度幅度，并为模型优化提供适中（不太小的）梯度幅度，有助于更稳定的训练。线性函数和自适应裕度方案是互补的。结合它们，我们获得了所提出的线性自适应加性角度裕度（L3AM）损失。为了证明 L3AM 损失的有效性，我们对 7 个与手部相关的身份验证数据集进行了广泛的实验，将其与 25 个最先进的 (SOTA) 损失函数进行比较，并将其应用于 8 个 SOTA 手势身份验证模型。实验结果表明，L3AM损失进一步提高了8种认证模型的性能，并且优于25种损失。代码可在 https://github.com/SCUT-BIP-Lab/L3AM 获取。