Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

提出了一种新的softmax函数(Wraped Cauchy Distributed Angular Softmax)，可以解决视觉识别中不平衡数据和长尾数据的问题。该方法使用基于高斯核的数据智能，并且可以对类别的角度表示进行分布，可以动态地调整紧致性和各个类别的边界。在多个基准数据集上的实验结果表明，该方法优于其他最先进的基于softmax的方法。

基于威布尔–柯西分布的角Softmax模型用于长尾视觉识别