  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.
