Classification is a pivotal task in deep learning not only because of its intrinsic importance, but also for providing embeddings with desirable properties in other tasks. To optimize these properties, a wide variety of loss functions have been proposed that attempt to minimize the intra-class distance and maximize the inter-class distance in the embeddings space. In this paper we argue that, in addition to these two, eliminating hierarchies within and among classes are two other desirable properties for classification embeddings. Furthermore, we propose the Angular Distance Distribution (ADD) Loss, which aims to enhance the four previous properties jointly. For this purpose, it imposes conditions on the first and second order statistical moments of the angular distance between embeddings. Finally, we perform experiments showing that our loss function improves all four properties and, consequently, performs better than other loss functions in audio classification tasks.

翻译：分类是深度学习中的一项关键任务，不仅因其内在重要性，更因其能为其他任务提供具有理想特性的嵌入表示。为优化这些特性，研究者提出了多种损失函数，旨在最小化嵌入空间中的类内距离并最大化类间距离。本文认为，除上述两点外，消除类内与类间的层级结构亦是分类嵌入应具备的另外两项理想特性。为此，我们提出角度距离分布损失函数，旨在同时增强前述四项特性。该函数通过对嵌入间角度距离的一阶与二阶统计矩施加约束来实现目标。最终实验表明，该损失函数能有效改善所有四项特性，进而在音频分类任务中表现优于其他损失函数。