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.
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