Finding and analyzing meaningful representations of data is the purpose of machine learning. The idea of representation learning is to extract representations from the data itself, e.g., by utilizing deep neural networks. In this work, we examine representation learning from a geometric perspective. Especially, we focus on the convexity of classes and clusters as a natural and desirable representation property, for which robust and scalable measures are still lacking. To address this, we propose a new approach called Random Polytope Descriptor that allows a convex description of data points based on the construction of random convex polytopes. This ties in with current methods for statistical disentanglement. We demonstrate the use of our technique on well-known deep learning methods for representation learning. Specifically we find that popular regularization variants such as the Variational Autoencoder can destroy crucial information that is relevant for tasks such as out-of-distribution detection.

中文翻译：

---

随机凸多边形的几何解缠结

寻找和分析有意义的数据表示是机器学习的目的。表征学习的思想是从数据本身中提取表征，例如，通过利用深度神经网络。在这项工作中，我们从几何角度检查表示学习。特别是，我们将类和集群的凸性作为一种自然的和理想的表示属性，对此仍然缺乏稳健和可扩展的措施。为了解决这个问题，我们提出了一种称为随机多面体描述符的新方法，它允许基于随机凸多面体的构造对数据点进行凸描述。这与当前的统计解开方法有关。我们展示了我们的技术在用于表征学习的著名深度学习方法上的使用。