Teaching Neural Networks a Sense of Geometry

By taking neural networks back to the school bench and teaching them some elements of geometry and topology, we can build algorithms that can reason about the shape of data. Surprisingly these methods can be useful not only for computer vision but in a wide range of applications, such as evaluating and improving the learning of embeddings or the distribution of samples originating from generative models. This is the promise of the emerging field of Topological Data Analysis (TDA) which we will introduce and review recent works at its intersection with machine learning.