Using Topological Data Analysis to Understand the Behavior of Convolutional Neural Networks

TLDR: Neural Networks are powerful but complex and opaque tools. Using Topological Data Analysis, we can describe the functioning and learning of a convolutional neural network in a compact and understandable way. The implications of the finding are profound and can accelerate the development of a wide range of applications from self-driving everything to GDPR. Neural networks have demonstrated a great deal of success in the study of various kinds of data, including images, text, time series, and many others. One issue that restricts their applicability, however, is the fact that it is not understood in any kind of detail how they work.