Topological Structure is Predictive of Deep Neural Network Success in Learning

Machine learning has become a fundamental tool in modern science, yet its limitations are still not fully understood. Using a simple children's game, we show that the topological structure of the underlying training data can have a dramatic effect on the ability of a deep neural network (DNN) classifier to learn to classify data. We then take insights obtained from this toy model and apply them to two physical data sets (one from particle physics and one from acoustics), which are known to be amenable to classification by DNN's. We show that the simplicity in their topological structure explains the majority of the DNN's ability to operate on these data sets by showing that fully interpretable topological classifiers are able to perform nearly as well as their DNN counterparts.