Topological data analysis of decision boundaries with application to model selection

Abstract

We propose the labeled Cech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary from samples. Our main objective is quantification of deep neural network complexity to enable matching of datascts to pre-trained models to facilitate the functioning of AI marketplaces; we report results for experiments using MNIST, FashionMNIST, and CI-FAR10.