We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully connected networks (FCN), we present an extended analysis using Cubical homology instead, with a variety of popular deep architectures and real image datasets. We demonstrate that as depth increases, a topologically complicated dataset is transformed into a simple one, resulting in Be…