Activation Landscapes as a Topological Summary of Neural Network Performance
Abstract
We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize this information using persistence landscapes. The resulting feature map provides both an informative visual ization of the network and a kernel for statistical analysis and machine learning. We observe that the topological complexity often increases with training and that the topological complexity does not decrease with each layer.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10136
 Bibcode:
 2021arXiv211010136W
 Keywords:

 Computer Science  Machine Learning;
 Mathematics  Algebraic Topology
 EPrint:
 4 pages, 5 figures