An Empirical Study on the Application of TDA to Deep Neural Networks
Keywords: deep neural networks, convolutional networks, topological data analysis, persistent homology, Betti numbers, Betti curves, Betti curve similarity, ImageNet, functional graph
TL;DR: An empirical study across data-subsets of the ImageNet dataset and training epochs for several CNNs, where we compare and contrast their functional graphs by means of the Betti curve similarity.
Abstract: This study aims to analyze the global structure of the functional subgraph of DNNs using tools from topological data analysis (TDA), namely persistent homology (PH) and the curve similarity. Using these methods we present an empirical study on the application of TDA to DNNs in order to gain a better understanding of their architecture and to provide a framework for a similarity measure between DNNs. The study is conducted by training several convolutional neural networks (CNNs) on disjoint subsets of the ImageNet dataset and then by analyzing the structure of their functional graphs across datasets using the Betti curve similarity. Results show that the Betti curve similarity is able to distinguish between different DNN models across datasets and can be a tool for detecting a departure from previous internal representations of those datasets, providing a new method for the analysis of DNNs and a potential path forward for their theoretical development.
Primary Area: interpretability and explainable AI
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Submission Number: 8039
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