Topological Data Analysis of Decision Boundaries with Application to Model Selection
This work addresses model selection for deep learning practitioners by providing a method to assess network complexity, though it appears incremental as it builds on existing topological analysis techniques.
The authors tackled the problem of quantifying deep neural network complexity to match datasets with pre-trained models by proposing topological data analysis methods to infer decision boundaries, reporting experimental results on MNIST, FashionMNIST, and CIFAR10.
We propose the labeled Čech 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 datasets to pre-trained models; we report results for experiments using MNIST, FashionMNIST, and CIFAR10.