Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
Abstract
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.
Cite
Text
Rieck et al. "Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology." International Conference on Learning Representations, 2019.Markdown
[Rieck et al. "Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology." International Conference on Learning Representations, 2019.](https://mlanthology.org/iclr/2019/rieck2019iclr-neural/)BibTeX
@inproceedings{rieck2019iclr-neural,
title = {{Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology}},
author = {Rieck, Bastian and Togninalli, Matteo and Bock, Christian and Moor, Michael and Horn, Max and Gumbsch, Thomas and Borgwardt, Karsten},
booktitle = {International Conference on Learning Representations},
year = {2019},
url = {https://mlanthology.org/iclr/2019/rieck2019iclr-neural/}
}