Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
This provides a novel tool for analyzing neural network architectures, addressing a gap in structural understanding for researchers and practitioners, though it is incremental as it builds on existing topological methods.
The authors tackled the problem of characterizing structural properties of neural networks by proposing neural persistence, a complexity measure based on topological data analysis, and showed it reflects practices like dropout and batch normalization while enabling a stopping criterion that shortens training with comparable accuracy to validation loss-based early stopping.
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.