Topological Approaches to Deep Learning
This work addresses the challenge of interpretability and efficiency in deep learning for researchers and practitioners, offering incremental improvements through topological methods.
The paper tackles the problem of understanding and improving deep neural networks by applying topological data analysis to their internal states, resulting in faster computations and better generalization across digit datasets.
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed up computations and (b) improve generalization from one data set of digits to another. One byproduct of the analysis is the production of a geometry on new sets of features on data sets of images, and use this observation to develop a methodology for constructing analogues of CNN's for many other geometries, including the graph structures constructed by topological data analysis.