  The layered structure of deep neural networks hinders the use of numerous
analysis tools and thus the development of its interpretability. Inspired by
the success of functional brain networks, we propose a novel framework for
interpretability of deep neural networks, that is, the functional network. We
construct the functional network of fully connected networks and explore its
small-worldness. In our experiments, the mechanisms of regularization methods,
namely, batch normalization and dropout, are revealed using graph theoretical
analysis and topological data analysis. Our empirical analysis shows the
following: (1) Batch normalization enhances model performance by increasing the
global e ciency and the number of loops but reduces adversarial robustness by
lowering the fault tolerance. (2) Dropout improves generalization and
robustness of models by improving the functional specialization and fault
tolerance. (3) The models with dierent regularizations can be clustered
correctly according to their functional topological dierences, re ecting the
great potential of the functional network and topological data analysis in
interpretability.
