Adaptive Activation Thresholding: Dynamic Routing Type Behavior for Interpretability in Convolutional Neural Networks

There is a growing interest in strategies that can help us understand or interpret neural networks -- that is, not merely provide a prediction, but also offer additional context explaining why and how. While many current methods offer tools to perform this analysis for a given (trained) network post-hoc, recent results (especially on capsule networks) suggest that when classes map to a few high level ``concepts'' in the preceding layers of the network, the behavior of the network is easier to interpret or explain. Such training may be accomplished via dynamic/EM routing where the network ``routes'' for individual classes (or subsets of images) are dynamic and involve few nodes even if the full network may not be sparse. In this paper, we show how a simple modification of the SGD scheme can help provide dynamic/EM routing type behavior in convolutional neural networks. Through extensive experiments, we evaluate the effect of this idea for interpretability where we obtain promising results, while also showing that no compromise in attainable accuracy is involved. Further, we show that the minor modification is seemingly ad-hoc, the new algorithm can be analyzed by an approximate method which provably matches known rates for SGD.