Detecting Modularity in Deep Neural Networks

A neural network is modular to the extent that parts of its computational graph (i.e. structure) can be represented as performing some comprehensible subtask relevant to the overall task (i.e. functionality). Are modern deep neural networks modular? How can this be quantified? In this paper, we consider the problem of assessing the modularity exhibited by a partitioning of a network's neurons. We propose two proxies for this: importance, which reflects how crucial sets of neurons are to network performance; and coherence, which reflects how consistently their neurons associate with features of the inputs. To measure these proxies, we develop a set of statistical methods based on techniques conventionally used to interpret individual neurons. We apply the proxies to partitionings generated by spectrally clustering a graph representation of the network's neurons with edges determined either by network weights or correlations of activations. We show that these partitionings, even ones based only on weights (i.e. strictly from non-runtime analysis), reveal groups of neurons that are important and coherent. These results suggest that graph-based partitioning can reveal modularity and help us understand how deep neural networks function.