How Important is a Neuron

The problem of attributing a deep network’s prediction to its input/base features is well-studied (cf. Simonyan et al. (2013)). We introduce the notion of conductance to extend the notion of attribution to understanding the importance of hidden units. Informally, the conductance of a hidden unit of a deep network is the flow of attribution via this hidden unit. We can use conductance to understand the importance of a hidden unit to the prediction for a specific input, or over a set of inputs. We justify conductance in multiple ways via a qualitative comparison with other methods, via some axiomatic results, and via an empirical evaluation based on a feature selection task. The empirical evaluations are done using the Inception network over ImageNet data, and a convolutinal network over text data. In both cases, we demonstrate the effectiveness of conductance in identifying interesting insights about the internal workings of these networks.