Clustering-Based Interpretation of Deep ReLU Network

Abstract: Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the learned parameters, and to allow for efficient backpropagation. In this paper, we recognize that the non-linear behavior of the ReLU function gives rise to a natural clustering when the pattern of active neurons is considered. This observation helps to deepen the learning mechanism of the network; in fact, we demonstrate that, within each cluster, the network can be fully represented as an affine map. The consequence is that we are able to recover an explanation, in the form of feature importance, for the predictions done by the network to the instances belonging to the cluster. Therefore, the methodology we propose is able to increase the level of interpretability of a fully connected feedforward ReLU neural network, downstream from the fitting phase of the model, without altering the structure of the network. A simulation study and the empirical application to the Titanic dataset, show the capability of the method to bridge the gap between the algorithm optimization and the human understandability of the black box deep ReLU networks.