Deep Neural Networks as Complex Networks

Deep Neural Networks are, from a physical perspective, graphs whose `links`and `vertices` iteratively process data and solve tasks sub-optimally. We useComplex Network Theory (CNT) to represents Deep Neural Networks (DNNs) asdirected weighted graphs: within this framework, we introduce metrics to studyDNNs as dynamical systems, with a granularity that spans from weights tolayers, including neurons. CNT discriminates networks that differ in the numberof parameters and neurons, the type of hidden layers and activations, and theobjective task. We further show that our metrics discriminate low vs. highperforming networks. CNT is a comprehensive method to reason about DNNs and acomplementary approach to explain a model's behavior that is physicallygrounded to networks theory and goes beyond the well-studied input-outputrelation.