Motivated by graph theory, artificial neural networks (ANNs) are traditionally structured as layers of neurons (nodes), which learn useful information by the passage of data through interconnections (edges). In the machine learning realm, graph structures (i.e., neurons and connections) of ANNs have recently been explored using various graph-theoretic measures linked to their predictive performance. On the other hand, in network science (NetSci), certain graph measures including entropy and curvature are known to provide insight into the robustness and fragility of real-world networks. In this work, we use these graph measures to explore the robustness of various ANNs to adversarial attacks. To this end, we (1) explore the design space of inter-layer and intra-layers connectivity regimes of ANNs in the graph domain and record their predictive performance after training under different types of adversarial attacks, (2) use graph representations for both inter-layer and intra-layers connectivity regimes to calculate various graph-theoretic measures, including curvature and entropy, and (3) analyze the relationship between these graph measures and the adversarial performance of ANNs. We show that curvature and entropy, while operating in the graph domain, can quantify the robustness of ANNs without having to train these ANNs. Our results suggest that the real-world networks, including brain networks, financial networks, and social networks may provide important clues to the neural architecture search for robust ANNs. We propose a search strategy that efficiently finds robust ANNs amongst a set of well-performing ANNs without having a need to train all of these ANNs.
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