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.Comment: 18 pages, 15 figure