The architectures of deep artificial neural networks (DANNs) are routinely
studied to improve their predictive performance. However, the relationship
between the architecture of a DANN and its robustness to noise
and adversarial attacks is less explored. We investigate how the robustness
of DANNs relates to their underlying graph architectures or structures.
This study: (1) starts by exploring the design space of architectures
of DANNs using graph-theoretic robustness measures; (2) transforms the
graphs to DANN architectures to train/validate/test on various image
classification tasks; (3) explores the relationship between the robustness
of trained DANNs against noise and adversarial attacks and the robustness
of their underlying architectures estimated via graph-theoretic
measures. We show that the topological entropy and Olivier-Ricci curvature
of the underlying graphs can quantify the robustness performance
of DANNs. The said relationship is stronger for complex tasks and large
DANNs. Our work will allow autoML and neural architecture search
community to explore design spaces of robust and accurate DANNs.