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

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, especially in computer vision applications. Here we investigate the relationship between the robustness of DANNs in a vision task and their underlying graph architectures or structures. First we explored the design space of architectures of DANNs using graph-theoretic robustness measures and transformed the graphs to DANN architectures using various image classification tasks. Then we explored the relationship between the robustness of trained DANNs against noise and adversarial attacks and their underlying architectures. We show that robustness performance of DANNs can be quantified before training using graph structural properties such as topological entropy and Olivier-Ricci curvature, with the greatest reliability for complex tasks and large DANNs. Our results can also be applied for tasks other than computer vision such as natural language processing and recommender systems.

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.