Exploring Robust Architectures for Deep Artificial Neural Networks

TL;DR

This paper investigates how the robustness of deep neural networks relates to their underlying graph architectures, using graph-theoretic measures to predict and enhance robustness against noise and adversarial attacks.

Contribution

It introduces a novel approach linking graph-theoretic measures to neural network robustness, aiding in the design of more resilient architectures.

Findings

Topological entropy correlates with robustness performance.

Olivier-Ricci curvature effectively quantifies robustness.

Relationship stronger for complex tasks and larger networks.

Abstract

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.