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Neural networks, being susceptible to adversarial attacks, should face astrict level of scrutiny before being deployed in critical or adversarialapplications. This paper uses ideas from Chaos Theory to explain, analyze, andquantify the degree to which neural networks are susceptible to or robustagainst adversarial attacks. To this end, we present a new metric, the"susceptibility ratio," given by $\hat \Psi(h, \theta)$, which captures howgreatly a model's output will be changed by perturbations to a given input.  Our results show that susceptibility to attack grows significantly with thedepth of the model, which has safety implications for the design of neuralnetworks for production environments. We provide experimental evidence of therelationship between $\hat \Psi$ and the post-attack accuracy of classificationmodels, as well as a discussion of its application to tasks lacking harddecision boundaries. We also demonstrate how to quickly and easily approximatethe certified robustness radii for extremely large models, which until now hasbeen computationally infeasible to calculate directly.

Chaos Theory and Adversarial Robustness