  Convolutional neural networks have shown to be widely applicable to a large
number of fields when large amounts of labelled data are available. The recent
trend has been to use models with increasingly larger sets of tunable
parameters to increase model accuracy, reduce model loss, or create more
adversarially robust models -- goals that are often at odds with one another.
In particular, recent theoretical work raises questions about the ability for
even larger models to generalize to data outside of the controlled train and
test sets. As such, we examine the role of the number of hidden layers in the
ResNet model, demonstrated on the MNIST, CIFAR10, CIFAR100 datasets. We test a
variety of parameters including the size of the model, the floating point
precision, and the noise level of both the training data and the model output.
To encapsulate the model's predictive power and computational cost, we provide
a method that uses induced failures to model the probability of failure as a
function of time and relate that to a novel metric that allows us to quickly
determine whether or not the cost of training a model outweighs the cost of
attacking it. Using this approach, we are able to approximate the expected
failure rate using a small number of specially crafted samples rather than
increasingly larger benchmark datasets. We demonstrate the efficacy of this
technique on both the MNIST and CIFAR10 datasets using 8-, 16-, 32-, and 64-bit
floating-point numbers, various data pre-processing techniques, and several
attacks on five configurations of the ResNet model. Then, using empirical
measurements, we examine the various trade-offs between cost, robustness,
latency, and reliability to find that larger models do not significantly aid in
adversarial robustness despite costing significantly more to train.
