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Measuring neural net robustness with constraints
Despite having high accuracy, neural nets have been shown to be susceptible
to adversarial examples, where a small perturbation to an input can cause it to
become mislabeled. We propose metrics for measuring the robustness of a neural
net and devise a novel algorithm for approximating these metrics based on an
encoding of robustness as a linear program. We show how our metrics can be used
to evaluate the robustness of deep neural nets with experiments on the MNIST
and CIFAR-10 datasets. Our algorithm generates more informative estimates of
robustness metrics compared to estimates based on existing algorithms.
Furthermore, we show how existing approaches to improving robustness "overfit"
to adversarial examples generated using a specific algorithm. Finally, we show
that our techniques can be used to additionally improve neural net robustness
both according to the metrics that we propose, but also according to previously
proposed metrics
Exploring the assortativity-clustering space of a network's degree sequence
Nowadays there is a multitude of measures designed to capture different
aspects of network structure. To be able to say if the structure of certain
network is expected or not, one needs a reference model (null model). One
frequently used null model is the ensemble of graphs with the same set of
degrees as the original network. In this paper we argue that this ensemble can
be more than just a null model -- it also carries information about the
original network and factors that affect its evolution. By mapping out this
ensemble in the space of some low-level network structure -- in our case those
measured by the assortativity and clustering coefficients -- one can for
example study how close to the valid region of the parameter space the observed
networks are. Such analysis suggests which quantities are actively optimized
during the evolution of the network. We use four very different biological
networks to exemplify our method. Among other things, we find that high
clustering might be a force in the evolution of protein interaction networks.
We also find that all four networks are conspicuously robust to both random
errors and targeted attacks
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