  Adversarial examples are often cited by neuroscientists and machine learning
researchers as an example of how computational models diverge from biological
sensory systems. Recent work has proposed adding biologically-inspired
components to visual neural networks as a way to improve their adversarial
robustness. One surprisingly effective component for reducing adversarial
vulnerability is response stochasticity, like that exhibited by biological
neurons. Here, using recently developed geometrical techniques from
computational neuroscience, we investigate how adversarial perturbations
influence the internal representations of standard, adversarially trained, and
biologically-inspired stochastic networks. We find distinct geometric
signatures for each type of network, revealing different mechanisms for
achieving robust representations. Next, we generalize these results to the
auditory domain, showing that neural stochasticity also makes auditory models
more robust to adversarial perturbations. Geometric analysis of the stochastic
networks reveals overlap between representations of clean and adversarially
perturbed stimuli, and quantitatively demonstrates that competing geometric
effects of stochasticity mediate a tradeoff between adversarial and clean
performance. Our results shed light on the strategies of robust perception
utilized by adversarially trained and stochastic networks, and help explain how
stochasticity may be beneficial to machine and biological computation.
