  While the relative trade-offs between sparse and distributed representations
in deep neural networks (DNNs) are well-studied, less is known about how these
trade-offs apply to representations of semantically-meaningful information.
Class selectivity, the variability of a unit's responses across data classes or
dimensions, is one way of quantifying the sparsity of semantic representations.
Given recent evidence showing that class selectivity can impair generalization,
we sought to investigate whether it also confers robustness (or vulnerability)
to perturbations of input data. We found that mean class selectivity predicts
vulnerability to naturalistic corruptions; networks regularized to have lower
levels of class selectivity are more robust to corruption, while networks with
higher class selectivity are more vulnerable to corruption, as measured using
Tiny ImageNetC and CIFAR10C. In contrast, we found that class selectivity
increases robustness to multiple types of gradient-based adversarial attacks.
To examine this difference, we studied the dimensionality of the change in the
representation due to perturbation, finding that decreasing class selectivity
increases the dimensionality of this change for both corruption types, but with
a notably larger increase for adversarial attacks. These results demonstrate
the causal relationship between selectivity and robustness and provide new
insights into the mechanisms of this relationship.
