  Representational sparsity is known to affect robustness to input
perturbations in deep neural networks (DNNs), but less is known about how the
semantic content of representations affects robustness. 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
that class selectivity may not be necessary for, and in some cases can impair
generalization, we investigate whether it also confers robustness (or
vulnerability) to perturbations of input data. We found that networks
regularized to have lower levels of class selectivity were more robust to
average-case (naturalistic) perturbations, while networks with higher class
selectivity are more vulnerable. In contrast, class selectivity increases
robustness to multiple types of worst-case (i.e. white box adversarial)
perturbations, suggesting that while decreasing class selectivity is helpful
for average-case perturbations, it is harmful for worst-case perturbations. To
explain this difference, we studied the dimensionality of the networks'
representations: we found that the dimensionality of early-layer
representations is inversely proportional to a network's class selectivity, and
that adversarial samples cause a larger increase in early-layer dimensionality
than corrupted samples. Furthermore, the input-unit gradient is more variable
across samples and units in high-selectivity networks compared to
low-selectivity networks. These results lead to the conclusion that units
participate more consistently in low-selectivity regimes compared to
high-selectivity regimes, effectively creating a larger attack surface and
hence vulnerability to worst-case perturbations.
