  Despite the remarkable success of deep neural networks in a myriad of
settings, several works have demonstrated their overwhelming sensitivity to
near-imperceptible perturbations, known as adversarial attacks. On the other
hand, prior works have also observed that deep networks can be under-sensitive,
wherein large-magnitude perturbations in input space do not induce appreciable
changes to network activations. In this work, we study in detail the phenomenon
of under-sensitivity in vision models such as CNNs and Transformers, and
present techniques to study the geometry and extent of "equi-confidence" level
sets of such networks. We propose a Level Set Traversal algorithm that
iteratively explores regions of high confidence with respect to the input space
using orthogonal components of the local gradients. Given a source image, we
use this algorithm to identify inputs that lie in the same equi-confidence
level set as the source image despite being perceptually similar to arbitrary
images from other classes. We further observe that the source image is linearly
connected by a high-confidence path to these inputs, uncovering a star-like
structure for level sets of deep networks. Furthermore, we attempt to identify
and estimate the extent of these connected higher-dimensional regions over
which the model maintains a high degree of confidence. The code for this
project is publicly available at
https://github.com/SriramB-98/blindspots-neurips-sub
