  Predictions made by deep neural networks were shown to be highly sensitive to
small changes made in the input space where such maliciously crafted data
points containing small perturbations are being referred to as adversarial
examples. On the other hand, recent research suggests that the same networks
can also be extremely insensitive to changes of large magnitude, where
predictions of two largely different data points can be mapped to approximately
the same output. In such cases, features of two data points are said to
approximately collide, thus leading to the largely similar predictions. Our
results improve and extend the work of Li et al.(2019), laying out theoretical
grounds for the data points that have colluding features from the perspective
of weights of neural networks, revealing that neural networks not only suffer
from features that approximately collide but also suffer from features that
exactly collide. We identify the necessary conditions for the existence of such
scenarios, hereby investigating a large number of DNNs that have been used to
solve various computer vision problems. Furthermore, we propose the Null-space
search, a numerical approach that does not rely on heuristics, to create data
points with colliding features for any input and for any task, including, but
not limited to, classification, localization, and segmentation.
