Title: On the Limitation of Local Intrinsic Dimensionality for Characterizing the Subspaces of Adversarial Examples,
Abstract: Understanding and characterizing the subspaces of adversarial examples aid in
studying the robustness of deep neural networks (DNNs) to adversarial
perturbations. Very recently, Ma et al. (ICLR 2018) proposed to use local
intrinsic dimensionality (LID) in layer-wise hidden representations of DNNs to
study adversarial subspaces. It was demonstrated that LID can be used to
characterize the adversarial subspaces associated with different attack
methods, e.g., the Carlini and Wagner's (C&W) attack and the fast gradient sign
attack.
In this paper, we use MNIST and CIFAR-10 to conduct two new sets of
experiments that are absent in existing LID analysis and report the limitation
of LID in characterizing the corresponding adversarial subspaces, which are (i)
oblivious attacks and LID analysis using adversarial examples with different
confidence levels; and (ii) black-box transfer attacks. For (i), we find that
the performance of LID is very sensitive to the confidence parameter deployed
by an attack, and the LID learned from ensembles of adversarial examples with
varying confidence levels surprisingly gives poor performance. For (ii), we
find that when adversarial examples are crafted from another DNN model, LID is
ineffective in characterizing their adversarial subspaces. These two findings
together suggest the limited capability of LID in characterizing the subspaces
of adversarial examples.