  An important aspect of developing reliable deep learning systems is devising
strategies that make these systems robust to adversarial attacks. There is a
long line of work that focuses on developing defenses against these attacks,
but recently, researchers have began to study ways to reverse engineer the
attack process. This allows us to not only defend against several attack
models, but also classify the threat model. However, there is still a lack of
theoretical guarantees for the reverse engineering process. Current approaches
that give any guarantees are based on the assumption that the data lies in a
union of linear subspaces, which is not a valid assumption for more complex
datasets. In this paper, we build on prior work and propose a novel framework
for reverse engineering of deceptions which supposes that the clean data lies
in the range of a GAN. To classify the signal and attack, we jointly solve a
GAN inversion problem and a block-sparse recovery problem. For the first time
in the literature, we provide deterministic linear convergence guarantees for
this problem. We also empirically demonstrate the merits of the proposed
approach on several nonlinear datasets as compared to state-of-the-art methods.
