  Adversarial examples are carefully constructed modifications to an input that
completely change the output of a classifier but are imperceptible to humans.
Despite these successful attacks for continuous data (such as image and audio
samples), generating adversarial examples for discrete structures such as text
has proven significantly more challenging. In this paper we formulate the
attacks with discrete input on a set function as an optimization task. We prove
that this set function is submodular for some popular neural network text
classifiers under simplifying assumption. This finding guarantees a $1-1/e$
approximation factor for attacks that use the greedy algorithm. Meanwhile, we
show how to use the gradient of the attacked classifier to guide the greedy
search. Empirical studies with our proposed optimization scheme show
significantly improved attack ability and efficiency, on three different text
classification tasks over various baselines. We also use a joint sentence and
word paraphrasing technique to maintain the original semantics and syntax of
the text. This is validated by a human subject evaluation in subjective metrics
on the quality and semantic coherence of our generated adversarial text.
