  While progress has been made in crafting visually imperceptible adversarial
examples, constructing semantically meaningful ones remains a challenge. In
this paper, we propose a framework to generate semantics preserving adversarial
examples. First, we present a manifold learning method to capture the semantics
of the inputs. The motivating principle is to learn the low-dimensional
geometric summaries of the inputs via statistical inference. Then, we perturb
the elements of the learned manifold using the Gram-Schmidt process to induce
the perturbed elements to remain in the manifold. To produce adversarial
examples, we propose an efficient algorithm whereby we leverage the semantics
of the inputs as a source of knowledge upon which we impose adversarial
constraints. We apply our approach on toy data, images and text, and show its
effectiveness in producing semantics preserving adversarial examples which
evade existing defenses against adversarial attacks.
