  We outline a detection method for adversarial inputs to deep neural networks.
By viewing neural network computations as graphs upon which information flows
from input space to out- put distribution, we compare the differences in graphs
induced by different inputs. Specifically, by applying persistent homology to
these induced graphs, we observe that the structure of the most persistent
subgraphs which generate the first homology group differ between adversarial
and unperturbed inputs. Based on this observation, we build a detection
algorithm that depends only on the topological information extracted during
training. We test our algorithm on MNIST and achieve 98% detection adversary
accuracy with F1-score 0.98.
