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Previous work has shown that a neural network with the rectified linear unit(ReLU) activation function leads to a convex polyhedral decomposition of theinput space. These decompositions can be represented by a dual graph withvertices corresponding to polyhedra and edges corresponding to polyhedrasharing a facet, which is a subgraph of a Hamming graph. This paper illustrateshow one can utilize the dual graph to detect and analyze adversarial attacks inthe context of digital images. When an image passes through a networkcontaining ReLU nodes, the firing or non-firing at a node can be encoded as abit ($1$ for ReLU activation, $0$ for ReLU non-activation). The sequence of allbit activations identifies the image with a bit vector, which identifies itwith a polyhedron in the decomposition and, in turn, identifies it with avertex in the dual graph. We identify ReLU bits that are discriminators betweennon-adversarial and adversarial images and examine how well collections ofthese discriminators can ensemble vote to build an adversarial image detector.Specifically, we examine the similarities and differences of ReLU bit vectorsfor adversarial images, and their non-adversarial counterparts, using apre-trained ResNet-50 architecture. While this paper focuses on adversarialdigital images, ResNet-50 architecture, and the ReLU activation function, ourmethods extend to other network architectures, activation functions, and typesof datasets.

Dual Graphs of Polyhedral Decompositions for the Detection of Adversarial Attacks