  As an emerging type of Neural Networks (NNs), Transformers are used in many
domains ranging from Natural Language Processing to Autonomous Driving. In this
paper, we study the robustness problem of Transformers, a key characteristic as
low robustness may cause safety concerns. Specifically, we focus on
Sparsemax-based Transformers and reduce the finding of their maximum robustness
to a Mixed Integer Quadratically Constrained Programming (MIQCP) problem. We
also design two pre-processing heuristics that can be embedded in the MIQCP
encoding and substantially accelerate its solving. We then conduct experiments
using the application of Land Departure Warning to compare the robustness of
Sparsemax-based Transformers against that of the more conventional
Multi-Layer-Perceptron (MLP) NNs. To our surprise, Transformers are not
necessarily more robust, leading to profound considerations in selecting
appropriate NN architectures for safety-critical domain applications.
