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Adversarial Examples Detection (AED) is a crucial defense technique against adversarial attacks and has drawn increasing attention from the Natural Language Processing (NLP) community. Despite the surge of new AED methods, our studies show that existing methods heavily rely on a shortcut to achieve good performance. In other words, current search-based adversarial attacks in NLP stop once model predictions change, and thus most adversarial examples generated by those attacks are located near model decision boundaries. To surpass this shortcut and fairly evaluate AED methods, we propose to test AED methods with \textbf{F}ar \textbf{B}oundary (\textbf{FB}) adversarial examples. Existing methods show worse than random guess performance under this scenario. To overcome this limitation, we propose a new technique, \textbf{ADDMU}, \textbf{a}dversary \textbf{d}etection with \textbf{d}ata and \textbf{m}odel \textbf{u}ncertainty, which combines two types of uncertainty estimation for both regular and FB adversarial example detection. Our new method outperforms previous methods by 3.6 and 6.0 \emph{AUC} points under each scenario. Finally, our analysis shows that the two types of uncertainty provided by \textbf{ADDMU} can be leveraged to characterize adversarial examples and identify the ones that contribute most to model's robustness in adversarial training.