Adversarial examples (AEs) are images that can mislead deep neural network (DNN) classifiers via introducing slight perturbations into original images. Recent work has shown that detecting AEs can be more effective than making the DNN robust against AEs. However, the state-of-the-art AE detection shows a high false positive rate, thereby rejecting a considerable fraction of normal images, and appears easy to bypass through reverse engineering attacks. To address this issue, we propose HAWKEYE, which is a separate classifier that analyzes the output layer of the DNN and detects AEs by comparing to the output of a quantized version of the input image similar to prior work. However, instead of merely computing a simple statistic and then thresholding to detect AEs, we train a separate simple classifier to distinguish the variation characteristics of the difference between the DNN output on an input image and the quantized reference image. By using a classifier, the detection rate is higher, and thus we can cascade our AE detectors that are trained for different quantization step sizes to significantly reduce the false positive rate, while keeping the detection rate high. We provide extensive empirical evaluations of HAWKEYE under various scenarios including white-box attacks against the detector itself.