maps*]{} to visually represent the result of the grid search that extracts FRIs. As shown in the FRI map of Figure \[fig:MapGeneration\], each pixel of the map indicates whether the corresponding window in the original image is an FRI. The second and third panel show a visualization of the FRI map generation process. Figure \[fig:MinImgMapEx\] shows an ImageNet image and each of its FRI maps.

Fragile Recognition Images of State-of-the-art DNNs {#sec:results}
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In this Section, we will first discuss occurrence of fragile recognition for state-of-the-art object recognition models through results based on ImageNet [@Deng_etal_2009]. Then, we analyze if data augmentation and regularization help reduce fragile recognition through experiments in CIFAR-10 [@Krizhevsky_etal_2009].

Fragile recognition images for state-of-the-art DNNs in ImageNet
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The following experiments are performed on $500$ images, randomly sampled from ImageNet’s validation set, which consists of $50,000$ images and ground-truth object bound-in boxes [@Deng_etal_2009]. The images are sampled from 10 supercategories (dog, snake, monkey, fish, vegetable, musical instrument, boat, land vehicle, drinks, furniture), each of which covers a set of ImageNet categories. Correctness is measured as top-$5$ accuracy, which is commonly used in ImageNet. FRIs are extracted for three architectures: VGG-16 [@Simonyan_etal_2015], Inception [@Szegedy_etal_2014], and ResNet [@He_etal_2016]. Experiments 