are run in eight K80 NVIDIA GPUs. The exhaustive grid search takes about $5$ minutes for one image using all eight GPUs. In the following paragraphs, we report the results of the experiments.

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   ![ *Fragile recognition images (FRIs) in ImageNet.* FRIs are generally less frequent for larger regions of the image. (a) Loose shrink FRIs, which indicate the general fragility of DNNs to a slight reduction in the visible region. (b) Strict shrink FRIs, which are the equivalent to human minimal images. Shift FRIs also follow this pattern (see Figure \[fig:PctMinImgVCropSize\_ext\]). []{data-label="fig:PctMinImgVCropSize"}](imagenet_figures/loose_scale_vs_cropsize.pdf "fig:"){width="6.6cm"}   ![ *Fragile recognition images (FRIs) in ImageNet.* FRIs are generally less frequent for larger regions of the image. (a) Loose shrink FRIs, which indicate the general fragility of DNNs to a slight reduction in the visible region. (b) Strict shrink FRIs, which are the equivalent to human minimal images. Shift FRIs also follow this pattern (see Figure \[fig:PctMinImgVCropSize\_ext\]). []{data-label="fig:PctMinImgVCropSize"}](imagenet_figures/strict_scale_vs_cropsize.pdf "fig:"){width="6.6cm"}
                                                                                                                                                                                                                                               \(a) loose shrink FRIs                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \(b) strict shrink FRIs
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We evaluate how much a DNN is affected by fragile recognition by quantifying the proportion of possible image regions that are FRIs, [*i*.*e*. ]{}we quantify the amount of regions affected by a shift or shrink. 