regions                                                                                                                                                                                                                                                                                                                                                                                                                                                        \(b) DNN with regularization
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For data augmentation, we augment the training dataset with FRI regions of at least a given size. For regularizers, we add weight decay, dropout, and distortions (e.g. reflections, altered brightness, altered contrast). Both the data augmentation and the regularizers improve the accuracy of the DNN for the different crop sizes (Figure \[fig:accuracy\_augmentation\_ext\]). Figure \[fig:improved\_generalization\] shows results for loose shift FRIs (see Figure \[fig:improved\_generalization\_ext\] for shrink FRIs); both data augmentation and regularization have a clear impact on FRI occurrence in all cases. The largest general improvement comes for the 12-pixel region size, as data augmentation and regularization both lead to decrease of more than 12% of FRIs. For regularizers specifically, dropout provides the most individual improvement. However, all of these generalization efforts still allow a high failure rate. They are also unable to bring the FRI effect to the human level, as the DNN FRIs are indistinguishable for humans. This is further discussed in Section \[sec:Human\_recognition\_compared\_with\_DNN\_minimal\_images\].

In ImageNet, smaller region sizes lead to higher FRI occurrence. In CIFAR-10, FRI occurrence in very small regions (smaller than 20 pixels) decreases with size. This is because 12- and 16-pixel regions are prohibitively small, so the number 