"fig:"){width="6.6cm"}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         ![ *Comparison of location invariance and fragile recognition images (CIFAR-10).* FRIs are distinct from translation-based adversarial examples. (a) shows that maximum pooling makes the DNN almost entirely robust to translation by maximizing location invariance; the remaining $10\%$ of translations that do cause variation are generally at the edge of the black background and are due to edge effects (see Figure \[fig:translation\_invariance\_ext\]). By contrast, (b) shows that larger pooling sizes provide little to no robustness to slight shifts of the visible region. []{data-label="fig:pooling_invariance"}](confidence_maps/cifar_figures/shift_poolingmulti.pdf "fig:"){width="6.6cm"}
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \(a) output label changes due to                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \(b) output label changes due to shifts
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               shifts in object position                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  in visible region position
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Fragile recognition is not lack of Object Location invariance  {#sec:discussion}
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We now focus on the relationship of fragile recognition with recent works that show that DNNs are affected by small changes of the object location, scale and orientation [@Engstrom_etal_2017_NIPSW; @azulay2018deep]. The phenomenon described in previous works is referred to as lack of invariance due to affine transformations of the object. Here, we focus only on location changes, as it will allow to distinguish FRIs and these previous works.

The procedure to evaluate location invariance is the following, quoting from [@azulay2018deep]: “we embed 