  Although CNNs are believed to be invariant to translations, recent works have
shown this is not the case, due to aliasing effects that stem from downsampling
layers. The existing architectural solutions to prevent aliasing are partial
since they do not solve these effects, that originate in non-linearities. We
propose an extended anti-aliasing method that tackles both downsampling and
non-linear layers, thus creating truly alias-free, shift-invariant CNNs. We
show that the presented model is invariant to integer as well as fractional
(i.e., sub-pixel) translations, thus outperforming other shift-invariant
methods in terms of robustness to adversarial translations.
