  Convolutional neural networks encode images through a sequence of
convolutions, normalizations and non-linearities as well as downsampling
operations into potentially strong semantic embeddings. Yet, previous work
showed that even slight mistakes during sampling, leading to aliasing, can be
directly attributed to the networks' lack in robustness. To address such issues
and facilitate simpler and faster adversarial training, [12] recently proposed
FLC pooling, a method for provably alias-free downsampling - in theory. In this
work, we conduct a further analysis through the lens of signal processing and
find that such current pooling methods, which address aliasing in the frequency
domain, are still prone to spectral leakage artifacts. Hence, we propose
aliasing and spectral artifact-free pooling, short ASAP. While only introducing
a few modifications to FLC pooling, networks using ASAP as downsampling method
exhibit higher native robustness against common corruptions, a property that
FLC pooling was missing. ASAP also increases native robustness against
adversarial attacks on high and low resolution data while maintaining similar
clean accuracy or even outperforming the baseline.
