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Deep convolutional networks are vulnerable to image translation or shift,partly due to common down-sampling layers, e.g., max-pooling and stridedconvolution. These operations violate the Nyquist sampling rate and causealiasing. The textbook solution is low-pass filtering (blurring) beforedown-sampling, which can benefit deep networks as well. Even so, non-linearityunits, such as ReLU, often re-introduce the problem, suggesting that blurringalone may not suffice. In this work, first, we analyse deep features withFourier transform and show that Depth Adaptive Blurring is more effective, asopposed to monotonic blurring. To this end, we outline how this can replaceexisting down-sampling methods. Second, we introduce a novel activationfunction -- with a built-in low pass filter, to keep the problem fromreappearing. From experiments, we observe generalisation on other forms oftransformations and corruptions as well, e.g., rotation, scale, and noise. Weevaluate our method under three challenging settings: (1) a variety of imagetranslations; (2) adversarial attacks -- both $\ell_{p}$ bounded and unbounded;and (3) data corruptions and perturbations. In each setting, our methodachieves state-of-the-art results and improves clean accuracy on variousbenchmark datasets.

Anti-aliasing Deep Image Classifiers using Novel Depth Adaptive Blurring and Activation Function