  Randomized smoothing (RS) has been shown to be a fast, scalable technique for
certifying the robustness of deep neural network classifiers. However, methods
based on RS require augmenting data with large amounts of noise, which leads to
significant drops in accuracy. We propose a training-free, modified smoothing
approach, Smooth-Reduce, that leverages patching and aggregation to provide
improved classifier certificates. Our algorithm classifies overlapping patches
extracted from an input image, and aggregates the predicted logits to certify a
larger radius around the input. We study two aggregation schemes -- max and
mean -- and show that both approaches provide better certificates in terms of
certified accuracy, average certified radii and abstention rates as compared to
concurrent approaches. We also provide theoretical guarantees for such
certificates, and empirically show significant improvements over other
randomized smoothing methods that require expensive retraining. Further, we
extend our approach to videos and provide meaningful certificates for video
classifiers. A project page can be found at
https://nyu-dice-lab.github.io/SmoothReduce/
