HOSC: A Periodic Activation Function for Preserving Sharp Features in
  Implicit Neural Representations
Danzel Serrano Jakub Szymkowiak Przemyslaw Musialski
Recently proposed methods for implicitly representing signals such as images,
scenes, or geometries using coordinate-based neural network architectures often
do not leverage the choice of activation functions, or do so only to a limited
extent. In this paper, we introduce the Hyperbolic Oscillation function (HOSC),
a novel activation function with a controllable sharpness parameter. Unlike any
previous activations, HOSC has been specifically designed to better capture
sudden changes in the input signal, and hence sharp or acute features of the
underlying data, as well as smooth low-frequency transitions. Due to its
simplicity and modularity, HOSC offers a plug-and-play functionality that can
be easily incorporated into any existing method employing a neural network as a
way of implicitly representing a signal. We benchmark HOSC against other
popular activations in an array of general tasks, empirically showing an
improvement in the quality of obtained representations, provide the
mathematical motivation behind the efficacy of HOSC, and discuss its
limitations.