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.

本文介绍了一种新的激活函数 —— 超半波振荡函数（HOSC），其具有可控的锐度参数，并且相比于现有的激活函数，HOSC 更好地捕捉了输入信号的突变和锐利特征以及平滑的低频过渡。我们将 HOSC 与其他流行的激活函数进行了对比，并在多个一般任务中经验性地展示了 HOSC 所得到表示的质量的提升，并提供了 HOSC 有效性背后的数学原理以及讨论了它的局限性。