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.

翻译：近期提出的基于坐标神经网络架构的隐式信号（如图像、场景或几何体）表示方法，往往未充分利用激活函数的选择，或仅有限地使用。本文提出双曲振荡函数（HOSC），一种具有可控锐度参数的新型激活函数。与以往任何激活函数不同，HOSC专门设计用于更有效捕获输入信号中的突变，从而保留数据中的尖锐或锐利特征，同时兼顾平滑的低频过渡。由于其简单性和模块化特性，HOSC具备即插即用功能，可轻松集成到任何采用神经网络进行信号隐式表示的现有方法中。我们在一系列通用任务中将HOSC与其他流行激活函数进行基准测试，实验表明其能提升表示质量。同时，我们阐述了HOSC有效性的数学原理，并讨论了其局限性。