Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like black boxes, which precludes many signal manipulation tasks. In this paper, we propose a new class of neural fields called polynomial neural fields (PNFs). The key advantage of a PNF is that it can represent a signal as a composition of a number of manipulable and interpretable components without losing the merits of neural fields representation. We develop a general theoretical framework to analyze and design PNFs. We use this framework to design Fourier PNFs, which match state-of-the-art performance in signal representation tasks that use neural fields. In addition, we empirically demonstrate that Fourier PNFs enable signal manipulation applications such as texture transfer and scale-space interpolation. Code is available at https://github.com/stevenygd/PNF.

翻译：神经场作为一种新的信号表示范式，因其能紧凑表示信号且易于优化而崭露头角。然而在多数应用中，神经场被视作黑箱，这限制了诸多信号处理任务。本文提出一类新型神经场——多项式神经场（PNFs）。PNF的核心优势在于：在不损失神经场表示性能的前提下，能将信号表示为多个可操作、可解释组分的组合。我们建立了一个通用理论框架用于分析与设计PNFs，并基于该框架设计了傅里叶多项式神经场（Fourier PNFs），其在信号表示任务中达到与最先进方法相当的性能。此外，实验表明傅里叶多项式神经场能实现纹理迁移和尺度空间插值等信号操作应用。代码见https://github.com/stevenygd/PNF。