Polynomial Neural Fields for Subband Decomposition and Manipulation
This work addresses the need for interpretable and manipulable neural fields in signal processing, offering a novel method that is incremental but enhances existing paradigms.
The paper tackles the problem of neural fields being treated as black boxes, which limits signal manipulation tasks, by proposing polynomial neural fields (PNFs) that decompose signals into manipulable components while maintaining performance, achieving state-of-the-art results in representation tasks and enabling applications like texture transfer and scale-space interpolation.
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.