Enhancing Grid-based Neural Field Models through Theoretical Analysis and Adaptive Learning

The core message of this paper is to propose a theoretical framework for grid-based neural field models, which enables a systematic analysis of their approximation and generalization behaviors. The authors introduce the concept of grid tangent kernels (GTKs) to characterize the fundamental properties of grid-based models, and leverage this framework to develop a novel grid-based model called Multiplicative Fourier Adaptive Grid (MulFAGrid) that exhibits superior representation ability compared to existing grid-based approaches.