  Many contemporary studies utilize grid-based models for neural field
representation, but a systematic analysis of grid-based models is still
missing, hindering the improvement of those models. Therefore, this paper
introduces a theoretical framework for grid-based models. This framework points
out that these models' approximation and generalization behaviors are
determined by grid tangent kernels (GTK), which are intrinsic properties of
grid-based models. The proposed framework facilitates a consistent and
systematic analysis of diverse grid-based models. Furthermore, the introduced
framework motivates the development of a novel grid-based model named the
Multiplicative Fourier Adaptive Grid (MulFAGrid). The numerical analysis
demonstrates that MulFAGrid exhibits a lower generalization bound than its
predecessors, indicating its robust generalization performance. Empirical
studies reveal that MulFAGrid achieves state-of-the-art performance in various
tasks, including 2D image fitting, 3D signed distance field (SDF)
reconstruction, and novel view synthesis, demonstrating superior representation
ability. The project website is available at
https://sites.google.com/view/cvpr24-2034-submission/home.
