Grounding and Enhancing Grid-based Models for Neural Fields

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 frame-work points out that these models' approximation and generalization behaviors are determined by grid tangent ker-nels (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 this link.