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Grounding and Enhancing Grid-based Models for Neural Fields
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Proposes a grid tangent kernel (GTK) theory for grid-based neural field models and a new grid model, MulFAGrid (multiplicative Fourier adaptive grid), that achieves state-of-the-art results on 2D image fitting, 3D SDF reconstruction, and NeRF view synthesis.
Problem
Grid-based models for neural fields are widely used but lack a systematic theoretical analysis of their optimization and generalization behavior, which hinders principled design of better models.
Approach
Defines grid tangent kernels (the covariance of model gradients w.r.t. parameters) for grid-based models, shows they stay constant during gradient-descent training so the model behaves as a linear kernel model, derives a GTK-based generalization bound, and uses these insights to design MulFAGrid with multiplicative Fourier filters, node-wise normalization, and jointly learned kernel and grid featu
Key results
- On DIV2K 2D image fitting, MulFAGrid reaches 56.19 PSNR with 119K parameters versus 54.84 for NeuRBF (128K).
- On NeRF benchmarks, MulFAGrid reaches 34.68 PSNR on SyntheticNeRF versus 34.62 for NeuRBF, and 27.22 on LLFF versus 27.05 for NeuRBF.
- On 3D SDF reconstruction, MulFAGrid achieves NAE 4.51 versus 4.93 for NeuRBF with 823K parameters.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the learned kernel with an interpolation kernel (ablation) | MulFAGrid · 2D image fitting | PSNR: 56.19 -> 48.12 | Hurt |
| remove the normalization function (ablation) | MulFAGrid · 2D image fitting | PSNR: 56.19 -> 56.01 | Hurt |
| replace Fourier features with multi-frequency sinusoidal composition (MSC) (ablation) | MulFAGrid · 2D image fitting | PSNR: 56.19 -> 55.93 | Hurt |
| replace Fourier features with SIREN features (ablation) | MulFAGrid · 2D image fitting | PSNR: 56.19 -> 51.54 | Hurt |
| replace joint optimization with decoupled learning (ablation) | MulFAGrid · 2D image fitting | PSNR: 56.19 -> 55.12 | Hurt |
Surprising findings
- Rendering speed of MulFAGrid is much lower than 3DGS, despite competitive quality with point-cloud initialization.
Limitations
- Rendering speed is much lower than 3DGS.
- Adaptive learning jointly optimizes kernel and grid parameters rather than the theoretically motivated alternating scheme.
Experimental setup
Datasets: DIV2K Kodak Pluto sampled 3D models dataset (NeuRBF) SyntheticNeRF LLFF Tanks&Temples Mip-NeRF-360 SFMB
Benchmarks: DIV2K Kodak sampled 3D models dataset SyntheticNeRF LLFF Tanks&Temples Mip-NeRF-360 SFMB
Metrics: PSNR SSIM IoU normal angular error training time parameter count
Baselines: InstantNGP NFFB NeuRBF BACON MINER PNF NGLOD DVGOv2 Plenoxels 3DGS
Builds on: neural tangent kernel Fourier features multiplicative filter networks Instant-NGP NeuRBF
Closest papers by meaning
- How Learnable Grids Recover Fine Detail in Low Dimensions: A Neural Tangent Kernel Analysis of Multigrid Parametric Encodings (ICLR 2025 · similarity 0.85)
- Learning Robust Generalizable Radiance Field with Visibility and Feature Augmented Point Representation (ICLR 2024 · similarity 0.84)
- Grids Often Outperform Implicit Neural Representation at Compressing Dense Signals (NeurIPS 2025 · similarity 0.83)
- MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representation (CVPR 2025 · similarity 0.83)
- Coordinate-Aware Modulation for Neural Fields (ICLR 2024 · similarity 0.83)
- Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains (ICML 2024 · similarity 0.83)
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