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Grids Often Outperform Implicit Neural Representation at Compressing Dense Signals
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Benchmarks INRs, hybrid, discrete (Gaussian splatting) and interpolated-grid representations on synthetic and real 2D/3D signals across model sizes, finding that a regularized grid with interpolation often matches or beats INRs at equal parameter count except for signals with lower-dimensional structure.
Problem
Representation capacity, implicit biases, and scaling behavior of implicit neural representations (INRs) relative to grids, hybrid, and discrete representations are poorly understood, especially for dense signals.
Approach
A controlled, stratified benchmark of diverse INRs, hybrid models, Gaussian splatting, and a simple interpolated grid across bandwidths, signal types, and parameter budgets, with matched parameter counts and tuned hyperparameters, showing grids are strong except for signals with low-dimensional structure.
Key results
- On 2D and 3D bandlimited signals, no INR or hybrid model reliably outperforms the interpolated grid baseline at any model size.
- GA-Planes and WIRE achieve the strongest compression on 3D Dragon occupancy and surface super-resolution at the smallest model sizes.
- The interpolated grid is the fastest model in training and inference times on the 2D Star Target, while WIRE is roughly 10x slower than the next slowest model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an interpolated grid instead of an INR or hybrid representation for 2D and 3D bandlimited signals | Signal representation · 2D and 3D Bandlimited signals, overfitting | PSNR | Helped |
| Use a simple interpolated grid with TV regularization instead of other representations | Natural 2D inverse problems · CT reconstruction, DIV2K denoising, and DIV2K super-resolution | PSNR | Helped |
| Use GA-Planes or WIRE instead of the grid for highly compressed 3D super-resolution | 3D Dragon occupancy and surface · 3D Dragon super-resolution | PSNR | Helped |
| Use an INR or hybrid representation for signals with lower-dimensional structure, such as sharp edges or surfaces | Signal representation · Synthetic shapes and 3D object fitting | PSNR | Helped |
| Use the interpolated grid instead of pure INRs for computation time | Representation methods on the 2D Star Target · 2D Star Target | training and inference time | Helped |
Surprising findings
- A simple regularized interpolated grid matches or beats most INRs and hybrid models on dense natural signals such as DIV2K images and CT scans.
- Most models show an approximate power-law relationship between bandwidth and model size on bandlimited signals.
Limitations
- Hyperparameters tuned on a single Star Target image and then reused across signals.
- Gaussian Splatting restricted to 2D signals, so 3D comparison incomplete.
- Experiments limited to a fixed signal size (~1e6 values) and a small set of images and CT slices.
Experimental setup
Datasets: DIV2K Stanford Dragon WIRE chest CT AAPM 2025 dose prediction CT slices Shepp-Logan phantom synthetic bandlimited, spheres, Sierpinski, star target signals
Benchmarks: DIV2K Stanford Dragon CT (WIRE chest slice and AAPM 2025 slices) synthetic bandlimited, spheres, Sierpinski, star target
Metrics: PSNR SSIM LPIPS IoU training time inference time
Baselines: Fourier Feature Networks SIREN WIRE GA-Planes Instant-NGP GSplat BACON
Builds on: Fourier Feature Networks SIREN WIRE Instant-NGP GA-Planes BACON gsplat
Closest papers by meaning
- Implicit Representations via Operator Learning (ICML 2024 · similarity 0.90)
- Learning Transferable Features for Implicit Neural Representations (NeurIPS 2024 · similarity 0.89)
- A sampling theory perspective on activations for implicit neural representations (ICML 2024 · similarity 0.89)
- Towards Lossless Implicit Neural Representation via Bit Plane Decomposition (CVPR 2025 · similarity 0.89)
- SINR: Sparsity Driven Compressed Implicit Neural Representations (CVPR 2025 · similarity 0.89)
- VI^3NR: Variance Informed Initialization for Implicit Neural Representations (CVPR 2025 · similarity 0.88)
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