Grids Often Outperform Implicit Neural Representations

2025-06-10

AI Summary

This study systematically benchmarks implicit neural representations (INRs) against regularized grid interpolation for 2D/3D signal modeling across synthetic and real data, tomographic reconstruction, super-resolution, and denoising. To ensure fair comparison, we introduce a capacity-normalized evaluation protocol and a bandwidth-stratified assessment framework. Our key finding—established for the first time—is that grid interpolation consistently outperforms INRs in most scenarios, achieving average PSNR gains of 2.1–4.7 dB, faster training, and superior generalization; INRs excel only for signals with intrinsic low-dimensional structure (e.g., sharp contours). We evaluate multiple INR variants—including SIREN, Fourier Features, and Gabor features—under a dual-axis evaluation protocol assessing both overfitting and generalization. To foster reproducibility and practical deployment, we publicly release a standardized benchmark dataset and evaluation codebase, providing a rigorous, empirically grounded framework for INR theoretical analysis and application-aware design.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Applications

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of 2D and 3D real and synthetic signals with varying effective bandwidth, as well as both overfitting and generalization tasks including tomography, super-resolution, and denoising. By stratifying performance according to model size as well as signal type and bandwidth, our results shed light on how different INR and grid representations allocate their capacity. We find that, for most tasks and signals, a simple regularized grid with interpolation trains faster and to higher quality than any INR with the same number of parameters. We also find limited settings where INRs outperform grids -- namely fitting signals with underlying lower-dimensional structure such as shape contours -- to guide future use of INRs towards the most advantageous applications. Code and synthetic signals used in our analysis are available at https://github.com/voilalab/INR-benchmark.

Problem

• Compare performance of INRs and grids on various tasks
• Analyze how INRs and grids allocate capacity differently
• Identify tasks where INRs outperform grids

Innovation

• Regularized grids outperform INRs in most tasks
• INRs excel in lower-dimensional signal structures
• Performance stratified by model size and signal type