网格表示在压缩密集信号时，常比隐式神经表示更优。
Grids Often Outperform Implicit Neural Representations at Compressing Dense Signals
- 用规则网格加插值替代隐式神经表示，训练更快更稳定。
- 相同参数量下，网格在多数任务中达到更高或相当的重建质量。
- 仅在二值形状轮廓等特定场景，隐式表示才具优势。
隐式神经表示（INRs）近年来表现优异，但其基本容量、隐含偏差及缩放行为仍不清晰。本文在多种2D与3D真实和合成信号上，考察了不同INRs在不同有效带宽下的性能，涵盖过拟合与泛化任务，如断层扫描、超分辨率与去噪。通过按模型规模、信号类型与带宽分层分析，揭示了各类表示如何分配容量。结果表明：在多数涉及密集信号的任务中，简单正则化的规则网格配合插值，在相同参数量下训练更快且重建质量更高或相当；仅在二值信号（如形状轮廓）等有限场景，INRs表现优于网格，为未来开发与应用提供方向。
原文摘要 · Abstract (English)
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 many tasks involving dense signals, a simple regularized grid with interpolation trains faster and to higher or comparable quality than any INR with the same number of parameters. We also find limited settings -- namely fitting binary signals such as shape contours -- where INRs outperform grids, to guide future development and use of INRs towards the most advantageous applications.
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