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 this https URL.
Abstract (translated)
最近，隐式神经表示（INR）展示了令人印象深刻的结果，但它们的基本容量、内在偏置和扩展行为仍然缺乏深入理解。我们研究了不同种类的INRs在一系列2D和3D真实及合成信号上的表现，这些信号的有效带宽各不相同，并且还涵盖了过拟合和泛化任务，如断层成像、超分辨率处理以及去噪等。 通过根据不同模型大小、信号类型和有效带宽对性能进行分类，我们的结果揭示了不同INR和网格表示如何分配其容量。我们发现，在大多数任务和信号上，一个简单的正则化网格（带有插值功能）训练速度更快，并且能达到更高的质量，与具有相同数量参数的任何INR相比都是如此。 此外，我们也找到了一些特定情况下INRs优于网格的情况——例如拟合具有潜在低维结构的信号，如形状轮廓。这些发现可以为未来的INR应用提供指导，使其应用于最有利的应用场景中。 用于我们分析的代码和合成信号可在以下网址获取：[此链接]（请将[此链接]替换为您实际提供的URL）。
URL
https://arxiv.org/abs/2506.11139
