揭示多分辨率哈希编码如何提升神经场表达能力
A New Perspective To Understanding Multi-resolution Hash Encoding For Neural Fields
- 从域操作视角解析哈希网格如何增强信号拟合能力
- 实验证明哈希结构通过生成线性段复制品提升表达力
- 为超参数调优提供理论依据，适合神经渲染研究者
近年来，Instant-NGP 成为神经场的最先进架构，其出色的信号拟合能力通常归功于多分辨率哈希网格结构，并被后续大量工作借鉴与改进。然而，该哈希网格为何能大幅提升神经网络性能，目前尚缺乏原理性解释。这种理解缺失导致 Instant-NGP 所伴随的大量超参数只能凭经验调优，缺乏指导原则。本文提出一种新视角——域操作，从底层机制出发，解释特征网格如何学习目标信号，并通过人为生成已有线性段的多个副本，提升神经场的表达能力。我们在精心设计的一维信号上进行了多项实验，以实证支持该观点。尽管分析主要聚焦于一维情形，但结果表明该思想可推广至高维空间。
原文摘要 · Abstract (English)
Instant-NGP has been the state-of-the-art architecture of neural fields in recent years. Its incredible signal-fitting capabilities are generally attributed to its multi-resolution hash grid structure and have been used and improved in numerous following works. However, it is unclear how and why such a hash grid structure improves the capabilities of a neural network by such great margins. A lack of principled understanding of the hash grid also implies that the large set of hyperparameters accompanying Instant-NGP could only be tuned empirically without much heuristics. To provide an intuitive explanation of the working principle of the hash grid, we propose a novel perspective, namely domain manipulation. This perspective provides a ground-up explanation of how the feature grid learns the target signal and increases the expressivity of the neural field by artificially creating multiples of pre-existing linear segments. We conducted numerous experiments on carefully constructed 1-dimensional signals to support our claims empirically and aid our illustrations. While our analysis mainly focuses on 1-dimensional signals, we show that the idea is generalizable to higher dimensions.
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