The use of Implicit Neural Representation (INR) through a hash-table has
demonstrated impressive effectiveness and efficiency in characterizing
intricate signals. However, current state-of-the-art methods exhibit
insufficient regularization, often yielding unreliable and noisy results during
interpolations. We find that this issue stems from broken gradient flow between
input coordinates and indexed hash-keys, where the chain rule attempts to model
discrete hash-keys, rather than the continuous coordinates. To tackle this
concern, we introduce RHINO, in which a continuous analytical function is
incorporated to facilitate regularization by connecting the input coordinate
and the network additionally without modifying the architecture of current
hash-based INRs. This connection ensures a seamless backpropagation of
gradients from the network's output back to the input coordinates, thereby
enhancing regularization. Our experimental results not only showcase the
broadened regularization capability across different hash-based INRs like DINER
and Instant NGP, but also across a variety of tasks such as image fitting,
representation of signed distance functions, and optimization of 5D static / 6D
dynamic neural radiance fields. Notably, RHINO outperforms current
state-of-the-art techniques in both quality and speed, affirming its
superiority.

通过引入连续的解析函数，RHINO 能够以无缺陷的反向传播从网络输出回到输入坐标，从而增强正则化，提高了多种基于哈希的隐式神经表征模型的性能。

RHINO：基于哈希的隐式神经表示的正则化

RHINO: Regularizing the Hash-based Implicit Neural Representation

Implicit neural representation (INR) characterizes the attributes of a signal
as a function of corresponding coordinates which emerges as a sharp weapon for
solving inverse problems. However, the expressive power of INR is limited by
the spectral bias in the network training. In this paper, we find that such a
frequency-related problem could be greatly solved by re-arranging the
coordinates of the input signal, for which we propose the disorder-invariant
implicit neural representation (DINER) by augmenting a hash-table to a
traditional INR backbone. Given discrete signals sharing the same histogram of
attributes and different arrangement orders, the hash-table could project the
coordinates into the same distribution for which the mapped signal can be
better modeled using the subsequent INR network, leading to significantly
alleviated spectral bias. Furthermore, the expressive power of the DINER is
determined by the width of the hash-table. Different width corresponds to
different geometrical elements in the attribute space, \textit{e.g.}, 1D curve,
2D curved-plane and 3D curved-volume when the width is set as $1$, $2$ and $3$,
respectively. More covered areas of the geometrical elements result in stronger
expressive power. Experiments not only reveal the generalization of the DINER
for different INR backbones (MLP vs. SIREN) and various tasks (image/video
representation, phase retrieval, refractive index recovery, and neural radiance
field optimization) but also show the superiority over the state-of-the-art
algorithms both in quality and speed. \textit{Project page:}
https://ezio77.github.io/DINER-website/

本研究通过对输入信号进行重新排列，提出了混沌不变的隐式神经表示（DINER）。DINER 通过将哈希表添加到传统的 INR 骨干网络中，将坐标投影到相同的分布中，在减轻频谱偏差的同时，提高了信号建模的表现力。