RHINO: Regularizing the Hash-based Implicit Neural Representation

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.

Disorder-invariant 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:} \url{https://ezio77.github.io/DINER-website/}