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.

翻译：通过哈希表使用隐式神经表示在表征复杂信号方面展现了显著的有效性和效率。然而，当前最先进方法的正则化不足，常在插值过程中产生不可靠且带有噪声的结果。我们发现该问题源于输入坐标与索引哈希键之间的梯度流断裂，即链式法则试图建模离散的哈希键，而非连续坐标。为解决此问题，我们提出RHINO方法，其中引入连续解析函数，在不修改现有基于哈希的隐式神经表示架构的前提下，通过额外连接输入坐标与网络来促进正则化。该连接确保梯度从网络输出无缝反向传播至输入坐标，从而增强正则化效果。实验结果表明，RHINO不仅在DINER和Instant NGP等不同基于哈希的隐式神经表示中拓展了正则化能力，还在图像拟合、有符号距离函数表征、五维静态/六维动态神经辐射场优化等多种任务中表现优异。值得注意地，RHINO在质量和速度上均超越当前最先进技术，证实了其优越性。