# RHINO: Regularizing the Hash-based Implicit Neural Representation

arXiv: https://arxiv.org/abs/2309.12642 · HTML: https://mlsanity.com/paper/2309.12642/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 103 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 30 of 69)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)

## Built on by (most cited first, 9 of 9)

- [Diffusion Time-step Curriculum for One Image to 3D Generation](https://mlsanity.com/paper/2404.04562/) (2024)
- [SHINOBI: Shape and Illumination using Neural Object Decomposition via BRDF Optimization In-the-wild](https://mlsanity.com/paper/2401.10171/) (2024)
- [FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation](https://mlsanity.com/paper/2407.19434/) (2024)
- [SAID-NeRF: Segmentation-AIDed NeRF for Depth Completion of Transparent Objects](https://mlsanity.com/paper/2403.19607/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Towards the Spectral bias Alleviation by Normalizations in Coordinate Networks](https://mlsanity.com/paper/2407.17834/) (2024)
- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)
- [InstantGeoAvatar: Effective Geometry and Appearance Modeling of Animatable Avatars from Monocular Video](https://mlsanity.com/paper/2411.01512/) (2024)
- [Texture-preserving implicit neural representation for Cone beam CT truncated reconstruction](https://mlsanity.com/paper/2606.06039/) (2026)

## Abstract (arXiv)

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.