# ReLU Fields: The Little Non-linearity That Could

arXiv: https://arxiv.org/abs/2205.10824 · HTML: https://mlsanity.com/paper/2205.10824/

## Key facts

- Cited by 87 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 22 May 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [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)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Neural Point-Based Graphics](https://mlsanity.com/paper/1906.08240/) (2019)
- [NeX: Real-time View Synthesis with Neural Basis Expansion](https://mlsanity.com/paper/2103.05606/) (2021)
- [Multi-view Supervision for Single-view Reconstruction via Differentiable Ray Consistency](https://mlsanity.com/paper/1704.06254/) (2017)
- [Escaping Plato's Cave: 3D Shape From Adversarial Rendering](https://mlsanity.com/paper/1811.11606/) (2018)
- [BlockGAN: Learning 3D Object-aware Scene Representations from Unlabelled Images](https://mlsanity.com/paper/2002.08988/) (2020)
- [ACORN: Adaptive Coordinate Networks for Neural Scene Representation](https://mlsanity.com/paper/2105.02788/) (2021)
- [MatryODShka: Real-time 6DoF Video View Synthesis using Multi-Sphere Images](https://mlsanity.com/paper/2008.06534/) (2020)

## Built on by (most cited first, 30 of 87)

- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation](https://mlsanity.com/paper/2212.00774/) (2022)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [MERF: Memory-Efficient Radiance Fields for Real-time View Synthesis in Unbounded Scenes](https://mlsanity.com/paper/2302.12249/) (2023)
- [A Hierarchical 3D Gaussian Representation for Real-Time Rendering of Very Large Datasets](https://mlsanity.com/paper/2406.12080/) (2024)
- [DiffRF: Rendering-Guided 3D Radiance Field Diffusion](https://mlsanity.com/paper/2212.01206/) (2022)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [NeRSemble: Multi-view Radiance Field Reconstruction of Human Heads](https://mlsanity.com/paper/2305.03027/) (2023)
- [Co-SLAM: Joint Coordinate and Sparse Parametric Encodings for Neural Real-Time SLAM](https://mlsanity.com/paper/2304.14377/) (2023)
- [HyperReel: High-Fidelity 6-DoF Video with Ray-Conditioned Sampling](https://mlsanity.com/paper/2301.02238/) (2023)
- [Compact 3D Scene Representation via Self-Organizing Gaussian Grids](https://mlsanity.com/paper/2312.13299/) (2023)
- [Vox-E: Text-guided Voxel Editing of 3D Objects](https://mlsanity.com/paper/2303.12048/) (2023)
- [HoloDiffusion: Training a 3D Diffusion Model using 2D Images](https://mlsanity.com/paper/2303.16509/) (2023)
- [RobustNeRF: Ignoring Distractors with Robust Losses](https://mlsanity.com/paper/2302.00833/) (2023)
- [GauFRe: Gaussian Deformation Fields for Real-time Dynamic Novel View Synthesis](https://mlsanity.com/paper/2312.11458/) (2023)
- [3DGSR: Implicit Surface Reconstruction with 3D Gaussian Splatting](https://mlsanity.com/paper/2404.00409/) (2024)
- [Adaptive Shells for Efficient Neural Radiance Field Rendering](https://mlsanity.com/paper/2311.10091/) (2023)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [GO-Surf: Neural Feature Grid Optimization for Fast, High-Fidelity RGB-D Surface Reconstruction](https://mlsanity.com/paper/2206.14735/) (2022)
- [Understanding Pure CLIP Guidance for Voxel Grid NeRF Models](https://mlsanity.com/paper/2209.15172/) (2022)
- [GeoGaussian: Geometry-aware Gaussian Splatting for Scene Rendering](https://mlsanity.com/paper/2403.11324/) (2024)
- [nerf2nerf: Pairwise Registration of Neural Radiance Fields](https://mlsanity.com/paper/2211.01600/) (2022)
- [SHAP-EDITOR: Instruction-guided Latent 3D Editing in Seconds](https://mlsanity.com/paper/2312.09246/) (2023)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [Sparse Voxels Rasterization: Real-time High-fidelity Radiance Field Rendering](https://mlsanity.com/paper/2412.04459/) (2024)
- [NeRF-Casting: Improved View-Dependent Appearance with Consistent Reflections](https://mlsanity.com/paper/2405.14871/) (2024)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [SurfelNeRF: Neural Surfel Radiance Fields for Online Photorealistic Reconstruction of Indoor Scenes](https://mlsanity.com/paper/2304.08971/) (2023)

## Abstract (arXiv)

In many recent works, multi-layer perceptions (MLPs) have been shown to be suitable for modeling complex spatially-varying functions including images and 3D scenes. Although the MLPs are able to represent complex scenes with unprecedented quality and memory footprint, this expressive power of the MLPs, however, comes at the cost of long training and inference times. On the other hand, bilinear/trilinear interpolation on regular grid based representations can give fast training and inference times, but cannot match the quality of MLPs without requiring significant additional memory. Hence, in this work, we investigate what is the smallest change to grid-based representations that allows for retaining the high fidelity result of MLPs while enabling fast reconstruction and rendering times. We introduce a surprisingly simple change that achieves this task -- simply allowing a fixed non-linearity (ReLU) on interpolated grid values. When combined with coarse to-fine optimization, we show that such an approach becomes competitive with the state-of-the-art. We report results on radiance fields, and occupancy fields, and compare against multiple existing alternatives. Code and data for the paper are available at https://geometry.cs.ucl.ac.uk/projects/2022/relu_fields.