# GNF: Gaussian Neural Fields for Multidimensional Signal Representation and Reconstruction

arXiv: https://arxiv.org/abs/2503.06762 · HTML: https://mlsanity.com/paper/2503.06762/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Builds on (most cited first, 30 of 34)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (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)
- [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)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [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)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Compressed 3D Gaussian Splatting for Accelerated Novel View Synthesis](https://mlsanity.com/paper/2401.02436/) (2023)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [HAC: Hash-grid Assisted Context for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2403.14530/) (2024)
- [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)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Reducing the Memory Footprint of 3D Gaussian Splatting](https://mlsanity.com/paper/2406.17074/) (2024)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimation](https://mlsanity.com/paper/2204.05735/) (2022)
- [TermiNeRF: Ray Termination Prediction for Efficient Neural Rendering](https://mlsanity.com/paper/2111.03643/) (2021)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [Factor Fields: A Unified Framework for Neural Fields and Beyond](https://mlsanity.com/paper/2302.01226/) (2023)
- [Multi-View Photometric Stereo: A Robust Solution and Benchmark Dataset for Spatially Varying Isotropic Materials](https://mlsanity.com/paper/2001.06659/) (2020)

## Built on by (most cited first, 2 of 2)

- [Scientific Machine Learning with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2507.22959/) (2025)
- [Recent Advances and Trends in Learning-based 3D Representations](https://mlsanity.com/paper/2606.04871/) (2026)

## Abstract (arXiv)

Neural fields have emerged as a powerful framework for representing continuous multidimensional signals such as images and videos, 3D and 4D objects and scenes, and radiance fields. While efficient, achieving high-quality representation requires the use of wide and deep neural networks. These, however, are slow to train and evaluate. Although several acceleration techniques have been proposed, they either trade memory for faster training and/or inference, rely on thousands of fitted primitives with considerable optimization time, or compromise the smooth, continuous nature of neural fields. In this paper, we introduce Gaussian Neural Fields (GNF), a novel compact neural decoder that maps learned feature grids into continuous non-linear signals, such as RGB images, Signed Distance Functions (SDFs), and radiance fields, using a single compact layer of Gaussian kernels defined in a high-dimensional feature space. Our key observation is that neurons in traditional MLPs perform simple computations, usually a dot product followed by an activation function, necessitating wide and deep MLPs or high-resolution feature grids to model complex functions. In this paper, we show that replacing MLP-based decoders with Gaussian kernels whose centers are learned features yields highly accurate representations of 2D (RGB), 3D (geometry), and 5D (radiance fields) signals with just a single layer of such kernels. This representation is highly parallelizable, operates on low-resolution grids, and trains in under 15 seconds for 3D geometry and under 11 minutes for view synthesis. GNF matches the accuracy of deep MLP-based decoders with far fewer parameters and significantly higher inference throughput.