# N-Dimensional Gaussians for Fitting of High Dimensional Functions

arXiv: https://arxiv.org/abs/2405.20067 · HTML: https://mlsanity.com/paper/2405.20067/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [NeX: Real-time View Synthesis with Neural Basis Expansion](https://mlsanity.com/paper/2103.05606/) (2021)
- [Real-time Neural Radiance Caching for Path Tracing](https://mlsanity.com/paper/2106.12372/) (2021)
- [Dr.Jit: A Just-In-Time Compiler for Differentiable Rendering](https://mlsanity.com/paper/2202.01284/) (2022)
- [Active Exploration for Neural Global Illumination of Variable Scenes](https://mlsanity.com/paper/2203.08272/) (2022)

## Built on by (most cited first, 17 of 17)

- [3D Gaussian Splatting: Survey, Technologies, Challenges, and Opportunities](https://mlsanity.com/paper/2407.17418/) (2024)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [DDGS-CT: Direction-Disentangled Gaussian Splatting for Realistic Volume Rendering](https://mlsanity.com/paper/2406.02518/) (2024)
- [6DGS: Enhanced Direction-Aware Gaussian Splatting for Volumetric Rendering](https://mlsanity.com/paper/2410.04974/) (2024)
- [Orientation-anchored Hyper-Gaussian for 4D Reconstruction from Casual Videos](https://mlsanity.com/paper/2509.23492/) (2025)
- [Anti-Aliased 2D Gaussian Splatting](https://mlsanity.com/paper/2506.11252/) (2025)
- [High-Dynamic Radar Sequence Prediction for Weather Nowcasting Using Spatiotemporal Coherent Gaussian Representation](https://mlsanity.com/paper/2502.14895/) (2025)
- [Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity for Efficient Relighting and Geometry Reconstruction](https://mlsanity.com/paper/2509.18497/) (2025)
- [Universal Beta Splatting](https://mlsanity.com/paper/2510.03312/) (2025)
- [TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting](https://mlsanity.com/paper/2506.13348/) (2025)
- [LOD-GS: Level-of-Detail-Sensitive 3D Gaussian Splatting for Detail Conserved Anti-Aliasing](https://mlsanity.com/paper/2507.00554/) (2025)
- [HyperGaussians: High-Dimensional Gaussian Splatting for High-Fidelity Animatable Face Avatars](https://mlsanity.com/paper/2507.02803/) (2025)
- [ClipGS: Clippable Gaussian Splatting for Interactive Cinematic Visualization of Volumetric Medical Data](https://mlsanity.com/paper/2507.06647/) (2025)
- [SurfSplat: Conquering Feedforward 2D Gaussian Splatting with Surface Continuity Priors](https://mlsanity.com/paper/2602.02000/) (2026)
- [3D Gaussian Point Encoders](https://mlsanity.com/paper/2511.04797/) (2025)
- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)
- [CompactSplat: Spatially Adaptive Gaussian Distribution for Feedforward Scene Reconstruction](https://mlsanity.com/paper/2610.13177/) (2026)

## Abstract (arXiv)

In the wake of many new ML-inspired approaches for reconstructing and representing high-quality 3D content, recent hybrid and explicitly learned representations exhibit promising performance and quality characteristics. However, their scaling to higher dimensions is challenging, e.g. when accounting for dynamic content with respect to additional parameters such as material properties, illumination, or time. In this paper, we tackle these challenges for an explicit representations based on Gaussian mixture models. With our solutions, we arrive at efficient fitting of compact N-dimensional Gaussian mixtures and enable efficient evaluation at render time: For fast fitting and evaluation, we introduce a high-dimensional culling scheme that efficiently bounds N-D Gaussians, inspired by Locality Sensitive Hashing. For adaptive refinement yet compact representation, we introduce a loss-adaptive density control scheme that incrementally guides the use of additional capacity towards missing details. With these tools we can for the first time represent complex appearance that depends on many input dimensions beyond position or viewing angle within a compact, explicit representation optimized in minutes and rendered in milliseconds.