# From ex(p) to poly: Gaussian Splatting with Polynomial Kernels

arXiv: https://arxiv.org/abs/2603.18707 · HTML: https://mlsanity.com/paper/2603.18707/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 23 of 23)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [StopThePop: Sorted Gaussian Splatting for View-Consistent Real-time Rendering](https://mlsanity.com/paper/2402.00525/) (2024)
- [Speedy-Splat: Fast 3D Gaussian Splatting with Sparse Pixels and Sparse Primitives](https://mlsanity.com/paper/2412.00578/) (2024)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [FlashGS: Efficient 3D Gaussian Splatting for Large-scale and High-resolution Rendering](https://mlsanity.com/paper/2408.07967/) (2024)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [3D-HGS: 3D Half-Gaussian Splatting](https://mlsanity.com/paper/2406.02720/) (2024)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media](https://mlsanity.com/paper/2405.15425/) (2024)
- [Beyond Gaussians: Fast and High-Fidelity 3D Splatting with Linear Kernels](https://mlsanity.com/paper/2411.12440/) (2024)
- [Quadratic Gaussian Splatting: High Quality Surface Reconstruction with Second-order Geometric Primitives](https://mlsanity.com/paper/2411.16392/) (2024)
- [Deformable Radial Kernel Splatting](https://mlsanity.com/paper/2412.11752/) (2024)
- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [AAA-Gaussians: Anti-Aliased and Artifact-Free 3D Gaussian Rendering](https://mlsanity.com/paper/2504.12811/) (2025)
- [TC-GS: A Faster Gaussian Splatting Module Utilizing Tensor Cores](https://mlsanity.com/paper/2505.24796/) (2025)
- [DisC-GS: Discontinuity-aware Gaussian Splatting](https://mlsanity.com/paper/2405.15196/) (2024)
- [GCC: A 3DGS Inference Architecture with Gaussian-Wise and Cross-Stage Conditional Processing](https://mlsanity.com/paper/2507.15300/) (2025)
- [DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions](https://mlsanity.com/paper/2501.12369/) (2025)

## Abstract (arXiv)

Recent advancements in Gaussian Splatting (3DGS) have introduced various modifications to the original kernel, resulting in significant performance improvements. However, many of these kernel changes are incompatible with existing datasets optimized for the original Gaussian kernel, presenting a challenge for widespread adoption. In this work, we address this challenge by proposing an alternative kernel that maintains compatibility with existing datasets while improving computational efficiency. Specifically, we replace the original exponential kernel with a polynomial approximation combined with a ReLU function. This modification allows for more aggressive culling of Gaussians, leading to enhanced performance across different 3DGS implementations. Our results show a notable performance improvement of 4 to 15% with negligible impact on image quality. We also provide a detailed mathematical analysis of the new kernel and discuss its potential benefits for 3DGS implementations on NPU hardware.