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

2026-03-19

AI Summary

This work addresses the limited compatibility of existing Gaussian Splatting (3DGS) methods, where enhanced kernel functions often fail to generalize across original datasets. To overcome this, the authors propose a polynomial kernel fused with ReLU activation that serves as an efficient approximation to the original Gaussian kernel. This design maintains full compatibility with existing datasets while significantly improving computational efficiency and enabling more aggressive Gaussian pruning strategies. Evaluated across multiple 3DGS implementations, the method achieves performance gains of 4%–15% with negligible loss in image quality. Furthermore, its streamlined computation demonstrates strong potential for deployment on heterogeneous hardware platforms such as Neural Processing Units (NPUs).

Technology Category

• Machine Learning: Kernel Methods
• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Gaussian Splatting
• kernel compatibility
• 3DGS
• dataset compatibility
• computational efficiency

Innovation

• Gaussian Splatting
• polynomial kernel
• ReLU
• culling
• NPU acceleration