efunc: An Efficient Function Representation without Neural Networks

TL;DR

This paper introduces efunc, a parameter-efficient, neural network-free function representation framework that uses polynomial interpolation with radial basis functions, achieving high-quality approximations with reduced computational resources.

Contribution

The paper presents a novel, compact function representation based on polynomials and radial basis functions, eliminating neural networks and improving efficiency in function approximation.

Findings

Achieves comparable or better performance than state-of-the-art methods

Reduces computational time and memory usage to less than 10%

Validates effectiveness on 3D signed distance functions

Abstract

Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many parameters, limiting their practical applicability. In contrast, we pursue high-quality function approximation using parameter-efficient representations that eliminate the dependency on neural networks entirely. We first propose a novel framework for continuous function modeling. Most existing works can be formulated using this framework. We then introduce a compact function representation, which is based on polynomials interpolated using radial basis functions, bypassing both neural networks and complex/hierarchical data structures. We also develop memory-efficient CUDA-optimized algorithms that reduce computational time and memory consumption to less than 10% compared to conventional automatic differentiation frameworks. Finally, we validate our representation and optimization pipeline through extensive experiments on 3D signed distance functions (SDFs). The proposed representation achieves comparable or superior performance to state-of-the-art techniques (e.g., octree/hash-grid techniques) with significantly fewer parameters.