efunc: An Efficient Function Representation without Neural Networks
This addresses the practical applicability issue of neural network-based methods in function fitting for computer graphics and engineering applications, offering an incremental improvement in efficiency.
The paper tackles the problem of high-quality function approximation in computer graphics by proposing a parameter-efficient representation that eliminates neural networks, achieving comparable or superior performance to state-of-the-art methods with significantly fewer parameters and reducing computational time and memory consumption to less than 10% compared to conventional frameworks.
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.