Title: SharpNet: Empowering MLPs to Model Functions with Prescribed Non-differentiability

Abstract:

While Multi-layer perceptrons (MLPs) are widely utilized for function approximation and learning, their inherent nature limits them to generating globally smooth outputs. This characteristic makes it difficult for standard MLPs to represent continuous functions that possess specific, non-differentiable features (specifically, those requiring prescribed $C^0$ sharpness) without relying on ad hoc post-processing techniques. To address this limitation, we introduce SharpNet, an enhanced MLP architecture designed to incorporate user-defined sharp features. SharpNet achieves this by integrating an auxiliary feature function, which is derived as the solution to Poisson’s equation subject to jump Neumann boundary conditions. This auxiliary component is computed through an efficient local integral and remains fully differentiable concerning the positions of the features. Consequently, this design enables the simultaneous optimization of feature locations and MLP parameters to accurately reconstruct the target function or geometry. The proposed framework offers exact control over the placement of non-differentiability, ensuring the intended $C^0$ behavior at designated feature points while maintaining smoothness in all other regions. We evaluated SharpNet’s performance on both 2D tasks and 3D CAD reconstruction, benchmarking it against various state-of-the-art methods. In these experiments, SharpNet successfully reconstructed sharp edges and corners while preserving smoothness elsewhere, outperforming existing approaches that typically blur gradient discontinuities. Both qualitative assessments and quantitative metrics confirm the efficacy of our method. The project website, source code, and models are publicly accessible at https://sharpnettech.github.io.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC