Multi-layer perceptrons (MLPs) are a standard tool for learning and function approximation, but they inherently yield outputs that are globally smooth. As a result, they struggle to represent functions that are continuous yet deliberately non-differentiable (i.e., with prescribed $C^0$ sharp features) without relying on ad hoc post-processing. We present SharpNet, a modified MLP architecture capable of encoding functions with user-defined sharp features by enriching the network with an auxiliary feature function, which is defined as the solution to a Poisson equation with jump Neumann boundary conditions. It is evaluated via an efficient local integral that is fully differentiable with respect to the feature locations, enabling our method to jointly optimize both the feature locations and the MLP parameters to recover the target functions/models. The $C^0$-continuity of SharpNet is precisely controllable, ensuring $C^0$-continuity at the feature locations and smoothness elsewhere. We validate SharpNet on 2D problems and 3D CAD model reconstruction, and compare it against several state-of-the-art baselines. In both types of tasks, SharpNet accurately recovers sharp edges and corners while maintaining smooth behavior away from those features, whereas existing methods tend to smooth out gradient discontinuities. Both qualitative and quantitative evaluations highlight the benefits of our approach.

翻译：多层感知机（MLP）是用于学习和函数逼近的标准工具，但其固有输出具有全局光滑性。因此，若不依赖特定的事后处理，MLP难以表示连续但刻意不可微（即具有预设$C^0$尖锐特征）的函数。本文提出SharpNet，一种改进的MLP架构，能够通过为网络引入辅助特征函数来编码具有用户定义尖锐特征的函数；该辅助函数定义为具有跳跃诺伊曼边界条件的泊松方程的解。该函数通过一个高效局部积分进行评估，该积分对特征位置完全可微，使得我们的方法能够联合优化特征位置与MLP参数以恢复目标函数/模型。SharpNet的$C^0$连续性可精确控制，确保在特征位置处满足$C^0$连续性，而在其他区域保持光滑性。我们在二维问题与三维CAD模型重建任务上验证了SharpNet，并与多种先进基线方法进行了比较。在两类任务中，SharpNet均能准确恢复尖锐边缘与角点，同时在这些特征以外的区域保持光滑行为，而现有方法往往会使梯度不连续处过度平滑。定性与定量评估均凸显了我们方法的优势。