SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiability 文章

arXiv:2601.19683v2 Announce Type: replace Abstract: Multi-layer perceptrons (MLPs) are a standard tool for learning and function approximation, but they inherently produce globally smooth outputs. Consequently, they struggle to represent functions that are continuous yet intentionally non-differentiable (i.e., functions with prescribed $C^0$ sharp features) without ad hoc post-processing. We present SharpNet, a modified MLP architecture that encodes user-specified sharp features by augmenting the network with an auxiliary feature function defined as the solution to Poisson's equation with jump Neumann boundary conditions. This feature function is evaluated via an efficient local integral and is fully differentiable with respect to the feature locations, allowing us to jointly optimize both the feature locations and the MLP parameters to recover the target function or geometry.