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

arXiv: https://arxiv.org/abs/2601.19683 · HTML: https://mlsanity.com/paper/2601.19683/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 47 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Deep Neural Networks Learn Non-Smooth Functions Effectively](https://mlsanity.com/paper/1802.04474/) (2018)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [Point2CAD: Reverse Engineering CAD Models from 3D Point Clouds](https://mlsanity.com/paper/2312.04962/) (2023)
- [TransCAD: A Hierarchical Transformer for CAD Sequence Inference from Point Clouds](https://mlsanity.com/paper/2407.12702/) (2024)
- [NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud](https://mlsanity.com/paper/2303.16465/) (2023)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)
- [Neural Shape Parsers for Constructive Solid Geometry](https://mlsanity.com/paper/1912.11393/) (2019)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)
- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [A three layer neural network can represent any multivariate function](https://mlsanity.com/paper/2012.03016/) (2020)
- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [RFEPS: Reconstructing Feature-line Equipped Polygonal Surface](https://mlsanity.com/paper/2212.03600/) (2022)
- [NURBGen: High-Fidelity Text-to-CAD Generation through LLM-Driven NURBS Modeling](https://mlsanity.com/paper/2511.06194/) (2025)
- [Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation](https://mlsanity.com/paper/2209.10191/) (2022)
- [Lifting the Winding Number: Precise Discontinuities in Neural Fields for Physics Simulation](https://mlsanity.com/paper/2502.00626/) (2025)
- [Precise Gradient Discontinuities in Neural Fields for Subspace Physics](https://mlsanity.com/paper/2505.20421/) (2025)
- [2D Neural Fields with Learned Discontinuities](https://mlsanity.com/paper/2408.00771/) (2024)
- [NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling](https://mlsanity.com/paper/2506.13050/) (2025)

## Abstract (arXiv)

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 C0 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. This construction provides precise control over where non-differentiability occurs, enforcing the desired C0 behavior at feature locations while preserving smoothness elsewhere. We validate SharpNet on 2D problems and 3D CAD reconstruction, and compare it with several state-of-the-art baselines. In both settings, SharpNet accurately recovers sharp edges and corners while remaining smooth away from them, whereas existing methods tend to blur gradient discontinuities. Qualitative and quantitative results demonstrate the effectiveness of our approach. Our project page, code and models are publicly available at https://sharpnettech.github.io.