# Controlling Neural Level Sets

arXiv: https://arxiv.org/abs/1905.11911 · HTML: https://mlsanity.com/paper/1905.11911/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 30 of 76)

- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [OmniObject3D: Large-Vocabulary 3D Object Dataset for Realistic Perception, Reconstruction and Generation](https://mlsanity.com/paper/2301.07525/) (2023)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [MINE: Towards Continuous Depth MPI with NeRF for Novel View Synthesis](https://mlsanity.com/paper/2103.14910/) (2021)
- [Light Field Neural Rendering](https://mlsanity.com/paper/2112.09687/) (2021)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [Voxurf: Voxel-based Efficient and Accurate Neural Surface Reconstruction](https://mlsanity.com/paper/2208.12697/) (2022)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Learning Neural Parametric Head Models](https://mlsanity.com/paper/2212.02761/) (2022)
- [Unified Implicit Neural Stylization](https://mlsanity.com/paper/2204.01943/) (2022)
- [How Deep Learning Sees the World: A Survey on Adversarial Attacks & Defenses](https://mlsanity.com/paper/2305.10862/) (2023)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Generative Occupancy Fields for 3D Surface-Aware Image Synthesis](https://mlsanity.com/paper/2111.00969/) (2021)
- [Signal Processing for Implicit Neural Representations](https://mlsanity.com/paper/2210.08772/) (2022)
- [Practical Evaluation of Adversarial Robustness via Adaptive Auto Attack](https://mlsanity.com/paper/2203.05154/) (2022)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [DrapeNet: Garment Generation and Self-Supervised Draping](https://mlsanity.com/paper/2211.11277/) (2022)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Exploring and Exploiting Decision Boundary Dynamics for Adversarial Robustness](https://mlsanity.com/paper/2302.03015/) (2023)
- [PartNeRF: Generating Part-Aware Editable 3D Shapes without 3D Supervision](https://mlsanity.com/paper/2303.09554/) (2023)
- [DISCO: Adversarial Defense with Local Implicit Functions](https://mlsanity.com/paper/2212.05630/) (2022)
- [NeuralHDHair: Automatic High-fidelity Hair Modeling from a Single Image Using Implicit Neural Representations](https://mlsanity.com/paper/2205.04175/) (2022)
- [AI-Generated Content (AIGC) for Various Data Modalities: A Survey](https://mlsanity.com/paper/2308.14177/) (2023)
- [LAFEAT: Piercing Through Adversarial Defenses with Latent Features](https://mlsanity.com/paper/2104.09284/) (2021)
- [NeuSample: Neural Sample Field for Efficient View Synthesis](https://mlsanity.com/paper/2111.15552/) (2021)
- [Pixel2Mesh++: 3D Mesh Generation and Refinement from Multi-View Images](https://mlsanity.com/paper/2204.09866/) (2022)
- [Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs](https://mlsanity.com/paper/2105.04404/) (2021)

## Abstract (arXiv)

The level sets of neural networks represent fundamental properties such as decision boundaries of classifiers and are used to model non-linear manifold data such as curves and surfaces. Thus, methods for controlling the neural level sets could find many applications in machine learning. In this paper we present a simple and scalable approach to directly control level sets of a deep neural network. Our method consists of two parts: (i) sampling of the neural level sets, and (ii) relating the samples' positions to the network parameters. The latter is achieved by a sample network that is constructed by adding a single fixed linear layer to the original network. In turn, the sample network can be used to incorporate the level set samples into a loss function of interest. We have tested our method on three different learning tasks: improving generalization to unseen data, training networks robust to adversarial attacks, and curve and surface reconstruction from point clouds. For surface reconstruction, we produce high fidelity surfaces directly from raw 3D point clouds. When training small to medium networks to be robust to adversarial attacks we obtain robust accuracy comparable to state-of-the-art methods.