Controlling Neural Level Sets

Controlling Neural Level Sets

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.

控制神经水平集

神经网络的水平集表示基本属性（例如，分类器的决策边界），并用于对非线性流形数据（例如曲线和曲面）进行建模。因此，控制神经水平集的方法可以在机器学习中找到许多应用。.. 在本文中，我们提出了一种简单且可扩展的方法来直接控制深度神经网络的级别集。我们的方法包括两个部分：（i）对神经水平集进行采样，以及（ii）将样本的位置与网络参数相关联。后者是通过示例网络实现的，该示例网络是通过将单个固定线性层添加到原始网络来构建的。反过来，样本网络可用于将水平集样本合并到感兴趣的损失函数中。我们已经在三种不同的学习任务上测试了我们的方法：改进了对看不见的数据的泛化，对对抗攻击具有鲁棒性的训练网络以及从点云进行曲线和曲面重构。对于曲面重建，我们直接从原始3D点云中生成高保真曲面。 （阅读更多）