Controlling Neural Level Sets

TL;DR

This paper introduces a scalable method to control neural network level sets, enabling applications like improved generalization, adversarial robustness, and 3D surface reconstruction by sampling and manipulating level sets through an added linear layer.

Contribution

The authors propose a novel approach that directly controls neural level sets by sampling and relating them to network parameters via a simple linear layer, applicable across various tasks.

Findings

Enhanced generalization to unseen data

Achieved robustness to adversarial attacks comparable to state-of-the-art

Produced high-fidelity 3D surface reconstructions from point clouds

Abstract

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.