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.
Matan Atzmon (Weizmann Institute Of Science)
Niv Haim (Weizmann Institute of Science)
Lior Yariv (Weizmann Institute of Science)
Ofer Israelov (Weizmann Institute of Science)
Haggai Maron (NVIDIA Research)
I am a PhD student at the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science under the supervision of Prof. Yaron Lipman. My main fields of interest are machine learning, optimization and shape analysis. More specifically I am working on applying deep learning to irregular domains (e.g., graphs, point clouds, and surfaces) and graph/shape matching problems. I serve as a reviewer for NeurIPS, ICCV, SIGGRAPH, SIGGRAPH Asia, ACM TOG, JAIR, TVCG and SGP.