Robust Structured Declarative Classifiers for 3D Point Clouds: Defending Adversarial Attacks with Implicit Gradients

TL;DR

This paper introduces a novel family of robust classifiers for 3D point clouds that leverage implicit gradients and bilevel optimization to significantly improve resistance against adversarial attacks, outperforming existing defenses.

Contribution

The authors propose structured declarative classifiers with implicit gradients and a bilevel optimization framework, including an efficient instantiation called Lattice Point Classifier (LPC), for robust 3D point cloud classification.

Findings

Achieves state-of-the-art robustness on ModelNet40 and ScanNet datasets.

Outperforms existing defenses like DUP-Net and IF-Defense by ~70% under JGBA attacker.

Demonstrates effectiveness of implicit gradient-based defense mechanisms.

Abstract

Deep neural networks for 3D point cloud classification, such as PointNet, have been demonstrated to be vulnerable to adversarial attacks. Current adversarial defenders often learn to denoise the (attacked) point clouds by reconstruction, and then feed them to the classifiers as input. In contrast to the literature, we propose a family of robust structured declarative classifiers for point cloud classification, where the internal constrained optimization mechanism can effectively defend adversarial attacks through implicit gradients. Such classifiers can be formulated using a bilevel optimization framework. We further propose an effective and efficient instantiation of our approach, namely, Lattice Point Classifier (LPC), based on structured sparse coding in the permutohedral lattice and 2D convolutional neural networks (CNNs) that is end-to-end trainable. We demonstrate state-of-the-art robust point cloud classification performance on ModelNet40 and ScanNet under seven different attackers. For instance, we achieve 89.51% and 83.16% test accuracy on each dataset under the recent JGBA attacker that outperforms DUP-Net and IF-Defense with PointNet by ~70%. Demo code is available at https://zhang-vislab.github.io.