# 3DVerifier: Efficient Robustness Verification for 3D Point Cloud Models

arXiv: https://arxiv.org/abs/2207.07539 · HTML: https://mlsanity.com/paper/2207.07539/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 15 Jul 2022.

## Builds on (most cited first, 30 of 34)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Multi-View 3D Object Detection Network for Autonomous Driving](https://mlsanity.com/paper/1611.07759/) (2016)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Deep Continuous Fusion for Multi-Sensor 3D Object Detection](https://mlsanity.com/paper/2012.10992/) (2020)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Generating 3D Adversarial Point Clouds](https://mlsanity.com/paper/1809.07016/) (2018)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks](https://mlsanity.com/paper/1902.08722/) (2019)
- [Extending Adversarial Attacks and Defenses to Deep 3D Point Cloud Classifiers](https://mlsanity.com/paper/1901.03006/) (2019)
- [Shape Completion Enabled Robotic Grasping](https://mlsanity.com/paper/1609.08546/) (2016)
- [Robustness Verification for Transformers](https://mlsanity.com/paper/2002.06622/) (2020)
- [Adversarial Attack and Defense on Point Sets](https://mlsanity.com/paper/1902.10899/) (2019)
- [Adversarial Objects Against LiDAR-Based Autonomous Driving Systems](https://mlsanity.com/paper/1907.05418/) (2019)
- [Robustness of 3D Deep Learning in an Adversarial Setting](https://mlsanity.com/paper/1904.00923/) (2019)
- [CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networks](https://mlsanity.com/paper/1811.12395/) (2018)
- [On Isometry Robustness of Deep 3D Point Cloud Models under Adversarial Attacks](https://mlsanity.com/paper/2002.12222/) (2020)
- [Enhancing Adversarial Training with Second-Order Statistics of Weights](https://mlsanity.com/paper/2203.06020/) (2022)
- [How does Weight Correlation Affect the Generalisation Ability of Deep Neural Networks](https://mlsanity.com/paper/2010.05983/) (2020)
- [ShapeAdv: Generating Shape-Aware Adversarial 3D Point Clouds](https://mlsanity.com/paper/2005.11626/) (2020)

## Built on by (most cited first, 5 of 5)

- [Towards Verifying the Geometric Robustness of Large-scale Neural Networks](https://mlsanity.com/paper/2301.12456/) (2023)
- [Reachability Analysis of Neural Network Control Systems](https://mlsanity.com/paper/2301.12100/) (2023)
- [Certified Policy Smoothing for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2212.11746/) (2022)
- [Reward Certification for Policy Smoothed Reinforcement Learning](https://mlsanity.com/paper/2312.06436/) (2023)
- [Model-Agnostic Reachability Analysis on Deep Neural Networks](https://mlsanity.com/paper/2304.00813/) (2023)

## Abstract (arXiv)

3D point cloud models are widely applied in safety-critical scenes, which delivers an urgent need to obtain more solid proofs to verify the robustness of models. Existing verification method for point cloud model is time-expensive and computationally unattainable on large networks. Additionally, they cannot handle the complete PointNet model with joint alignment network (JANet) that contains multiplication layers, which effectively boosts the performance of 3D models. This motivates us to design a more efficient and general framework to verify various architectures of point cloud models. The key challenges in verifying the large-scale complete PointNet models are addressed as dealing with the cross-non-linearity operations in the multiplication layers and the high computational complexity of high-dimensional point cloud inputs and added layers. Thus, we propose an efficient verification framework, 3DVerifier, to tackle both challenges by adopting a linear relaxation function to bound the multiplication layer and combining forward and backward propagation to compute the certified bounds of the outputs of the point cloud models. Our comprehensive experiments demonstrate that 3DVerifier outperforms existing verification algorithms for 3D models in terms of both efficiency and accuracy. Notably, our approach achieves an orders-of-magnitude improvement in verification efficiency for the large network, and the obtained certified bounds are also significantly tighter than the state-of-the-art verifiers. We release our tool 3DVerifier via https://github.com/TrustAI/3DVerifier for use by the community.