# CAPM: Fast and Robust Verification on Maxpool-based CNN via Dual Network

arXiv: https://arxiv.org/abs/2407.09550 · HTML: https://mlsanity.com/paper/2407.09550/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Builds on (most cited first, 30 of 36)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [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)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Adversarial Examples: Attacks and Defenses for Deep Learning](https://mlsanity.com/paper/1712.07107/) (2017)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Event-based Vision meets Deep Learning on Steering Prediction for Self-driving Cars](https://mlsanity.com/paper/1804.01310/) (2018)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [EAD: Elastic-Net Attacks to Deep Neural Networks via Adversarial Examples](https://mlsanity.com/paper/1709.04114/) (2017)
- [Generative Adversarial Perturbations](https://mlsanity.com/paper/1712.02328/) (2017)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (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)
- [ComDefend: An Efficient Image Compression Model to Defend Adversarial Examples](https://mlsanity.com/paper/1811.12673/) (2018)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)

## Abstract (arXiv)

This study uses CAPM (Convex Adversarial Polytope for Maxpool-based CNN) to improve the verified bound for general purpose maxpool-based convolutional neural networks (CNNs) under bounded norm adversarial perturbations. The maxpool function is decomposed as a series of ReLU functions to extend the convex relaxation technique to maxpool functions, by which the verified bound can be efficiently computed through a dual network. The experimental results demonstrate that this technique allows the state-of-the-art verification precision for maxpool-based CNNs and involves a much lower computational cost than current verification methods, such as DeepZ, DeepPoly and PRIMA. This method is also applicable to large-scale CNNs, which previous studies show to be often computationally prohibitively expensive. Under certain circumstances, CAPM is 40-times, 20-times or twice as fast and give a significantly higher verification bound (CAPM 98% vs. PRIMA 76%/DeepPoly 73%/DeepZ 8%) as compared to PRIMA/DeepPoly/DeepZ. Furthermore, we additionally present the time complexity of our algorithm as O(W2NK), where W is the maximum width of the neural network, N is the number of neurons, and K is the size of the maxpool layer's kernel.