mlsanityData to 7 Oct 2026

Towards Evaluating and Training Verifiably Robust Neural Networks

arXiv 2104.00447 ↗First posted 1 Apr 2021cs.CV cs.CR cs.LGcited by 15

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Abstract (arXiv)

Recent works have shown that interval bound propagation (IBP) can be used to train verifiably robust neural networks. Reseachers observe an intriguing phenomenon on these IBP trained networks: CROWN, a bounding method based on tight linear relaxation, often gives very loose bounds on these networks. We also observe that most neurons become dead during the IBP training process, which could hurt the representation capability of the network. In this paper, we study the relationship between IBP and CROWN, and prove that CROWN is always tighter than IBP when choosing appropriate bounding lines. We further propose a relaxed version of CROWN, linear bound propagation (LBP), that can be used to verify large networks to obtain lower verified errors than IBP. We also design a new activation function, parameterized ramp function (ParamRamp), which has more diversity of neuron status than ReLU. We conduct extensive experiments on MNIST, CIFAR-10 and Tiny-ImageNet with ParamRamp activation and achieve state-of-the-art verified robustness. Code and the appendix are available at https://github.com/ZhaoyangLyu/VerifiablyRobustNN.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 25 of its 35 references that are in the map. First posted on arXiv 1 Apr 2021.

Builds on

25 of 35 references.

References · 25

  1. 2016Densely Connected Convolutional Networkscited by 6,691
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2016Wide Residual Networkscited by 3,057
  5. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  6. 2016Aggregated Residual Transformations for Deep Neural Networkscited by 2,540
  7. 2016Adversarial examples in the physical worldcited by 1,762
  8. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  9. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  10. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  11. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  12. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
13 more
  1. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 542
  2. 2020Overfitting in adversarially robust deep learningcited by 504
  3. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  4. 2018Certified Defenses against Adversarial Examplescited by 305
  5. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  6. 2019Towards Stable and Efficient Training of Verifiably Robust Neural Networkscited by 204
  7. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  8. 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
  9. 2017Maximum Resilience of Artificial Neural Networkscited by 97
  10. 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
  11. 2018Training verified learners with learned verifierscited by 50
  12. 2018CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networkscited by 50
  13. 2019Fastened CROWN: Tightened Neural Network Robustness Certificatescited by 39

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 6; 2023: 4; 2024: 2; 2025: 1; 2026: 1.

15 papers.

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  1. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  2. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  3. 2024Quantifying and Enhancing Multi-modal Robustness with Modality Preferencecited by 16
  4. 2022Double Bubble, Toil and Trouble: Enhancing Certified Robustness through Transitivitycited by 15
  5. 2022Robust Natural Language Processing: Recent Advances, Challenges, and Future Directionscited by 9
  6. 2022InfoAT: Improving Adversarial Training Using the Information Bottleneck Principlecited by 7
  7. 2024Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errorscited by 7
  8. 2022On the Convergence of Certified Robust Training with Interval Bound Propagationcited by 5
  9. 2023OccRob: Efficient SMT-Based Occlusion Robustness Verification of Deep Neural Networkscited by 5
  10. 2023DeepBern-Nets: Taming the Complexity of Certifying Neural Networks using Bernstein Polynomial Activations and Precise Bound Propagationcited by 5
  11. 2023Et Tu Certifications: Robustness Certificates Yield Better Adversarial Examplescited by 4
  12. 2025Position: Certified Robustness Does Not (Yet) Imply Model Securitycited by 4
3 more
  1. 2022Interval Bound Interpolation for Few-shot Learning with Few Taskscited by 1
  2. 2023Boosting Verified Training for Robust Image Classifications via Abstractioncited by 1
  3. 2026Halt Fast! Early Stopping for Certified Robustnesscited by 0