mlsanityData to 7 Oct 2026

Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativity

arXiv 2111.12906 ↗First posted 25 Nov 2021cs.LG cs.AI cs.SYcited by 7

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Abstract (arXiv)

Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees. Recently, some robustness certificates have appeared in the literature based on system theoretic notions. This work proposes an incremental dissipativity-based robustness certificate for neural networks in the form of a linear matrix inequality for each layer. We also propose an equivalent spectral norm bound for this certificate which is scalable to neural networks with multiple layers. We demonstrate the improved performance against adversarial attacks on a feed-forward neural network trained on MNIST and an Alexnet trained using CIFAR-10.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 26 of its 41 references that are in the map. First posted on arXiv 25 Nov 2021.

Builds on

26 of 41 references.

References · 26

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2015Domain-Adversarial Training of Neural Networkscited by 3,023
  5. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  6. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  7. 2017Ensemble Adversarial Training: Attacks and Defensescited by 833
  8. 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 675
  9. 2019Adversarial Training for Free!cited by 638
  10. 2017One pixel attack for fooling deep neural networkscited by 579
  11. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 542
  12. 2015Empirical Evaluation of Rectified Activations in Convolutional Networkcited by 515
14 more
  1. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  2. 2017Spectral Norm Regularization for Improving the Generalizability of Deep Learningcited by 178
  3. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 100
  4. 2020Training robust neural networks using Lipschitz boundscited by 98
  5. 2018The Singular Values of Convolutional Layerscited by 95
  6. 2020Lipschitz constant estimation of Neural Networks via sparse polynomial optimizationcited by 87
  7. 2019Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operatorscited by 54
  8. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  9. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 42
  10. 2021Adversarial Robustness with Semi-Infinite Constrained Learningcited by 39
  11. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
  12. 2019Cross-Entropy Loss and Low-Rank Features Have Responsibility for Adversarial Examplescited by 17
  13. 2019Robust Design of Deep Neural Networks against Adversarial Attacks based on Lyapunov Theorycited by 13
  14. 2016On the Effectiveness of Defensive Distillationcited by 6

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Cited by year

Citing papers per year: 2022: 3; 2023: 1; 2024: 2; 2025: 1.

7 papers.

  1. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 49
  2. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  3. 2022Lipschitz constant estimation for 1D convolutional neural networkscited by 13
  4. 2022Improving Adversarial Robustness via Joint Classification and Multiple Explicit Detection Classescited by 4
  5. 2024State space representations of the Roesser type for convolutional layerscited by 3
  6. 2024LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layerscited by 2
  7. 2025Robust Convolution Neural ODEs via Contractivity-promoting regularizationcited by 0