mlsanityData to 14 Oct 2026

Asymmetric Certified Robustness via Feature-Convex Neural Networks

arXiv 2302.01961 ↗First posted 3 Feb 2023cs.LGcited by 8

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Abstract (arXiv)

Recent works have introduced input-convex neural networks (ICNNs) as learning models with advantageous training, inference, and generalization properties linked to their convex structure. In this paper, we propose a novel feature-convex neural network architecture as the composition of an ICNN with a Lipschitz feature map in order to achieve adversarial robustness. We consider the asymmetric binary classification setting with one "sensitive" class, and for this class we prove deterministic, closed-form, and easily-computable certified robust radii for arbitrary ℓp-norms. We theoretically justify the use of these models by characterizing their decision region geometry, extending the universal approximation theorem for ICNN regression to the classification setting, and proving a lower bound on the probability that such models perfectly fit even unstructured uniformly distributed data in sufficiently high dimensions. Experiments on Malimg malware classification and subsets of MNIST, Fashion-MNIST, and CIFAR-10 datasets show that feature-convex classifiers attain state-of-the-art certified ℓ1-radii as well as substantial ℓ2- and ℓ∞-radii while being far more computationally efficient than any competitive baseline.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 56 of its 88 references that are in the map. First posted on arXiv 3 Feb 2023.

Builds on

56 of 88 references.

References · 56

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  4. 2021Convex optimizationcited by 2,515
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  6. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,268
  7. 2016End to End Learning for Self-Driving Carscited by 1,009
  8. 2016Adversarial Machine Learning at Scalecited by 936
  9. 2014Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Imagescited by 776
  10. 2017Evasion Attacks against Machine Learning at Test Timecited by 689
  11. 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 672
  12. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 567
38 more
  1. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 546
  2. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 468
  3. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  4. 2016Input Convex Neural Networkscited by 414
  5. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 330
  6. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  7. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 255
  8. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 228
  9. 2018Adversarial Risk and the Dangers of Evaluating Against Weak Attackscited by 221
  10. 2019Optimal transport mapping via input convex neural networkscited by 206
  11. 2017Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulationcited by 185
  12. 2018Certified Adversarial Robustness with Additive Noisecited by 180
  13. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 179
  14. 2020Randomized Smoothing of All Shapes and Sizescited by 147
  15. 2019Robust Learning with Jacobian Regularizationcited by 129
  16. 2020MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radiuscited by 114
  17. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  18. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 85
  19. 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
  20. 2021Learning in High Dimension Always Amounts to Extrapolationcited by 66
  21. 2016SqueezeDet: Unified, Small, Low Power Fully Convolutional Neural Networks for Real-Time Object Detection for Autonomous Drivingcited by 55
  22. 2020Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Frameworkcited by 46
  23. 2021Adversarial Attacks for Tabular Data: Application to Fraud Detection and Imbalanced Datacited by 45
  24. 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
  25. 2022The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Resultscited by 39
  26. 2019Wasserstein Smoothing: Certified Robustness against Wasserstein Adversarial Attackscited by 25
  27. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  28. 2021ANCER: Anisotropic Certification via Sample-wise Volume Maximizationcited by 23
  29. 2018Non-Negative Networks Against Adversarial Attackscited by 20
  30. 2020A Convex Neural Network Solver for DCOPF with Generalization Guaranteescited by 17
  31. 2020The Curious Case of Convex Neural Networkscited by 16
  32. 2018CIFAR10 to Compare Visual Recognition Performance between Deep Neural Networks and Humanscited by 14
  33. 2020Tightened Convex Relaxations for Neural Network Robustness Certificationcited by 14
  34. 2018Unsupervised Learning using Pretrained CNN and Associative Memory Bankcited by 12
  35. 2020Adversarial Network Traffic: Towards Evaluating the Robustness of Deep Learning-Based Network Traffic Classificationcited by 11
  36. 2021Deep Learning Generalization and the Convex Hull of Training Setscited by 10
  37. 2020CIFAR-10 Image Classification Using Feature Ensemblescited by 6
  38. 2020A Sequential Framework Towards an Exact SDP Verification of Neural Networkscited by 6

50 most cited of 56 All 56 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 2; 2026: 1.

8 papers.

  1. 2024MixedNUTS: Training-Free Accuracy-Robustness Balance via Nonlinearly Mixed Classifierscited by 16
  2. 2023Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learningcited by 4
  3. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 3
  4. 2024Living off the Analyst: Harvesting Features from Yara Rules for Malware Detectioncited by 3
  5. 2023Tight Certified Robustness via Min-Max Representations of ReLU Neural Networkscited by 2
  6. 2025CertDW: Towards Certified Dataset Ownership Verification via Conformal Calibrationcited by 0
  7. 2025Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustnesscited by 0
  8. 2026Representation Learning for Exact Preimagescited by 0