mlsanityData to 7 Oct 2026

Fast SDP certification of neural networks : towards large multi-class datasets

arXiv 2607.03232 ↗First posted 3 Jul 2026math.CO stat.MLcited by 0

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Abstract (arXiv)

We present a new quadratic model for the certification problem in adversarial robustness, which simultaneously accounts for all possible target classes. Building on this model, we propose a novel semidefinite programming (SDP) relaxation for incomplete verification. A key advantage of our approach is that it certifies robustness in a single optimization, avoiding the need for a separate resolution per class. This yields a significant computational speed-up and enables scalability to large datasets with many classes. To further improve efficiency, we also propose an effective pruning strategy of active neurons, thus reducing the problem dimensionality and accelerating convergence.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 47 references that are in the map. First posted on arXiv 3 Jul 2026.

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References · 31

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  4. 2016Adversarial examples in the physical worldcited by 1,762
  5. 2015DeepFool: a simple and accurate method to fool deep neural networkscited by 1,315
  6. 2015The Limitations of Deep Learning in Adversarial Settingscited by 784
  7. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  8. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  9. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 328
  10. 2016Safety Verification of Deep Neural Networkscited by 262
  11. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  12. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
19 more
  1. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
  2. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  3. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
  4. 2020Continual Learning with Node-Importance based Adaptive Group Sparse Regularizationcited by 102
  5. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  6. 2020SoK: Certified Robustness for Deep Neural Networkscited by 100
  7. 2017Maximum Resilience of Artificial Neural Networkscited by 97
  8. 2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
  9. 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
  10. 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
  11. 2019Neural Network Branching for Neural Network Verificationcited by 45
  12. 2020Lossless Compression of Deep Neural Networkscited by 34
  13. 2024Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planescited by 33
  14. 2020On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examplescited by 14
  15. 2025SDP-CROWN: Efficient Bound Propagation for Neural Network Verification with Tightness of Semidefinite Programmingcited by 10
  16. 2021Neural Network Branch-and-Bound for Neural Network Verificationcited by 6
  17. 2022Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxationscited by 4
  18. 2024Accelerating Low-Rank Factorization-Based Semidefinite Programming Algorithms on GPUcited by 3
  19. 2025Solution-aware vs global ReLU selection: partial MILP strikes back for DNN verificationcited by 1

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