mlsanityData to 14 Oct 2026

Training Safe Neural Networks with Global SDP Bounds

arXiv 2409.09687 ↗First posted 15 Sep 2024cs.LG cs.AI math.OCcited by 0

Not on the map. Why?

Abstract (arXiv)

This paper presents a novel approach to training neural networks with formal safety guarantees using semidefinite programming (SDP) for verification. Our method focuses on verifying safety over large, high-dimensional input regions, addressing limitations of existing techniques that focus on adversarial robustness bounds. We introduce an ADMM-based training scheme for an accurate neural network classifier on the Adversarial Spheres dataset, achieving provably perfect recall with input dimensions up to d=40. This work advances the development of reliable neural network verification methods for high-dimensional systems, with potential applications in safe RL policies.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 27 references that are in the map. First posted on arXiv 15 Sep 2024.

Builds on

17 of 27 references.

References · 17

  1. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 641
  2. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 445
  3. 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 187
  4. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  5. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 179
  6. 2020Neural Lyapunov Controlcited by 142
  7. 2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
  8. 2020Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programmingcited by 43
  9. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  10. 2023The Fourth International Verification of Neural Networks Competition (VNN-COMP 2023): Summary and Resultscited by 38
  11. 2023Provably Bounding Neural Network Preimagescited by 29
  12. 2017DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimizationcited by 19
5 more
  1. 2020Adversarial Training and Provable Robustness: A Tale of Two Objectivescited by 12
  2. 2022A Unified View of SDP-based Neural Network Verification through Completely Positive Programmingcited by 12
  3. 2022Sparse Polynomial Optimisation for Neural Network Verificationcited by 8
  4. 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
  5. 2021Sparse non-SOS Putinar-type Positivstellens"atzecited by 2

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2025Robustness Certificates for Neural Networks Against Data Poisoning and Evasion Attacks
  2. 2025Advancing Neural Network Verification through Hierarchical Safety Abstract Interpretation
  3. 2024Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization
  4. 2026Learning Better Certified Models from Empirically-Robust Teachers
  5. 2021Verifying Quantized Neural Networks using SMT-Based Model Checking
  6. 2024Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systems
  7. 2021Integer-arithmetic-only Certified Robustness for Quantized Neural Networks
  8. 2026Empirical Validation of the Classification-Verification Dichotomy for AI Safety Gates