mlsanityData to 14 Oct 2026

Training verified learners with learned verifiers

arXiv 1805.10265 ↗First posted 25 May 2018cs.LG stat.MLcited by 50

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Abstract (arXiv)

This paper proposes a new algorithmic framework, predictor-verifier training, to train neural networks that are verifiable, i.e., networks that provably satisfy some desired input-output properties. The key idea is to simultaneously train two networks: a predictor network that performs the task at hand,e.g., predicting labels given inputs, and a verifier network that computes a bound on how well the predictor satisfies the properties being verified. Both networks can be trained simultaneously to optimize a weighted combination of the standard data-fitting loss and a term that bounds the maximum violation of the property. Experiments show that not only is the predictor-verifier architecture able to train networks to achieve state of the art verified robustness to adversarial examples with much shorter training times (outperforming previous algorithms on small datasets like MNIST and SVHN), but it can also be scaled to produce the first known (to the best of our knowledge) verifiably robust networks for CIFAR-10.

Key facts. Cited by 50 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 May 2018.

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Citing papers per year: 2018: 1; 2019: 0; 2020: 0; 2021: 22; 2022: 10; 2023: 8; 2024: 5; 2025: 2; 2026: 2.

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  1. 2018Scalable agent alignment via reward modeling: a research directioncited by 447
  2. 2023Certifying LLM Safety against Adversarial Promptingcited by 266
  3. 2021Adversarial GLUE: A Multi-Task Benchmark for Robustness Evaluation of Language Modelscited by 232
  4. 2021Towards Improving Adversarial Training of NLP Modelscited by 79
  5. 2021When Does Contrastive Learning Preserve Adversarial Robustness from Pretraining to Finetuning?cited by 77
  6. 2021Certified Robustness to Text Adversarial Attacks by Randomized [MASK]cited by 57
  7. 2021Fast Certified Robust Training with Short Warmupcited by 46
  8. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  9. 2021Policy Smoothing for Provably Robust Reinforcement Learningcited by 40
  10. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  11. 2021Learning to Give Checkable Answers with Prover-Verifier Gamescited by 32
  12. 2021Defending Pre-trained Language Models from Adversarial Word Substitutions Without Performance Sacrificecited by 30
38 more
  1. 2021On Fast Adversarial Robustness Adaptation in Model-Agnostic Meta-Learningcited by 29
  2. 2021Taxonomy of Machine Learning Safety: A Survey and Primercited by 25
  3. 2022Certified Robustness Against Natural Language Attacks by Causal Interventioncited by 24
  4. 2021Achieving Model Robustness through Discrete Adversarial Trainingcited by 23
  5. 2021P-Adapters: Robustly Extracting Factual Information from Language Models with Diverse Promptscited by 22
  6. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  7. 2021Center Smoothing: Certified Robustness for Networks with Structured Outputscited by 18
  8. 2023RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletioncited by 17
  9. 2021Towards Evaluating and Training Verifiably Robust Neural Networkscited by 15
  10. 2022Robust Probabilistic Time Series Forecastingcited by 15
  11. 2024Robust Neural Information Retrieval: An Adversarial and Out-of-distribution Perspectivecited by 15
  12. 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
  13. 2021Generating Adversarial Examples with Graph Neural Networkscited by 12
  14. 2022A Unified View of SDP-based Neural Network Verification through Completely Positive Programmingcited by 12
  15. 2022UniCR: Universally Approximated Certified Robustness via Randomized Smoothingcited by 10
  16. 2021Double Perturbation: On the Robustness of Robustness and Counterfactual Bias Evaluationcited by 9
  17. 2021Neural Network Branch-and-Bound for Neural Network Verificationcited by 6
  18. 2023Optimization and Optimizers for Adversarial Robustnesscited by 6
  19. 2021Fast Training of Provably Robust Neural Networks by SinglePropcited by 5
  20. 2022On the Convergence of Certified Robust Training with Interval Bound Propagationcited by 5
  21. 2022Rethinking Textual Adversarial Defense for Pre-trained Language Modelscited by 5
  22. 2024Certified Continual Learning for Neural Network Regressioncited by 5
  23. 2022A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tablescited by 4
  24. 2022Learning Neural Networks under Input-Output Specificationscited by 3
  25. 2024RoCoIns: Enhancing Robustness of Large Language Models through Code-Style Instructionscited by 2
  26. 2024CERT-ED: Certifiably Robust Text Classification for Edit Distancecited by 2
  27. 2026Relaxation-Informed Training of Neural Network Surrogate Modelscited by 2
  28. 2021Robust Upper Bounds for Adversarial Trainingcited by 1
  29. 2022Probabilistic Inverse Modeling: An Application in Hydrologycited by 1
  30. 2023Tight Mixed-Integer Optimization Formulations for Prescriptive Treescited by 1
  31. 2023Provable Robustness for Streaming Models with a Sliding Windowcited by 1
  32. 2024MISLEAD: Manipulating Importance of Selected features for Learning Epsilon in Evasion Attack Deceptioncited by 1
  33. 2025Bridging Efficiency and Safety: Formal Verification of Neural Networks with Early Exitscited by 1
  34. 2026Learning to Optimize by Differentiable Programmingcited by 1
  35. 2021Learning Neural Models for Natural Language Processing in the Face of Distributional Shiftcited by 0
  36. 2023Learn from the Past: A Proxy Guided Adversarial Defense Framework with Self Distillation Regularizationcited by 0
  37. 2023Assurance for Deployed Continual Learning Systemscited by 0
  38. 2025TriGuard: Testing Model Safety with Attribution Entropy, Verification, and Driftcited by 0