mlsanityData to 14 Oct 2026

POPQORN: Quantifying Robustness of Recurrent Neural Networks

arXiv 1905.07387 ↗First posted 17 May 2019cs.LG cs.CR cs.CVcited by 37

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Abstract (arXiv)

The vulnerability to adversarial attacks has been a critical issue for deep neural networks. Addressing this issue requires a reliable way to evaluate the robustness of a network. Recently, several methods have been developed to compute textitrobustness quantification for neural networks, namely, certified lower bounds of the minimum adversarial perturbation. Such methods, however, were devised for feed-forward networks, e.g. multi-layer perceptron or convolutional networks. It remains an open problem to quantify robustness for recurrent networks, especially LSTM and GRU. For such networks, there exist additional challenges in computing the robustness quantification, such as handling the inputs at multiple steps and the interaction between gates and states. In this work, we propose textitPOPQORN (Propagated-output Quantified Robustness for RNNs), a general algorithm to quantify robustness of RNNs, including vanilla RNNs, LSTMs, and GRUs. We demonstrate its effectiveness on different network architectures and show that the robustness quantification on individual steps can lead to new insights.

Key facts. Cited by 37 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 May 2019.

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Citing papers per year: 2021: 12; 2022: 7; 2023: 10; 2024: 3; 2025: 3; 2026: 2.

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  1. 2023A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validationcited by 93
  2. 2021On Guaranteed Optimal Robust Explanations for NLP Modelscited by 54
  3. 2022Causality-based Neural Network Repaircited by 47
  4. 2023Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attackscited by 34
  5. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  6. 2021Framing RNN as a kernel method: A neural ODE approachcited by 23
  7. 2022A Survey of Adversarial Defences and Robustness in NLPcited by 23
  8. 2021Certified Robustness to Programmable Transformations in LSTMscited by 18
  9. 2021Probabilistic Verification of Neural Networks Against Group Fairnesscited by 17
  10. 2024NLP Verification: Towards a General Methodology for Certifying Robustnesscited by 16
  11. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
  12. 2021Exploring Robust Architectures for Deep Artificial Neural Networkscited by 11
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  1. 2022LinSyn: Synthesizing Tight Linear Bounds for Arbitrary Neural Network Activation Functionscited by 10
  2. 2022Localized Randomized Smoothing for Collective Robustness Certificationcited by 10
  3. 2023TextDefense: Adversarial Text Detection based on Word Importance Entropycited by 9
  4. 2021DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splittingcited by 8
  5. 2023TextShield: Beyond Successfully Detecting Adversarial Sentences in Text Classificationcited by 8
  6. 2023Rate-Adaptive Coding Mechanism for Semantic Communications With Multi-Modal Datacited by 6
  7. 2021Fast Training of Provably Robust Neural Networks by SinglePropcited by 5
  8. 2023Repairing Deep Neural Networks Based on Behavior Imitationcited by 4
  9. 2023CertPri: Certifiable Prioritization for Deep Neural Networks via Movement Cost in Feature Spacecited by 4
  10. 2025Exact Verification of Graph Neural Networks with Incremental Constraint Solvingcited by 4
  11. 2021Robust Learning of Recurrent Neural Networks in Presence of Exogenous Noisecited by 3
  12. 2024A Certified Robust Watermark For Large Language Modelscited by 3
  13. 2022Robustness Analysis of Classification Using Recurrent Neural Networks with Perturbed Sequential Inputcited by 2
  14. 2022Tightening Robustness Verification of MaxPool-based Neural Networks via Minimizing the Over-Approximation Zonecited by 1
  15. 2023Model-Agnostic Reachability Analysis on Deep Neural Networkscited by 1
  16. 2023RNN-Guard: Certified Robustness Against Multi-frame Attacks for Recurrent Neural Networkscited by 1
  17. 2021Machine Learning and Deep Learning for Fixed-Text Keystroke Dynamicscited by 0
  18. 2021Machine Learning-Based Analysis of Free-Text Keystroke Dynamicscited by 0
  19. 2022A Domain-Theoretic Framework for Robustness Analysis of Neural Networkscited by 0
  20. 2023STR-Cert: Robustness Certification for Deep Text Recognition on Deep Learning Pipelines and Vision Transformerscited by 0
  21. 2024Towards General Robustness Verification of MaxPool-based Convolutional Neural Networks via Tightening Linear Approximationcited by 0
  22. 2025LTL Verification of Memoryful Neural Agentscited by 0
  23. 2025Tighter Truncated Rectangular Prism Approximation for RNN Robustness Verificationcited by 0
  24. 2026Probabilistic Verification of Recurrent Neural Networks for Single and Multi-Agent Reinforcement Learningcited by 0
  25. 2026Robustness Verification of Recurrent Neural Networks with Abstraction Refinementcited by 0