mlsanityData to 7 Oct 2026

Towards Robust Neural Networks via Close-loop Control

arXiv 2102.01862 ↗First posted 3 Feb 2021cs.LG cs.AIcited by 23

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Abstract (arXiv)

Despite their success in massive engineering applications, deep neural networks are vulnerable to various perturbations due to their black-box nature. Recent study has shown that a deep neural network can misclassify the data even if the input data is perturbed by an imperceptible amount. In this paper, we address the robustness issue of neural networks by a novel close-loop control method from the perspective of dynamic systems. Instead of modifying the parameters in a fixed neural network architecture, a close-loop control process is added to generate control signals adaptively for the perturbed or corrupted data. We connect the robustness of neural networks with optimal control using the geometrical information of underlying data to design the control objective. The detailed analysis shows how the embedding manifolds of state trajectory affect error estimation of the proposed method. Our approach can simultaneously maintain the performance on clean data and improve the robustness against many types of data perturbations. It can also further improve the performance of robustly trained neural networks against different perturbations. To the best of our knowledge, this is the first work that improves the robustness of neural networks with close-loop control.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 25 of its 32 references that are in the map. First posted on arXiv 3 Feb 2021.

Builds on

25 of 32 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  4. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  5. 2013Intriguing properties of neural networkscited by 5,114
  6. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  7. 2015DeepFool: a simple and accurate method to fool deep neural networkscited by 1,315
  8. 2016Pixel Recurrent Neural Networkscited by 814
  9. 2014Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Imagescited by 774
  10. 2019A Survey of Deep Learning Techniques for Autonomous Drivingcited by 401
  11. 2018Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Modelscited by 362
  12. 2017Stable Architectures for Deep Neural Networkscited by 340
13 more
  1. 2017PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examplescited by 243
  2. 2017On Detecting Adversarial Perturbationscited by 232
  3. 2019You Only Propagate Once: Accelerating Adversarial Training via Maximal Principlecited by 181
  4. 2017Towards Robust Neural Networks via Random Self-ensemblecited by 158
  5. 2018An overview of deep learning in medical imaging focusing on MRIcited by 140
  6. 2017Exploring the Landscape of Spatial Robustnesscited by 81
  7. 2017Maximum Principle Based Algorithms for Deep Learningcited by 77
  8. 2018A Mean-Field Optimal Control Formulation of Deep Learningcited by 67
  9. 2018On the Geometry of Adversarial Examplescited by 43
  10. 2017The Robust Manifold Defense: Adversarial Training using Generative Modelscited by 35
  11. 2020Amata: An Annealing Mechanism for Adversarial Training Accelerationcited by 5
  12. 2020DDPNOpt: Differential Dynamic Programming Neural Optimizercited by 4
  13. 2020A Differential Game Theoretic Neural Optimizer for Training Residual Networkscited by 1

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Citing papers per year: 2022: 8; 2023: 8; 2024: 4; 2025: 3.

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  2. 2022Evaluating the Adversarial Robustness of Adaptive Test-time Defensescited by 64
  3. 2022Visual Prompting for Adversarial Robustnesscited by 33
  4. 2022On Robust Prefix-Tuning for Text Classificationcited by 15
  5. 2023A Closer Look at the Adversarial Robustness of Deep Equilibrium Modelscited by 13
  6. 2025The Achilles' Heel of LLMs: How Altering a Handful of Neurons Can Cripple Language Abilitiescited by 7
  7. 2023In Search of netUnicorn: A Data-Collection Platform to Develop Generalizable ML Models for Network Security Problemscited by 6
  8. 2022Self-Healing Robust Neural Networks via Closed-Loop Controlcited by 5
  9. 2023PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networkscited by 4
  10. 2023Continual Adversarial Defensecited by 4
  11. 2022Towards Alternative Techniques for Improving Adversarial Robustness: Analysis of Adversarial Training at a Spectrum of Perturbationscited by 3
  12. 2023Robust Feature Inference: A Test-time Defense Strategy using Spectral Projectionscited by 3
11 more
  1. 2024PID Control-Based Self-Healing to Improve the Robustness of Large Language Modelscited by 3
  2. 2024Interpretability-Guided Test-Time Adversarial Defensecited by 3
  3. 2022Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systemscited by 2
  4. 2023Dynamic ensemble selection based on Deep Neural Network Uncertainty Estimation for Adversarial Robustnesscited by 2
  5. 2024Mitigating distribution shift in machine learning-augmented hybrid simulationcited by 2
  6. 2022Test-time adversarial detection and robustness for localizing humans using ultra wide band channel impulse responsescited by 1
  7. 2023A Gradient-based Approach for Online Robust Deep Neural Network Training with Noisy Labelscited by 1
  8. 2023Asymptotically Fair Participation in Machine Learning Models: an Optimal Control Perspectivecited by 1
  9. 2024Improving Adversarial Robustness via Feature Pattern Consistency Constraintcited by 1
  10. 2025Adversarial Examples in Environment Perception for Automated Driving (Review)cited by 1
  11. 2025Robust Convolution Neural ODEs via Contractivity-promoting regularizationcited by 0