Scaleable input gradient regularization for adversarial robustness
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Abstract (arXiv)
In this work we revisit gradient regularization for adversarial robustness with some new ingredients. First, we derive new per-image theoretical robustness bounds based on local gradient information. These bounds strongly motivate input gradient regularization. Second, we implement a scaleable version of input gradient regularization which avoids double backpropagation: adversarially robust ImageNet models are trained in 33 hours on four consumer grade GPUs. Finally, we show experimentally and through theoretical certification that input gradient regularization is competitive with adversarial training. Moreover we demonstrate that gradient regularization does not lead to gradient obfuscation or gradient masking.
Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 May 2019.
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Citing papers per year: 2021: 10; 2022: 9; 2023: 6; 2024: 12; 2025: 6; 2026: 2.
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- 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
- 2022Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networkscited by 126
- 2021Globally-Robust Neural Networkscited by 106
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- 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
- 2022Adversarial Rademacher Complexity of Deep Neural Networkscited by 18
- 2023Adversarial robustness of amortized Bayesian inferencecited by 17
- 2024Understanding polysemanticity in neural networks through coding theorycited by 17
- 2022Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Biascited by 16
- 2022Do Perceptually Aligned Gradients Imply Adversarial Robustness?cited by 15
- 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
33 more
- 2022Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problemscited by 10
- 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learningcited by 10
- 2024PAC-Bayes-Chernoff bounds for unbounded lossescited by 9
- 2024Enhancing Adversarial Robustness in SNNs with Sparse Gradientscited by 9
- 2021On the regularized risk of distributionally robust learning over deep neural networkscited by 8
- 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimizationcited by 8
- 2021Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problemscited by 7
- 2024Defense Against Adversarial Attacks on No-Reference Image Quality Models with Gradient Norm Regularizationcited by 7
- 2022Tikhonov Regularization is Optimal Transport Robust under Martingale Constraintscited by 6
- 2024Characterizing Model Robustness via Natural Input Gradientscited by 6
- 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce itcited by 4
- 2025Robustness questions the interpretability of graph neural networks: what to do?cited by 4
- 2024MIRACLE3D: Memory-efficient Integrated Robust Approach for Continual Learning on Point Clouds via Shape Model Constructioncited by 3
- 2024TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problemscited by 3
- 2023A Practical Upper Bound for the Worst-Case Attribution Deviationscited by 2
- 2024Adversarial Attacks and Defenses in Fault Detection and Diagnosis: A Comprehensive Benchmark on the Tennessee Eastman Processcited by 2
- 2024Minimax rates of convergence for nonparametric regression under adversarial attackscited by 2
- 2021Dynamic Efficient Adversarial Training Guided by Gradient Magnitudecited by 1
- 2021Dual Head Adversarial Trainingcited by 1
- 2022Enhancing Classifier Conservativeness and Robustness by Polynomialitycited by 1
- 2022Gradient Obfuscation Checklist Test Gives a False Sense of Securitycited by 1
- 2023Can Adversarial Examples Be Parsed to Reveal Victim Model Information?cited by 1
- 2024Is Adversarial Training with Compressed Datasets Effective?cited by 1
- 2024Do Counterfactual Examples Complicate Adversarial Training?cited by 1
- 2025A Survey of Adversarial Defenses in Vision-based Systems: Categorization, Methods and Challengescited by 1
- 2021An Interpretable Neural Network for Parameter Inferencecited by 0
- 2021Improving the Behaviour of Vision Transformers with Token-consistent Stochastic Layerscited by 0
- 2023Releasing Inequality Phenomenon in ℓ∞-norm Adversarial Training via Input Gradient Distillationcited by 0
- 2025Towards Understanding the Optimization Mechanisms in Deep Learningcited by 0
- 2025Framework GNN-AID: Graph Neural Network Analysis Interpretation and Defensecited by 0
- 2025DReS: Dual Reconstruction Smoothing for Functional Regularizationcited by 0
- 2026Self-Review Reinforcement Learning (SRRL) with Cross-Episode Memory and Policy Distillationcited by 0
- 2026Dynamics to decision: A mathematical theory of Lyapunov spectra and decision boundaries in deep classifierscited by 0
- 2026Dynamics to decision: A mathematical theory of Lyapunov spectra and decision boundaries in deep classifiers30 Sep 2026
- 2026Self-Review Reinforcement Learning (SRRL) with Cross-Episode Memory and Policy Distillation6 Jul 2026
- 2025DReS: Dual Reconstruction Smoothing for Functional Regularization30 Sep 2025
- 2025Framework GNN-AID: Graph Neural Network Analysis Interpretation and Defense6 May 2025
- 2025Robustness questions the interpretability of graph neural networks: what to do?5 May 2025
- 2025Towards Understanding the Optimization Mechanisms in Deep Learning29 Mar 2025
- 2025A Survey of Adversarial Defenses in Vision-based Systems: Categorization, Methods and Challenges1 Mar 2025
- 2025Towards LLM Unlearning Resilient to Relearning Attacks: A Sharpness-Aware Minimization Perspective and Beyond7 Feb 2025
- 2024TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems9 Dec 2024
- 2024Minimax rates of convergence for nonparametric regression under adversarial attacks12 Oct 2024
- 2024MIRACLE3D: Memory-efficient Integrated Robust Approach for Continual Learning on Point Clouds via Shape Model Construction8 Oct 2024
- 2024Characterizing Model Robustness via Natural Input Gradients30 Sep 2024
33 more
- 2024Enhancing Adversarial Robustness in SNNs with Sparse Gradients30 May 2024
- 2024Do Counterfactual Examples Complicate Adversarial Training?16 Apr 2024
- 2024H-Consistency Guarantees for Regression28 Mar 2024
- 2024Adversarial Attacks and Defenses in Fault Detection and Diagnosis: A Comprehensive Benchmark on the Tennessee Eastman Process20 Mar 2024
- 2024Defense Against Adversarial Attacks on No-Reference Image Quality Models with Gradient Norm Regularization18 Mar 2024
- 2024Is Adversarial Training with Compressed Datasets Effective?8 Feb 2024
- 2024Understanding polysemanticity in neural networks through coding theory31 Jan 2024
- 2024PAC-Bayes-Chernoff bounds for unbounded losses2 Jan 2024
- 2023Adversarial robustness of amortized Bayesian inference24 May 2023
- 2023Releasing Inequality Phenomenon in ℓ∞-norm Adversarial Training via Input Gradient Distillation16 May 2023
- 2023Can Adversarial Examples Be Parsed to Reveal Victim Model Information?13 Mar 2023
- 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization7 Mar 2023
- 2023A Practical Upper Bound for the Worst-Case Attribution Deviations1 Mar 2023
- 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it9 Jan 2023
- 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning28 Nov 2022
- 2022Adversarial Rademacher Complexity of Deep Neural Networks27 Nov 2022
- 2022Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems24 Nov 2022
- 2022Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Bias6 Oct 2022
- 2022Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints4 Oct 2022
- 2022Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networks27 Jul 2022
- 2022Do Perceptually Aligned Gradients Imply Adversarial Robustness?22 Jul 2022
- 2022Gradient Obfuscation Checklist Test Gives a False Sense of Security3 Jun 2022
- 2022Enhancing Classifier Conservativeness and Robustness by Polynomiality23 Mar 2022
- 2021Improving the Behaviour of Vision Transformers with Token-consistent Stochastic Layers30 Dec 2021
- 2021The Geometry of Adversarial Training in Binary Classification26 Nov 2021
- 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems1 Nov 2021
- 2021On the regularized risk of distributionally robust learning over deep neural networks13 Sep 2021
- 2021Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problems1 Aug 2021
- 2021An Interpretable Neural Network for Parameter Inference10 Jun 2021
- 2021Learning Security Classifiers with Verified Global Robustness Properties24 May 2021
- 2021Dual Head Adversarial Training21 Apr 2021
- 2021Dynamic Efficient Adversarial Training Guided by Gradient Magnitude4 Mar 2021
- 2021Globally-Robust Neural Networks16 Feb 2021
- 2024Do Counterfactual Examples Complicate Adversarial Training?16 Apr 2024
- 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
- 2022Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networkscited by 126
- 2021Globally-Robust Neural Networkscited by 106
- 2024H-Consistency Guarantees for Regressioncited by 21
- 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
- 2022Adversarial Rademacher Complexity of Deep Neural Networkscited by 18
- 2023Adversarial robustness of amortized Bayesian inferencecited by 17
- 2024Understanding polysemanticity in neural networks through coding theorycited by 17
- 2022Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Biascited by 16
- 2022Do Perceptually Aligned Gradients Imply Adversarial Robustness?cited by 15
- 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
- 2022Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problemscited by 10
12 most cited of 43 All 43 (JSON)
- 2026Dynamics to decision: A mathematical theory of Lyapunov spectra and decision boundaries in deep classifiers30 Sep 2026
- 2026Self-Review Reinforcement Learning (SRRL) with Cross-Episode Memory and Policy Distillation6 Jul 2026
- 2025DReS: Dual Reconstruction Smoothing for Functional Regularization30 Sep 2025
- 2025Framework GNN-AID: Graph Neural Network Analysis Interpretation and Defense6 May 2025
- 2025Robustness questions the interpretability of graph neural networks: what to do?5 May 2025
- 2025Towards Understanding the Optimization Mechanisms in Deep Learning29 Mar 2025
- 2025A Survey of Adversarial Defenses in Vision-based Systems: Categorization, Methods and Challenges1 Mar 2025
- 2024TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems9 Dec 2024
- 2024Minimax rates of convergence for nonparametric regression under adversarial attacks12 Oct 2024
- 2024MIRACLE3D: Memory-efficient Integrated Robust Approach for Continual Learning on Point Clouds via Shape Model Construction8 Oct 2024
- 2024Characterizing Model Robustness via Natural Input Gradients30 Sep 2024
- 2024Enhancing Adversarial Robustness in SNNs with Sparse Gradients30 May 2024
12 newest of 43 All 43 (JSON)