mlsanityData to 7 Oct 2026

Robust Learning with Jacobian Regularization

arXiv 1908.02729 ↗First posted 7 Aug 2019stat.ML cs.LGcited by 127

Not on the map. Why?

Abstract (arXiv)

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.

Key facts. Cited by 127 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Aug 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 14; 2022: 31; 2023: 23; 2024: 21; 2025: 19; 2026: 19.

127 papers.

Sort:

By area:

  1. 2021Fair Mixup: Fairness via Interpolationcited by 109
  2. 2022Learning Smooth Neural Functions via Lipschitz Regularizationcited by 86
  3. 2021Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalizationcited by 83
  4. 2021Stabilizing Equilibrium Models by Jacobian Regularizationcited by 71
  5. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  6. 2022A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologiescited by 44
  7. 2022Why neural networks find simple solutions: the many regularizers of geometric complexitycited by 38
  8. 2023Why Does Little Robustness Help? A Further Step Towards Understanding Adversarial Transferabilitycited by 32
  9. 2021Noisy Feature Mixupcited by 27
  10. 2022Predicting is not Understanding: Recognizing and Addressing Underspecification in Machine Learningcited by 26
  11. 2024Emergence in non-neural models: grokking modular arithmetic via average gradient outer productcited by 26
  12. 2023Defending against Adversarial Audio via Diffusion Modelcited by 20
38 more
  1. 2023Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularizationcited by 19
  2. 2021Local Disentanglement in Variational Auto-Encoders Using Jacobian L1 Regularizationcited by 17
  3. 2022Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Biascited by 16
  4. 2023Neural Architecture Design and Robustness: A Datasetcited by 15
  5. 2023Adversarial Training Should Be Cast as a Non-Zero-Sum Gamecited by 13
  6. 2024Remaining-data-free Machine Unlearning by Suppressing Sample Contributioncited by 13
  7. 2024Nuclear Norm Regularization for Deep Learningcited by 11
  8. 2021UniDrop: A Simple yet Effective Technique to Improve Transformer without Extra Costcited by 10
  9. 2024Jacobian Regularizer-based Neural Granger Causalitycited by 9
  10. 2021Critical Initialization of Wide and Deep Neural Networks through Partial Jacobians: General Theory and Applicationscited by 8
  11. 2022Adversarially Robust Models may not Transfer Better: Sufficient Conditions for Domain Transferability from the View of Regularizationcited by 8
  12. 2023Asymmetric Certified Robustness via Feature-Convex Neural Networkscited by 8
  13. 2025Semantic Causality-Aware Vision-Based 3D Occupancy Predictioncited by 8
  14. 2021Initializing LSTM internal states via manifold learningcited by 7
  15. 2021The Geometric Occam's Razor Implicit in Deep Learningcited by 7
  16. 2023Unfolded proximal neural networks for robust image Gaussian denoisingcited by 7
  17. 2022Tikhonov Regularization is Optimal Transport Robust under Martingale Constraintscited by 6
  18. 2022On minimal variations for unsupervised representation learningcited by 6
  19. 2023On progressive sharpening, flat minima and generalisationcited by 6
  20. 2023Augment then Smooth: Reconciling Differential Privacy with Certified Robustnesscited by 6
  21. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  22. 2025State Entropy Regularization for Robust Reinforcement Learningcited by 6
  23. 2022Controlling the Complexity and Lipschitz Constant improves polynomial netscited by 5
  24. 2022Exact Spectral Norm Regularization for Neural Networkscited by 5
  25. 2022Towards an Awareness of Time Series Anomaly Detection Models' Adversarial Vulnerabilitycited by 5
  26. 2022Stabilizing Machine Learning Prediction of Dynamics: Noise and Noise-inspired Regularizationcited by 5
  27. 2022Improving Interpretability via Regularization of Neural Activation Sensitivitycited by 5
  28. 2023TempT: Temporal consistency for Test-time adaptationcited by 5
  29. 2024Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimizationcited by 5
  30. 2021Jacobian Regularization for Mitigating Universal Adversarial Perturbationscited by 4
  31. 2021Neuron with Steady Response Leads to Better Generalizationcited by 4
  32. 2022Jacobian Ensembles Improve Robustness Trade-offs to Adversarial Attackscited by 4
  33. 2022On the Interpretability of Regularisation for Neural Networks Through Model Gradient Similaritycited by 4
  34. 2022Learning Optimal Transport Between two Empirical Distributions with Normalizing Flowscited by 4
  35. 2022Regularizing Deep Neural Networks with Stochastic Estimators of Hessian Tracecited by 4
  36. 2023The R-mAtrIx Netcited by 4
  37. 2024The Impact of Geometric Complexity on Neural Collapse in Transfer Learningcited by 4
  38. 2022Engineering flexible machine learning systems by traversing functionally-invariant pathscited by 3

50 most cited of 127 All 127 (JSON)