Does Order Matter : Connecting The Law of Robustness to Robust Generalization
#Robust Generalization #Law of Robustness #Lipschitz Constant #Overparameterization #Machine Learning #Rademacher Complexity #MNIST #AI Theory
📌 Key Takeaways
- Researchers resolved the open problem connecting law of robustness to robust generalization
- They established that robust generalization doesn't change the order of Lipschitz constant required
- Experiments on MNIST confirmed theoretical predictions about scaling with dataset size
- The research provides bounds on Lipschitz constants for achieving low robust generalization error
📖 Full Retelling
Researchers Himadri Mandal, Vishnu Varadarajan, Jaee Ponde, Aritra Das, Mihir More, and Debayan Gupta published a significant machine learning paper on arXiv on February 24, 2026, that resolves an open problem connecting the law of robustness to robust generalization in artificial intelligence systems. The paper addresses a fundamental question in machine learning theory regarding the relationship between model robustness and generalization capabilities. The law of robustness states that overparameterization is necessary for models to interpolate robustly, specifically requiring the learned function to be Lipschitz, while robust generalization questions whether small robust training loss implies small robust test loss. The researchers resolved this problem by explicitly connecting these two concepts for arbitrary data distributions, introducing a novel notion of robust generalization error and converting it into a lower bound on the expected Rademacher complexity of the induced robust loss class. Through mathematical analysis and experiments on the MNIST dataset, their work demonstrates that robust generalization does not fundamentally change the order of the Lipschitz constant required for smooth interpolation, while providing practical bounds for achieving low robust generalization error.
🏷️ Themes
Machine Learning Theory, Robust AI, Mathematical Foundations
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Original Source
--> Computer Science > Machine Learning arXiv:2602.20971 [Submitted on 24 Feb 2026] Title: Does Order Matter : Connecting The Law of Robustness to Robust Generalization Authors: Himadri Mandal , Vishnu Varadarajan , Jaee Ponde , Aritra Das , Mihir More , Debayan Gupta View a PDF of the paper titled Does Order Matter : Connecting The Law of Robustness to Robust Generalization, by Himadri Mandal and 5 other authors View PDF HTML Abstract: Bubeck and Sellke (2021) pose as an open problem the connection between the law of robustness and robust generalization. The law of robustness states that overparameterization is necessary for models to interpolate robustly; in particular, robust interpolation requires the learned function to be Lipschitz. Robust generalization asks whether small robust training loss implies small robust test loss. We resolve this problem by explicitly connecting the two for arbitrary data distributions. Specifically, we introduce a nontrivial notion of robust generalization error and convert it into a lower bound on the expected Rademacher complexity of the induced robust loss class. Our bounds recover the $\Omega(n^{1/d})$ regime of Wu et al.\ (2023) and show that, up to constants, robust generalization does not change the order of the Lipschitz constant required for smooth interpolation. We conduct experiments to probe the predicted scaling with dataset size and model capacity, testing whether empirical behavior aligns more closely with the predictions of Bubeck and Sellke (2021) or Wu et al.\ (2023). For MNIST, we find that the lower-bound Lipschitz constant scales on the order predicted by Wu et al.\ (2023). Informally, to obtain low robust generalization error, the Lipschitz constant must lie in a range that we bound, and the allowable perturbation radius is linked to the Lipschitz scale. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2602.20971 [cs.LG] (or arXiv:2602.20971v1 [cs.LG] for this version) https:...
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