Abstract:The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing defenses lack formal guarantees or rely on restrictive assumptions about the model class, attack type, extent of poisoning, or point-wise certification, limiting their practical reliability. This paper introduces a principled formal robustness certification framework that models gradient-based training as a discrete-time dynamical system (dt-DS) and formulates poisoning robustness as a formal safety verification problem. By adapting the concept of barrier certificates (BCs) from control theory, we introduce sufficient conditions to certify a robust radius ensuring that the terminal model remains safe under worst-case ${\ell}_p$-norm based poisoning. To make this practical, we parameterize BCs as neural networks trained on finite sets of poisoned trajectories. We further derive probably approximately correct (PAC) bounds by solving a scenario convex program (SCP), which yields a confidence lower bound on the certified robustness radius generalizing beyond the training set. Importantly, our framework also extends to certification against test-time attacks, making it the first unified framework to provide formal guarantees in both training and test-time attack settings. Experiments on MNIST, SVHN, and CIFAR-10 show that our approach certifies non-trivial perturbation budgets while being model-agnostic and requiring no prior knowledge of the attack or contamination level.
| Subjects: | Machine Learning (cs.LG); Systems and Control (eess.SY) |
| Cite as: | arXiv:2512.20865 [cs.LG] |
| (or arXiv:2512.20865v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2512.20865 arXiv-issued DOI via DataCite |
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| Journal reference: | IEEE Open Journal of Control Systems, 2026 |
| Related DOI: | https://doi.org/10.1109/OJCSYS.2026.3689712
DOI(s) linking to related resources |
From: Sara Taheri [view email]
[v1]
Wed, 24 Dec 2025 00:49:47 UTC (8,306 KB)
[v2]
Tue, 12 May 2026 15:04:55 UTC (3,650 KB)
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