Continual learning under adversarial conditions remains an open challenge, as existing methods often sacrifice robustness, scalability, or both. We propose a new framework that integrates Interval Bound Propagation (IBP) with a hypernetwork-based architecture to enable certifiably robust continual learning across sequential tasks. Our method, SHIELD, generates task-specific model parameters via a shared hypernetwork conditioned solely on compact task embeddings, avoiding replay buffers or full model copies, and scaling efficiently over time. To further enhance robustness, we introduce Interval MixUp, a novel training strategy that blends virtual examples represented as balls centered around MixUp points. By leveraging interval arithmetic, this approach guarantees certified robustness while mitigating the wrapping effect, leading to smoother decision boundaries. We evaluate SHIELD under strong white-box adversarial attacks such as PGD and AutoAttack across multiple benchmarks. It consistently outperforms existing robust continual learning methods, achieving state-of-the-art average accuracy while maintaining both scalability and certification. These results mark a significant step toward practical and theoretically grounded continual learning in adversarial settings.
Authors: Patryk Krukowski, Lukasz Gorczyca, Piotr Helm, Kamil Ksiazek, Przemyslaw Spurek
