Title: CerCE: Towards Certifiable Continual Learning
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Verifiable Machine Learning, Certifiable Machine Learning, Continual Learning

Abstract: Continual Learning (CL) aims to develop models capable of learning sequentially without catastrophic forgetting of previous tasks. However, most existing approaches rely on heuristics and lack formal guarantees, limiting their applicability in safety-critical domains. We introduce Certifiable Continual LEarning (CerCE), a CL framework that provides provable certificates of non-forgetting during training. CerCE leverages Linear Relaxation Perturbation Analysis (LiRPA) to reinterpret weight updates as structured perturbations, deriving constraints that guarantee the preservation of past knowledge. We formulate CL as a constrained optimization problem and propose practical optimization strategies, including gradient projection and Lagrangian relaxation, to efficiently satisfy these certification constraints. Furthermore, we connect our approach to PAC-Bayesian generalization theory, showing that CerCE naturally leads to tighter generalization bounds and reduced memory overfitting. Experiments on standard benchmarks and safety-critical datasets demonstrate that CerCE achieves strong empirical performance while uniquely offering formal guarantees of knowledge retention, marking a significant step toward verifiable continual learning for real-world applications.

TL;DR: We propose a novel method for performing continual learning with provable certificates of non-forgetting during training