On the one hand, there has been considerable progress on neural network verification in recent years, which makes certifying neural networks a possibility. On the other hand, neural networks in practice are often re-trained over time to cope with new data distribution or for solving different tasks (a.k.a. continual learning). Once re-trained, the verified correctness of the neural network is likely broken, particularly in the presence of the phenomenon known as catastrophic forgetting. In this work, we propose an approach called certified continual learning which improves existing continual learning methods by preserving, as long as possible, the established correctness properties of a verified network. Our approach is evaluated with multiple neural networks and on two different continual learning methods. The results show that our approach is efficient and the trained models preserve their certified correctness and often maintain high utility.
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