  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.
