Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent

In Continual Learning settings, deep neural networks are prone to\nCatastrophic Forgetting. Orthogonal Gradient Descent was proposed to tackle the\nchallenge. However, no theoretical guarantees have been proven yet. We present\na theoretical framework to study Continual Learning algorithms in the Neural\nTangent Kernel regime. This framework comprises closed form expression of the\nmodel through tasks and proxies for Transfer Learning, generalisation and tasks\nsimilarity. In this framework, we prove that OGD is robust to Catastrophic\nForgetting then derive the first generalisation bound for SGD and OGD for\nContinual Learning. Finally, we study the limits of this framework in practice\nfor OGD and highlight the importance of the Neural Tangent Kernel variation for\nContinual Learning with OGD.\n