Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent
This work addresses the theoretical underpinnings of continual learning algorithms, which is important for researchers developing robust AI systems, though it is incremental as it builds on existing OGD methods.
The paper tackled the problem of catastrophic forgetting in continual learning by providing theoretical guarantees for Orthogonal Gradient Descent (OGD), proving its robustness and deriving the first generalization bounds for SGD and OGD in this context.
In Continual Learning settings, deep neural networks are prone to Catastrophic Forgetting. Orthogonal Gradient Descent was proposed to tackle the challenge. However, no theoretical guarantees have been proven yet. We present a theoretical framework to study Continual Learning algorithms in the Neural Tangent Kernel regime. This framework comprises closed form expression of the model through tasks and proxies for Transfer Learning, generalisation and tasks similarity. In this framework, we prove that OGD is robust to Catastrophic Forgetting then derive the first generalisation bound for SGD and OGD for Continual Learning. Finally, we study the limits of this framework in practice for OGD and highlight the importance of the Neural Tangent Kernel variation for Continual Learning with OGD.