On the Theory of Continual Learning with Gradient Descent for Neural Networks

ArXi:2510.05573v2 Announce Type: replace-cross Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of continual learning in a tractable yet representative setting. Specifically, we analyze one-hidden-layer quadratic neural networks trained by gradient descent on a sequence of XOR-cluster datasets with Gaussian noise, where different tasks correspond to clusters with orthogonal means.