Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning

We investigate why deep neural networks suffer from \emph{loss of plasticity} in deep continual learning, failing to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. To characterize the necessary condition for successful training, we introduce the notion of $\tau$-trainability and show that current plasticity preserving algorithms can be unified under this framework. Targeting spectral collapse directly, we then discuss the Kronecker factored approximation of the Hessian, which motivates two regularization enhancements: maintaining high effective feature rank and applying $L2$ penalties. Experiments on continual supervised and reinforcement learning tasks confirm that combining these two regularizers effectively preserves plasticity.