Exploring Trajectory-Based Navigation to Mitigate Forgetting

Continual learning models suffer from $\textit{catastrophic forgetting}$ when trained sequentially on non-stationary data distributions. Previously, this has been addressed through weight regularization. While preconditioning gradients offer a promising alternative to mitigate forgetting, current approaches are myopic. Conversely, standard regularization methods apply rigid, scalar Euclidean penalties that entirely ignore the underlying Riemannian geometry of the parameter space. To overcome this gap, we propose TMLN ($\textbf{T}$rajectory-$\textbf{M}$odulatory $\textbf{L}$andscape $\textbf{N}$avigation), a normative navigation policy that formalizes continual learning as an optimal control problem over a curved loss landscape. TMLN utilizes a memory-efficient diagonal empirical Fisher Information Matrix (FIM) to define a localized Riemannian manifold. To compensate for the spatial limitations of the diagonal approximation, TMLN dynamically modulates a preconditioner using the normalized historical trajectory of the network's parameter values. By integrating this trajectory-based preconditioning directly into the gradient update, we actively shield historically critical parameter directions without relying on additive penalties. Empirical evaluations on class- and domain-incremental benchmarks demonstrate that TMLN significantly outperforms existing baselines. On Split CIFAR-100, TMLN achieves an absolute improvement of over 5.51% against the strongest baseline and achieves strong performance of 77.94% on CORe50. Crucially for resource-constrained applications, TMLN secures these stability-plasticity gains with minimal computational penalty, operating at 1.07$\times$ the time of naive SGD while avoiding the prohibitive memory scaling of Kronecker-factored approaches.