Exemplar-Free Continual Learning for State Space Models

State-Space Models (SSMs) excel at capturing long-range dependencies with structured recurrence, making them well-suited for sequence modeling. However, their evolving internal states pose unique challenges in Continual Learning (CL). Without access to the full distribution of previous tasks, updates to the state-space dynamics become unconstrained, leading to catastrophic forgetting. To address this, we propose $\textbf{Inf-SSM}$, a geometry-aware regularization framework for CL in SSMs. It constrains state evolution via the infinite-dimensional Grassmannian of SSM observability subspaces, without requiring any exemplars from past tasks. Unlike classical CL methods that restrict weight updates, Inf-SSM directly regularizes the infinite-horizon state evolution encoded by the extended observability subspace of the SSM. We show that enforcing this regularization requires solving a matrix equation known as the Sylvester equation, which typically incurs $\mathcal{O}(n^3)$ complexity. Thus, we develop a $\mathcal{O}(n^2)$ solution by exploiting the structure and properties of SSMs. This leads to an efficient regularization mechanism that can be seamlessly integrated into existing CL methods. Comprehensive experiments on challenging benchmarks of ImageNet-R, CIFAR-100, and Caltech-256 demonstrate a significant reduction in forgetting while improving accuracy across sequential tasks.