SPARCL Improves Continual Learning by Mitigating Spectral Interference.

This research introduces SPARCL, a novel approach to analytic continual learning that aims to mitigate "forgetting" in AI models. While analytic continual learning methods offer an exemplar-free alternative to gradient-based approaches by using closed-form ridge updates, they still suffer from performance drift on previously learned classes. The paper identifies "spectral interference" as the root cause: new task samples can dilute the shared inverse autocorrelation operator, perturbing old-class logits even when old data isn't revisited. SPARCL addresses this by partitioning the running autocorrelation into a high-energy core and a residual complement. It then freezes the classifier components for old classes within this core subspace, updating only the residual block through recursive least squares. This method includes an optional residual random-projection expansion and provides a provable invariance guarantee for the core contribution of old logits. Evaluations across various image datasets (CIFAR-100, CUB-200, ImageNet-R, ImageNet-A) show that SPARCL significantly closes the performance gap between classical analytic learners and more complex representation matchers, while also being complementary to other sparse feature-decorrelation techniques.