Beyond Parameter Protection: Fisher-Shaped EWC for Replay-Free Continual Learning

In replay-free continual learning, Elastic Weight Consolidation (EWC) uses Fisher information matrix (FIM) to protect acquired knowledge by penalizing changes to historically important parameters. However, a local importance estimate at the retained solution does not in general characterize sensitivity after finite parameter displacement. This motivates controlling Fisher sensitivity over a neighborhood of potential future updates. We propose Fisher-Shaped EWC (FS-EWC), which extends the role of FIM from parameter protection to solution formation for future retention. During task learning, FS-EWC minimizes the worst-case empirical FIM trace within a prescribed neighborhood, explicitly favoring solutions that are less sensitive to bounded future displacement. At task completion, trajectory-based model merging constructs the retained solution from multiple optimization states rather than a single terminal iterate, after which FIM is estimated for subsequent consolidation. Experiments across multiple benchmarks show that FS-EWC improves performance over EWC, while controlled studies indicate a more favorable stability--plasticity balance and greater tolerance to parameter drift. These results suggest that effective knowledge retention requires both forming solutions with future retention in mind and protecting acquired knowledge.