Normative Loss Landscape Navigation: A Trajectory-Based Approach to Mitigating Forgetting in Incremental Learning

The paper introduces TMLN (Trajectory-Modulatory Landscape Navigation), a method that treats continual learning as an optimal control problem on a curved loss landscape. It uses a diagonal empirical Fisher Information Matrix to approximate a local Riemannian manifold and dynamically modulates a preconditioner based on the network’s historical parameter trajectory. This trajectory‑based preconditioning is integrated into gradient updates to protect important parameter directions without adding explicit penalties, and experiments on class‑ and domain‑incremental benchmarks show a significant reduction in the loss barrier between tasks.

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