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This research introduces TMLN, a novel method for continual learning that addresses catastrophic forgetting by modeling the parameter space as a Riemannian manifold rather than applying standard Euclidean penalties. By dynamically modulating gradient updates based on historical trajectories, the approach effectively shields critical parameters without relying on additive regularization terms. The technique demonstrates significant reductions in loss barriers across incremental tasks, offering a more geometrically aware solution for non-stationary data distributions.
Normative Loss Landscape Navigation: A Trajectory-Based Approach to Mitigating Forgetting in Incremental Learning
arXiv:2609.35926v1 Announce Type: new Abstract: Continual learning models suffer from 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 (Trajectory-Modulatory Landscape Navigation), 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 our method significantly reduces the loss barrier between consecutive tasks.
Abstract:Continual learning models suffer from 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 (Trajectory-Modulatory Landscape Navigation), 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 our method significantly reduces the loss barrier between consecutive tasks.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2609.35926 [cs.LG]
(or arXiv:2609.35926v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.35926 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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