Locality-based continual learning in high dimensions

Establish whether locality-based training with spline activations in Kolmogorov–Arnold Networks prevents catastrophic forgetting in realistic high-dimensional continual learning tasks; in particular, define an appropriate notion of locality in high-dimensional feature spaces and demonstrate theoretical or empirical generalization.

Background

The paper demonstrates that KANs can avoid catastrophic forgetting on a simple 1D toy task via spline locality, but acknowledges uncertainty in high-dimensional settings where locality is harder to define.

Resolving this requires formalizing locality in high dimensions and verifying that the mechanism scales to realistic continual learning scenarios.