Spectral Constraints Resolve the Stability--Plasticity Tradeoff in Continual Learning

Catastrophic forgetting remains a central obstacle in continual learning, arising from uncontrolledparameter drift under sequential task updates. We introduce a structured spectral constraint thatdecomposes stability into two complementary mechanisms: geometric protection of a task-relevantsubspace and continuous dynamical contraction within that subspace. The resulting hybrid methodcombines hard projection with soft regularization. Across repeated-seed experiments, the proposed constraint suppresses catastrophic forgetting bynearly two orders of magnitude relative to unconstrained training while preserving forward performance. Extended multi-task chains further show that the method prevents cumulative degradationacross repeated task transitions, and scaling experiments demonstrate that its advantage persistswith increasing model size. These results identify structured spectral control as a minimal andeffective resolution of the stability–plasticity dilemma. "Supplementary Material & Licensing: This preprint is accompanied by the apexfullₛuite codebase, which empirically certifies the theorems. The software implementation is provided under the Apache License 2. 0. The theoretical constructs, operator-theoretic frameworks, and mathematical architectures described herein are governed by the custom Spectral Research License (SRL), requiring explicit attribution for academic or commercial use. See attached zip file for full license texts. "