From Neural Collapse Geometry to Structural Memory: Preserving Decision Structure in Continual Learning

Neural collapse (NC) reveals a structured geometry that links sample representations, class prototypes, and classification decisions, providing a unified perspective on how class knowledge can be organized across learning stages. Existing NC-based continual learning methods adopt fixed or progressively expanded simplex equiangular tight frames (ETFs) as learning targets. However, specifying such a geometric target does not by itself ensure that the induced discriminative structure persists across stages; in particular, globally expanding an ETF shifts prototypes that have already been established for old classes. We propose Structure-Preserving Continual Learning (SPCL), which treats the NC-induced decision structure as structural memory—the class reference, the coordinate response, and the decision margin of the established classes—and preserves it across stages. SPCL freezes established prototypes and embeds each new task's simplex block in the orthogonal complement of the old span; distills each sample's response distribution over the frozen prototypes; and penalizes old-class margin decreases on replayed samples in the post-plasticity window, with mixed-batch feature distillation stabilizing the underlying representation. These mechanisms preserve the class references and sample-level relations anchored to them, letting structural memory persist as the label space expands. Experiments on Seq-CIFAR-100 with a total replay buffer capacity of 500 samples show that SPCL improves final average accuracy while reducing average forgetting by approximately 70% relative to ProNC under matched protocols.