Continual learning methods usually preserve old behavior by regularizing parameters, matching old outputs, or replaying previous examples. These strategies can reduce forgetting, but they do not directly specify how the latent representation should evolve. We study a narrower geometric alternative for the regime where old and new data should remain on the same latent support: continual learning as continuation of a shared manifold. We instantiate this view within Support-Preserving Manifold Assimilation (SPMA) and evaluate a geometry-preserving variant, SPMA-OG, that combines sparse replay, output distillation, relational geometry preservation, local smoothing, and chart-assignment regularization on old anchors. On representative compatible-shift CIFAR10 and Tiny-ImageNet runs, SPMA-OG improves over sparse replay baselines in old-task retention and representation-preservation metrics while remaining competitive on new-task accuracy. On a controlled synthetic atlas-manifold benchmark, it achieves near-perfect anchor-geometry preservation while also improving new-task accuracy over replay. These results provide evidence that geometry-aware anchor regularization is a useful inductive bias when continual learning should preserve a shared latent support rather than create a new one.

翻译：连续学习方法通常通过正则化参数、匹配旧输出或重放先前样本来保持旧行为。这些策略可以减少遗忘，但并未直接规定潜在表示应如何演化。我们研究了一种更狭窄的几何替代方案，适用于新旧数据应保持在相同潜在支撑上的场景：将连续学习视为共享流形的延拓。我们在支持保持流形同化（SPMA）中实例化这一观点，并评估了一种几何保持变体SPMA-OG，该变体结合了稀疏重放、输出蒸馏、关系几何保持、局部平滑以及旧锚点上的图表分配正则化。在代表性兼容偏移CIFAR10和Tiny-ImageNet实验中，SPMA-OG在旧任务保留和表示保持指标上优于稀疏重放基线，同时在新任务准确率上保持竞争力。在一个受控的合成图册流形基准测试中，它实现了近乎完美的锚点几何保持，同时在新任务准确率上相比重放有所提升。这些结果表明，当连续学习旨在保留共享潜在支撑而非创建新支撑时，几何感知的锚点正则化是一种有用的归纳偏置。