让模型在学习新任务时保持旧数据的潜在结构，避免遗忘。
Continual Learning as Shared-Manifold Continuation Under Compatible Shift
- 以共享流形延续为核心思想，通过几何约束优化表示演化
- 在CIFAR10和Tiny-ImageNet上保留旧任务性能，同时提升表示一致性
- 适合需要稳定表征、防止灾难性遗忘的研究者
持续学习方法通常通过参数正则化、输出匹配或回放旧样本减少遗忘，但未明确潜空间如何演进。本文研究一种更窄的几何视角：当新旧数据应共享同一潜空间时，可将持续学习视为共享流形的延续。我们基于支持保持流形整合（SPMA）提出几何保真变体SPMA-OG，结合稀疏回放、输出蒸馏、关系几何保持、局部平滑及旧锚点图册正则化。在代表性兼容偏移的CIFAR10与Tiny-ImageNet实验中，SPMA-OG在旧任务保留与表示一致性指标上优于稀疏回放基线，新任务准确率仍具竞争力。在受控合成流形基准上，其近乎完美地保持锚点几何结构，并提升新任务准确率。结果表明，在需维持共享潜空间而非生成新空间的场景下，几何感知锚点正则化是一种有效的归纳偏置。
原文摘要 · Abstract (English)
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.
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