稀疏性、叠加与遗忘：持续学习中表示保持的机制研究
Sparsity, Superposition, and Forgetting: A Mechanistic Study of Representation Retention in Continual Learning
AI总结：
通过可控玩具框架研究持续学习中的遗忘机制，发现叠加随时间增加但任务边界处有瞬降，高稀疏性增加叠加但不必然导致遗忘，任务级有效秩随稀疏性增长。
摘要：
持续学习（CL）系统常常遗忘先前获得的知识，但由于真实数据集纠缠了许多因素，遗忘的机制在实践中难以孤立。我们提出了一个可控的玩具世界框架，使这些机制可观察和可测试。使用合成生成器-分离器流水线，我们定义了真实潜在特征，构建了具有可调稀疏性和重叠的任务，并引入了表示强度和叠加（特征间的方向重叠）的可测量量。然后，我们通过拟合保留、叠加和暴露历史之间的稀疏动态关系（通过SINDy）来研究保留动态——表示强度的时间变化。基于有效秩的互补任务级分析表征了表示能力如何在任务间分配。我们的受控实验得出三个要点。（1）叠加随时间增加，在任务边界处有瞬降，表明边界特定的干扰而非稳定漂移。（2）更高的特征稀疏性导致更多叠加，但不必然引起遗忘；当表示保持强时，尽管重叠，遗忘可以减少。（3）任务级有效秩随稀疏性增长，表明在稀疏机制下更广泛的能力使用。这些结果共同细化了常见直觉——更多叠加导致更多遗忘，通过显示重叠与表示强度和能力分配相互作用。我们的玩具分析为CL提供了可证伪的假设和诊断工具。
英文摘要：
Continual learning (CL) systems often forget previously acquired knowledge, yet the mechanisms driving forgetting remain hard to isolate in practice because real datasets entangle many factors. We present a controlled, toy-world framework that makes these mechanisms observable and testable. Using a synthetic generator-separator pipeline, we define ground-truth latent features, build tasks with tunable sparsity and overlap, and introduce measurable quantities for representation strength and superposition (directional overlap among features). We then study retention dynamics-the temporal change of representation strength by fitting sparse dynamical relations (via SINDy) between retention, superposition, and exposure history. A complementary task-level analysis based on effective rank characterizes how representational capacity is allocated across tasks. Our controlled experiments yield three takeaways. (1) Superposition tends to increase over time with transient dips at task boundaries, suggesting boundary-specific interference rather than steady drift. (2) Higher feature sparsity induces more superposition yet does not inevitably cause forgetting; when representations remain strong, forgetting can be reduced despite overlap. (3) Task-level effective rank grows with sparsity, indicating broader capacity usage under sparse regimes. Together, these results nuance the common intuition that more superposition leads to more forgetting by showing that overlap interacts with representation strength and capacity allocation. Our toy analysis provides falsifiable hypotheses and diagnostic tools for CL.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
