稳定恢复流形：持续学习中可恢复性的几何原理
The Stable Recovery Manifold: Geometric Principles Governing Recoverability in Continual Learning
AI总结：
通过分析Split CIFAR-100上ResNet-18的顺序学习，发现遗忘知识在表示重组后仍可紧凑解码，提出稳定恢复流形假说，表明灾难性遗忘主要是可访问性和流形对齐问题。
摘要：
灾难性遗忘通常被视为顺序学习过程中先前学习知识的破坏。基于可访问性崩溃框架，我们研究了持续学习中可恢复性的几何结构。使用Split CIFAR-100和顺序训练的ResNet-18，我们分析了十个任务上的可恢复性、表示漂移和恢复复杂度。我们引入了恢复子空间维度（k_t），即保持完整探针性能90%所需的最小奇异方向数量。与我们的可恢复性扩散假说相反，尽管存在显著的表示漂移，恢复维度在整个训练过程中保持稳定（平均k_t = 8.0）。主角度漂移强烈预测可恢复性（r = -0.862），一个简单的几何模型解释了82.2%的可恢复性方差。这些发现支持稳定恢复流形假说，表明遗忘的知识在表示重组后仍可紧凑解码。结果表明，灾难性遗忘主要是一个可访问性和流形对齐问题，而非信息破坏。
英文摘要：
Catastrophic forgetting is often viewed as the destruction of previously learned knowledge during sequential learning. Building on the Accessibility Collapse framework, we investigate the geometric structure of recoverability in continual learning. Using Split CIFAR-100 and a sequentially trained ResNet-18, we analyze recoverability, representational drift, and recovery complexity across ten tasks. We introduce Recovery Subspace Dimensionality (k_t), a measure of the minimum number of singular directions required to preserve 90 percent of full probe performance. Contrary to our Recoverability Diffusion hypothesis, recovery dimensionality remains stable throughout training (mean k_t = 8.0) despite substantial representational drift. Principal-angle drift strongly predicts recoverability (r = -0.862), and a simple geometric model explains 82.2 percent of recoverability variance. These findings support the Stable Recovery Manifold hypothesis, suggesting that forgotten knowledge remains compactly decodable despite representational reorganization. The results indicate that catastrophic forgetting is primarily an accessibility and manifold-alignment problem rather than information destruction.
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。
