The Stable Recovery Manifold: Geometric Principles Governing Recoverability in Continual Learning
中文标题: 稳定恢复流形：连续学习中可恢复性的几何原理
英文摘要
This paper investigates the geometric structure of recoverability in continual learning and introduces the Stable Recovery Manifold hypothesis. Using sequentially trained ResNet-18 on Split CIFAR-100, the authors define Recovery Subspace Dimensionality (k_t) as the minimum singular directions needed to retain 90% probe performance, and find it remains stable around a mean of 8.0 despite significant representational drift. Principal-angle drift between task subspaces strongly predicts recoverability (r = -0.862), and a simple geometric model explains 82.2% of recoverability variance. The results suggest catastrophic forgetting is primarily a problem of accessibility and manifold alignment, not information destruction, and that forgotten knowledge stays compactly decodable.
中文摘要
本文研究连续学习中可恢复性的几何结构，提出稳定恢复流形假设。作者在Split CIFAR-100上顺序训练ResNet-18，定义恢复子空间维度(k_t)为保持90%探测性能所需的最小奇异方向数，发现k_t均值稳定在8.0，尽管存在显著的表征漂移。任务子空间间的主角度漂移强烈预测可恢复性(r=-0.862)，简单几何模型解释82.2%的恢复性方差。结果表明灾难性遗忘主要是可访问性和流形对齐问题，而非信息摧毁，遗忘的知识仍可紧凑解码。
关键要点
Recovery Subspace Dimensionality (k_t) remains stable (mean 8.0) across sequential tasks, showing that forgotten knowledge stays compact despite representational drift.
恢复子空间维度(k_t)在多个连续任务中保持稳定（均值8.0），表明尽管表征漂移，遗忘的知识仍保持紧凑。
Principal-angle drift is a strong predictor of recoverability (r = -0.862), and a simple geometric model accounts for 82.2% of the variance in recoverability.
主角度漂移是恢复性的强预测指标（相关系数-0.862），一个简单几何模型解释了82.2%的恢复性方差。
The findings reframe catastrophic forgetting as an accessibility and manifold-alignment problem rather than permanent information loss, supporting the Stable Recovery Manifold hypothesis.
研究将灾难性遗忘重新定义为可访问性和流形对齐问题，而非永久性信息丢失，支持了稳定恢复流形假设。