The Stable Recovery Manifold: Geometric Principles Governing Recoverability in Continual Learning
English summary
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.
Chinese summary
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。
Key points
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。