记忆的几何：有限时间谱灵敏度作为流匹配模型的诊断方法
The Geometry of Memorization: Finite-Time Spectral Sensitivity as a Diagnostic for Flow Matching Models
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中文总结 AI 辅助
研究连续时间生成框架中路径变形问题，提出有限时间谱灵敏度g(t)，通过跟踪状态转移矩阵奇异值揭示流几何。利用其在数据稀缺时的表现开发内部几何审计框架，能仅依内部轨迹动态检测生成记忆。
中文摘要 AI 辅助
连续时间生成框架通过优化与时间相关的速度场在基础域和目标域之间构建概率路径。理论上期望轨迹是直的，但实际网络会产生复杂的路径变形。本文提出有限时间谱灵敏度（FTSS）g(t)，一种无梯度的前向传递度量，通过跟踪状态转移矩阵的均方根奇异值来揭示流几何。在数据稀缺时，g(t)能揭示不同的几何病态：泛化模型保持稳定有效维度，而过度拟合导致谱崩溃。利用此现象开发了基于g(t)的内部几何审计框架，能仅通过内部轨迹动态检测生成记忆，无需外部成员查询或基线数据比较。
英文摘要
Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations. This paper presents the Finite-Time Spectral Sensitivity (FTSS) g(t), a gradient-free, forward-pass metric that exposes flow geometry by tracking the root-mean-square singular value of the state-transition matrix. Serving as a continuous proxy for stable rank, g(t) reveals a distinct geometric pathology under data scarcity: while generalizing models maintain stable effective dimensions, overfitting causes a spectral collapse. We leverage this structural phenomenon to develop an internal geometric audit based on g(t). Our framework detects generative memorization using purely internal trajectory dynamics, removing the need for external membership queries or baseline data comparison.
