通过轨迹谱敏感度检测生成模型是否记忆数据
The Geometry of Memorization: Finite-Time Spectral Sensitivity as a Diagnostic for Flow Matching Models
- 用无梯度的谱敏感度衡量生成路径的几何结构
- 数据少时过拟合导致谱崩溃，而泛化模型保持稳定
- 仅靠内部轨迹就能发现记忆现象，无需外部数据
连续时间生成框架通过优化随时间变化的速度场，在基础分布与目标分布间构建概率路径。尽管理论最优为直线路径，实际网络却形成复杂路径变形。本文提出有限时间谱敏感度（FTSS）g(t)，一种无需梯度、仅需前向传播的指标，通过追踪状态转移矩阵的均方根奇异值来揭示流形几何。g(t)作为稳定秩的连续代理，揭示了数据稀缺下的几何病理性：泛化模型维持稳定的有效维度，而过拟合则引发谱崩溃。我们基于此结构现象构建内部几何审计框架，仅依赖内部轨迹动态即可检测生成记忆，无需外部成员查询或基线数据对比。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。