发表机构
EPFL; Télécom Paris, IP Paris（洛桑联邦理工学院; 巴黎电信学院，巴黎综合理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多元时间序列异常检测，提出基于图谱概率路径的流匹配框架GRASP，通过最小化动能与图Dirichlet能量获得闭式路径，利用加权速度差异检测异常，并在四个基准上验证了优越性能。
AI 中文摘要
多元时间序列异常检测通常依赖于评估观测值与在正常数据上训练的模型输出之间的差异。另一种视角是通过生成动力学，即流匹配模型的速度场，来刻画正常数据的分布。然而，标准流匹配通常采用线性概率路径，忽略了变量间的依赖关系，导致与结构化数据分布不对齐。为解决此问题，我们提出GRASP，一种具有图谱路径的流匹配框架，用于多元时间序列异常检测。GRASP通过最小化结合动能与图Dirichlet能量的固定端点作用量，将图结构融入概率路径。该公式产生基于图频率依赖的双曲插值的闭式路径。在正常数据上训练的速度预测器随后通过聚合跨源样本、流时间和图频率的加权速度差异来检测异常。理论上，我们证明GRASP对拉普拉斯特征基的选择具有不变性，并将其期望的oracle异常分数分解为有界端点不确定性和图频率加权的Fisher差异。在四个基准上的实验证明了GRASP优越的异常检测性能，并验证了其图谱路径和加权机制的有效性。
英文摘要
Multivariate time series anomaly detection typically relies on evaluating discrepancies between observations and outputs produced by models trained on normal data. An alternative perspective is to characterize the distribution of normal data through the generative dynamics, i.e., the velocity field, of flow matching models. However, standard flow matching typically adopts linear probability paths that overlook dependencies among variables, leading to a misalignment with the structured data distribution. To address this issue, we propose GRASP, a flow matching framework with a graph-spectral path for multivariate time series anomaly detection. GRASP incorporates graph structure into the probability path by minimizing a fixed-endpoint action that combines kinetic energy with graph Dirichlet energy. This formulation yields a closed-form path based on graph-frequency-dependent hyperbolic interpolation. A velocity predictor trained on normal data then detects anomalies using weighted velocity discrepancies aggregated across source samples, flow times, and graph frequencies. Theoretically, we establish that GRASP is invariant to the choice of Laplacian eigenbasis and decompose its expected oracle anomaly score into bounded endpoint uncertainty and graph-frequency-weighted Fisher discrepancy. Experiments on four benchmarks demonstrate the superior anomaly detection performance of GRASP and validate the effectiveness of its graph-spectral path and weighting mechanism.
