发表机构
University of Strathclyde（斯特拉斯克莱德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对脑网络等随时间变化的复杂系统，提出TVGL-CFM模型，通过对数欧几里得图和条件流匹配，可生成和预测时变网络轨迹，在多数据集上表现优于原始信号基线，直接生成结构化精度轨迹更可靠。
AI 中文摘要
许多复杂系统，如脑网络、金融市场和基因调控电路，由随时间变化的图描述。稀疏精度矩阵用于总结其结构，时变图形套索（TVGL）将多元信号转化为这些矩阵的平滑链。我们引入TVGL-CFM，它能学习此类链的分布，可生成给定类别的新的、现实的时变网络轨迹并预测观测轨迹的延续。通过对数欧几里得图将轨迹扁平化，训练简单的条件流匹配模型。在多个数据集上，TVGL-CFM生成保持真实数据类别判别结构的轨迹，预测未来连通性比原始信号基线更准确。直接生成结构化精度轨迹比先生成原始信号再估计连通性更可靠。
英文摘要
Many complex systems, including brain networks, financial markets, and gene-regulatory circuits, are better described by interaction structures that evolve over time than by a single fixed graph. The time-varying graphical lasso (TVGL) estimates this structure from multivariate signals as a temporally coherent sequence of sparse precision matrices. We introduce TVGL-CFM, a unified generative framework that learns distributions over complete SPD precision-matrix trajectories without requiring a pre-specified graph, supporting both class-conditional generation and history-conditioned forecasting. An SPD trajectory with T windows lies on the product Riemannian manifold (S++^p)^T. We construct a global log-Euclidean diffeomorphism from this product space to a Euclidean sequence space, enabling a non-autoregressive conditional flow-matching model with a Transformer backbone to generate all windows jointly and decode them to SPD matrices without post-hoc projection. For forecasting, we use two distinct data-dependent couplings so that the flow transforms an informative prior into a coherent future block. Across EEG motor-imagery data and three nonlinear dynamical systems, TVGL-CFM preserves class-discriminative dependency structure and forecasts future connectivity more accurately than several strongly matched baselines, opening new possibilities for generative dynamic graph models.
