TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching

Abstract:Many complex systems such as brain networks, financial markets, and gene-regulatory circuits are described not by a fixed graph but by one that changes over time. A standard way to summarise such structure at each instant is the sparse precision (inverse-covariance) matrix, and the time-varying graphical lasso (TVGL) turns a multivariate signal into a smooth chain of these matrices. We introduce TVGL-CFM, a single model that learns the distribution of such chains and can both generate new, realistic time-varying network trajectories for a given class and forecast how an observed trajectory will continue. Each precision matrix lives on a curved space of positive-definite matrices, but a log-Euclidean chart flattens an entire trajectory into an ordinary vector space, so a simple conditional flow-matching model can be trained and sampled there while every decoded matrix is guaranteed to be a valid precision matrix. For forecasting we start the flow not from noise but from a rough extrapolation of the recent history, so the model only has to learn a small correction. Across EEG motor-imagery, chaotic systems, and gene-expression data, TVGL-CFM generates trajectories that keep the class-discriminative structure of real data, and it forecasts future connectivity more accurately than raw-signal baselines. Generating the structured precision trajectory directly is therefore more faithful than generating raw signals and estimating connectivity afterwards.

Machine Learning (cs.LG)

arXiv:2607.16894 [cs.LG]

(or arXiv:2607.16894v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.16894 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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