Versatile Graph Foundation Models from Frozen Time-Series Foundation Models via Parallel Flows

Jielong Yang, Feng Ji

Graph foundation models aim to serve unseen graphs across tasks, feature spaces, and label sets. Most current models learn how to represent a new graph by pre-training on other graphs. Because graph data are scarce and differ across domains in features and structures, what they learn may not transfer to a graph from an unseen domain. We show that a frozen time-series foundation model, pre-trained on abundant time series, can instead serve as a graph foundation model without graph pre-training and without any gradient update on the target graph. Such a model reads ordered multivariate sequences, but a graph has no time axis, and covering all its edges with sequences is nontrivial because a node can have many neighbors. We therefore propose GraphFlowFM, which decomposes a graph into parallel flows, sets of vertex-disjoint paths that jointly cover every edge, and reads each path as a multivariate time series with the nodes as time steps. A frozen TimesFM encodes the paths with causal attention, which gives each node a self token and a context token, and a closed-form ridge readout weighs these tokens by their alignment with the labels. In node classification, GraphFlowFM attains the…