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

Jielong Yang; Feng Ji

cs.LGOct 31, 2026

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

Authors: Jielong Yang, Feng Ji

Organizations: Nanyang Technological University, Singapore.

Abstract

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 best average rank on 21 datasets among graph foundation models published in 2025 and 2026, ranks first on 17 datasets, and leads on six of the seven heterophilous datasets. It also exceeds pre-trained graph foundation models in link prediction on all six datasets and ranks second in molecule classification, behind only a model fine-tuned after pre-training on molecules.

Figures & tables

Fig. 1: Average rank of every compared method on three tasks, one panel per task with its own rank scale. Node classification covers the 21 datasets of Table I and every reported variant, link prediction six datasets, and graph classification five molecule benchmarks. Lower is better. Our method GraphFlowFM ranks first on node classification and link prediction. On graph classification it ranks second (3.00) behind GIT-S (2.20), but GIT-S is pre-trained on molecules and fine-tuned on each task, while the encoder of GraphFlowFM has never seen a molecule and makes no gradient update.

Fig. 2: Prior graph foundation models (left) learn graph knowledge from real or synthetic graphs before they are applied to a target graph. GraphFlowFM (right) decomposes the target graph into parallel flows, vertex-disjoint paths that jointly cover every edge (1), writes each path as a multivariate time series with one node per patch (2), and encodes it with a frozen time-series foundation model whose causal attention gives each node a self token and a context token (3). Since a node lies on paths of several flows, its tokens are averaged over all of its occurrences (4), and a closed-form ridge readout predicts node labels, links, or graph labels (5). The node features and the structural descriptors are encoded as two separate groups of variates, and no parameter is pre-trained on graphs or updated by gradient.

Homophilous
Dataset	GraphAny	TS-Mean	TS-GAT	NodePFN	RGVT	Ours
Cora	77.8	n/r	n/r	82.1	81.7	83.1
CiteSeer	67.5	68.7	68.7	67.3	70.1	70.4
PubMed	77.5	75.0	75.5	78.0	78.2	79.3
Photo	90.2	90.2	89.7	90.5	92.3	92.5
CS	90.8	90.9	91.1	91.5	92.3	93.0

TABLE I: Node classification accuracy (%) under the GraphAny protocol on 21 datasets, five seeds. Baselines are released numbers of graph foundation models from 2025 and 2026, and every baseline is trained on graph data. n/r means not reported. Rank is averaged over the datasets a method reports. Best in bold, second underlined. Standard deviations and further variants are in Section C-A .

Fig. 3: Link prediction on Cora, test ROC-AUC on groups of test pairs, against the Adamic-Adar heuristic, which scores a pair by its common neighbors weighted by inverse log degree. Hubs are the top 10% of nodes by degree in the training graph, and the groups No Hub, One Hub, and Two Hubs contain the test pairs with zero, one, or two hub endpoints. No Common Neighbor contains the pairs whose two nodes share no neighbor in the training graph.

Dataset	Best pre-trained GFM	Best per-dataset model	GraphFlowFM
Cora	89.27 (R-GFM)	87.34 (GCN)	92.86
CiteSeer	90.88 (R-GFM)	96.90 (DGI)	93.81
PubMed	92.26 (OFA)	91.16 (GCN)	95.89
AirUS	86.17 (GCOPE)	92.50 (DGI)	95.78
Amazon-ratings	98.49 (GIT-S)	98.05 (BGRL)	99.70
GitHub	86.72 (OpenGraph)	87.48 (GCN)	91.69

TABLE II: Link prediction (ROC-AUC, %). For each dataset, the best released result of a graph foundation model that is pre-trained on graphs and fine-tuned on the target graph, and of a model trained on the target graph alone. GraphFlowFM makes no gradient update. Table S4 in Section C-B lists every baseline.

Method	Graph training	HIV	BBBP	BACE	ToxCast	Tox21	Rank
GIN	Per-Dataset	76.83	67.36	75.55	62.92	72.26	4.6
BGRL	Per-Dataset	72.18	67.40	73.75	62.52	72.97	5.4
GraphMAE	Per-Dataset	69.54	66.43	66.56	62.52	74.13	5.4
OFA	Pre-Train + FT	76.48	65.79	77.88	63.49	73.00	4.0
GIT-G	Pre-Train + FT	73.63	68.33	79.28	63.00	73.81	3.2
GIT-S	Pre-Train + FT	74.75	68.72	81.10	63.63	73.78	2.2

TABLE III: Graph classification (ROC-AUC, %) on OGB molecule datasets with scaffold splits. Baselines are released numbers from Wang et al. [10] , trained on the target data from scratch (Per-Dataset) or after graph pre-training (Pre-Train + FT). GraphFlowFM makes no gradient update. Best bold, second underlined.

Fig. 4: Graph classification on HIV. (a) Test ROC-AUC of the best single candidate of each representation, selected on the validation set, and of the ensemble. (b) Test ROC-AUC of the ensemble on the test molecules split into three equal groups by number of atoms.

Fig. 5: Node classification analyses. (a) Change in test accuracy from the full GraphFlowFM when one component is changed. (b) Gain from TimesFM, the accuracy of the pretrained TimesFM minus that of a randomly initialized TimesFM of the same architecture, when every path is cut into windows of at most the given length. (c) The same gain when the tokens are read at different encoder layers. (d) Share of the alignment weight that the readout gives to the feature tokens, the feature signals, and the structure tokens. Exact numbers are in Appendix D ( Figures S1 , S2 and S3 ).

Fig. 6: Roman-empire, test accuracy (%) of GraphFlowFM with and without parallel flows, by local homophily (the share of a node’s neighbors in its own class) and by degree.

Fig. 7: Paths produced by three traversals on Roman-empire, all of which cover every edge with 7 or 8 flows. (a) Median length of the paths. (b) Test accuracy.

Fig. 8: Accuracy, token distance, and prediction disagreement against the number

K

of random vertex relabelings. Each relabeling randomly permutes the vertex ids and gives one decomposition, and the fused tokens are averaged over

K

relabelings before the readout, with the label splits fixed.

K=1

is a single relabeling. (a) Change in test accuracy relative to the original vertex ids. Error bars show the standard deviation over disjoint sets of

K

relabelings. (b) Relative distance

\|Z_{1}-Z_{2}\|_{F}/\sqrt{\|Z_{1}\|_{F}\|Z_{2}\|_{F}}

between the averaged tokens

Z_{1}

and

Z_{2}

of two disjoint sets of

K

relabelings, computed on 256-dimensional projections. (c) Share of test nodes whose predictions differ between two disjoint sets of

K

relabelings.

Fig. 9: Wall-clock time of one complete run with five seeds on one RTX 4090D, including the decomposition, the encoding of both groups, and the readout, against the number of nodes. All 21 datasets take 3.3 GPU hours in total. For reference, GraphAny reports hyperparameter searches of 4 GPU hours for GraphAny, 240 for MLP, GCN, and GAT together, and 672 for ACM-GNN [ 2 ] .

Dataset	Original	Relabeled	Range	Disagreement
Cora	83.1	82.0 $\pm$ 0.5	81.2–82.6	7.0%
Texas	83.8	80.8 $\pm$ 1.9	78.4–83.8	10.1%
Roman-empire	80.6	80.6 $\pm$ 0.2	80.4–80.9	7.0%
Amazon-ratings	50.8	50.6 $\pm$ 0.3	50.2–51.0	14.4%

TABLE IV: Sensitivity to the vertex order. Test accuracy (%) with the original vertex ids and over ten random relabelings of each dataset, each giving one deterministic decomposition, with the label splits fixed and the predictions mapped back to the original nodes. Disagreement is the share of test nodes whose prediction differs between two relabelings, averaged over all pairs. Original differs from Table I on Texas because the two splits are weighted equally here, whereas the five seeds of Table I use the first split three times.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Group	Dataset	Source	Domain	Nodes	Edges	Feat.	Classes	Hom.
Homophilous	Cora	Planetoid	citation	2,708	5,278	1,433	7	0.81
	CiteSeer	Planetoid	citation	3,327	4,552	3,703	6	0.74
	PubMed	Planetoid	citation	19,717	44,324	500	3	0.80
	Photo	Amazon (Shchur et al.)	co-purchase	7,650	119,081	745	8	0.83
	CS	Coauthor (Shchur et al.)	co-authorship	18,333	81,894	6,805	15	0.81
	Computers	Amazon (Shchur et al.)	co-purchase	13,752	245,861	767	10	0.78

Appendix

TABLE S1: The 21 node classification datasets, taken with their splits from GraphAny [ 2 ] . Edges are undirected, and Hom. is the edge homophily.

Component	Hyperparameter	Value
Node signals	feature group	32 SVD variates of the weighted features ( Section III-C )
	structure group	$\log(1+d_{v})$ , random-walk return probabilities for 1 to 7 steps
Parallel flows	DFS order	roots by decreasing degree, neighbors by increasing degree
	window, overlap	480 nodes, 64 nodes
	directions	both
Encoder	model	TimesFM-3, frozen, 20 layers, width 1,280

Appendix

TABLE S2: Hyperparameters of GraphFlowFM, shared by all datasets.

Homophilous
Dataset	GraphAny	GraphAny-Arxiv	TS-Mean	TS-GAT	NodePFN	RGVT	RGVT-Linear	TAG	GraphFlowFM
Cora	77.82	79.38	n/r	n/r	82.06	81.68	81.32	83.50	83.10 $\pm$ 0.00
CiteSeer	67.50	68.34	68.66	68.70	67.30	70.12	71.96	68.08	70.40 $\pm$ 0.00
PubMed	77.46	76.36	74.98	75.46	78.00	78.20	79.02	78.96	79.30 $\pm$ 0.00
Photo	90.18	90.60	90.18	89.66	90.53	92.29	92.02	89.63	92.47 $\pm$ 0.66
CS	90.85	90.45	90.92	91.13	91.55	92.28	91.32	90.49	93.04 $\pm$ 0.29

Appendix

TABLE S3: Node classification accuracy (%) on the 21 datasets under the GraphAny protocol. GraphFlowFM is reported as mean

\pm

standard deviation over five seeds. GraphFlowFM is deterministic, so its standard deviation reflects only the variation across splits and is zero where all seeds share one split or the splits give the same accuracy ( Section A-A ). GraphAny-Arxiv is GraphAny trained on ogbn-arxiv, RGVT-Linear is RGVT with a linear head, and TAG is not yet formally published and is listed for reference. n/r means not reported. Best in bold, second underlined.

Method	Graph Training	Cora	CiteSeer	PubMed	AirUS	Ratings	GitHub
GCOPE	Pre-Train + FT	88.71	88.60	90.84	86.17	–	82.16
SAMGPT	Pre-Train + FT	88.62	89.91	84.92	–	–	–
MDGFM	Pre-Train + FT	88.41	89.12	84.78	–	–	–
R-GFM	Pre-Train + FT	89.27	90.88	88.62	–	–	–
GFT	Pre-Train, No FT	–	–	55.83	–	–	–
RAGraph	Pre-Train, No FT	–	–	58.29	–	–	–

Appendix

TABLE S4: Link prediction (ROC-AUC, %). Graph Training states whether a method is trained on graph data: on each target graph (Per-Dataset), or by pre-training on a graph corpus followed by fine-tuning on the target graph (Pre-Train + FT) or without fine-tuning (Pre-Train, No FT). Baseline numbers are copied from Liu et al. [26] (first block), Sun et al. [27] (second block), Wang et al. [10] (third block) and Sun et al. [9] (fourth block); “–” means not reported. A method reported more than once (GCOPE, SAMGPT, MDGFM, GCN, and OFA) appears once, in the block of its first source, with the highest reported value on each dataset. GraphFlowFM makes no gradient update.

Fig. S1: Ablations on seven representative datasets. The first row is the test accuracy (%) of the full model, averaged over five seeds, and every other row is the change in accuracy from it.

Fig. S2: Test accuracy of the pretrained TimesFM and of a randomly initialized TimesFM of the same architecture. (a, b) Every path is cut into windows of at most the given number of nodes, and 480 is the default of GraphFlowFM. (c, d) The tokens are read at different encoder layers, and layer 15 is the default of GraphFlowFM.

Fig. S3: Alignment weights of the feature tokens, the feature signals, and the structure tokens in the alignment-weighted representation. The number above each bar is the share of the structure tokens. Questions uses the low-memory readout, which does not log the weights.

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Graph foundation models face several fundamental challenges including transferability across diverse domains and data scarcity, which calls into question the very feasibility of creating such models. However, despite similar challenges, the tabular domain has recently witnessed the emergence of the first successful foundation models such as TabPFN. These models are based on the prior-data fitted networks (PFN) framework, in which models are pretrained on carefully designed synthetic datasets to make predictions in an in-context learning setting. Recently, G2T-FM, a framework that converts graph node-level tasks into tabular tasks, has made the first step towards adopting PFNs for graphs, yet it is limited to hand-crafted features and was never pretrained on graph data. In this work, we make the next step by proposing GraphPFN, a PFN-based model designed and pretrained specifically for graph node-level tasks. Following the PFN framework, we first design a prior distribution of synthetic attributed graphs by using a novel combination of multi-level stochastic block models and a preferential attachment process for structure generation and graph-aware structured causal models for attribute generation. Then, we augment the tabular foundation model LimiX with attention-based graph neighborhood aggregation layers and train it on millions of synthetic graphs sampled from our prior. On diverse real-world graph datasets with node-level tasks, GraphPFN achieves state-of-the-art results in both in-context learning and finetuning regimes, outperforming G2T-FM, prior GFMs, and task-specific GNNs trained from scratch. More broadly, GraphPFN shows the potential of PFN-based models for building graph foundation models.

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