Can Graph Foundation Models Generalize Over Architecture?

Benjamin Gutteridge; Michael Bronstein; Xiaowen Dong

cs.LGMar 24, 2026

Can Graph Foundation Models Generalize Over Architecture?

Authors: Benjamin Gutteridge, Michael Bronstein, Xiaowen Dong

Organizations: University of Oxford · AITHYRA

Abstract

Graph foundation models (GFMs) have recently attracted interest due to the promise of graph neural network (GNN) architectures that generalize zero-shot across graphs of arbitrary scales, feature dimensions, and domains. While existing work has demonstrated this ability empirically across diverse real-world benchmarks, these tasks share a crucial hidden limitation: they admit a narrow set of effective GNN architectures. In particular, current domain-agnostic GFMs rely on fixed architectural backbones, implicitly assuming that a single message-passing regime suffices across tasks. In this paper, we argue that architecture adaptivity is a necessary requirement for true GFMs. We show that existing approaches are non-robust to task-dependent architectural attributes and, as a case study, use range as a minimal and measurable axis along which this limitation becomes explicit. With theoretical analysis and controlled synthetic experiments, we demonstrate that fixed-backbone GFMs provably under-reach on tasks whose architectural requirements differ from those seen at training time. To address this issue, we introduce a framework that adapts effective GNN architecture at inference time by discovering and mixing task-specific linear graph operators, enabling zero-shot generalization across tasks with heterogeneous architectural requirements, without retraining. We validate our approach on arbitrary-range synthetic tasks and a suite of real-world benchmarks, demonstrating improved performance and robustness over existing domain-agnostic GFMs.

Figures & tables

	End-to-end		Zero-shot
	MeanGNN	GAT	GraphAny	TS-Mean	GOBLIN
Actor ∗	32.03 $\pm$ 0.29	32.59 $\pm$ 0.83	27.54 $\pm$ 0.20	28.09 $\pm$ 0.93	25.36 $\pm$ 0.14
AirBrazil	32.31 $\pm$ 7.50	35.38 $\pm$ 4.21	33.84 $\pm$ 15.65	39.23 $\pm$ 5.70	50.77 $\pm$ 9.55
AirEU	39.12 $\pm$ 6.44	39.00 $\pm$ 4.30	41.25 $\pm$ 7.25	35.88 $\pm$ 6.91	41.25 $\pm$ 3.95
AirUS	43.93 $\pm$ 1.16	43.03 $\pm$ 2.08	43.35 $\pm$ 1.62	42.34 $\pm$ 2.12	51.78 $\pm$ 4.43
AmzComp	73.88 $\pm$ 0.88	70.94 $\pm$ 3.40	82.79 $\pm$ 1.13	81.37 $\pm$ 1.25	80.67 $\pm$ 2.43

Table 2: Mean

\pm

std % accuracy (5 seeds) across 25 benchmark graph datasets. End-to-end models are trained directly on each task, so are generally easier than the zero-shot setting. Non-GOBLIN columns are reproduced from Finkelshtein et al. (2025) . Heterophilic graphs are marked with an asterisk. First -/ second -best results per dataset are color-coded.

Figure 2: Range of GOBLIN on several benchmarks,

\pm\sigma

over seeds. Median is over all 25 benchmarks.

	MeanGNN	GAT	GraphAny	TS-GAT	GOBLIN
Paris	20.79 $\pm$ 0.25	20.73 $\pm$ 0.28	20.09 $\pm$ 0.10	16.36 $\pm$ 1.73	24.59 $\pm$ 0.00
Shanghai	22.86 $\pm$ 0.13	20.80 $\pm$ 0.18	19.72 $\pm$ 0.02	19.93 $\pm$ 1.45	23.53 $\pm$ 0.00
LA	19.34 $\pm$ 0.08	18.74 $\pm$ 0.25	17.19 $\pm$ 0.02	15.85 $\pm$ 1.27	24.29 $\pm$ 0.00
London	21.58 $\pm$ 0.12	21.13 $\pm$ 0.15	17.13 $\pm$ 0.01	17.60 $\pm$ 1.49	21.60 $\pm$ 0.00
Average	21.14 $\pm$ 0.14	20.35 $\pm$ 0.21	18.53 $\pm$ 0.04	17.44 $\pm$ 1.49	23.50 $\pm$ 0.00

Table 3: Mean

\pm

std % accuracy (5 seeds) on CityNetworks. We report TS-GAT as it performed better than TS-Mean.

Appendix figures & tables25 assets

Supplementary material from the paper’s appendix.

Appendix

	Hyperparameter	Search space	Chosen
Operator search	Train dataset	—	Cora
	BO objective	—	trimmed_20
	sample_budget	20, 25, 30, 35	25
	UCB $\beta$	2.0, 3.0, 4.0	3.0
	basis_size	3, 4, 5	4
	Diversity penalty $\lambda$	0.0, 0.1, 0.2, 0.3, 0.4, 0.5	0.2

Appendix

Table 4: Hyperparameter search space for GOBLIN, used in Figure 1 and Tables 2 & 3 .

Figure 3: Range of GOBLIN on synthetic and real-world benchmark tasks (

\pm\sigma

over 5 seeds).

Figure 4: Range of best-performing operator on each task, out of all operators selected by GOBLIN across all 5 seeds.

Figure 5: The relationship between task range (as captured by GOBLIN) and GOBLIN performance improvement (

\Delta

average % accuracy) over non-GOBLIN models (MPNNs, GraphAny and TS-GNN, as in Tables 2 & 3 ) for 29 real-world benchmarks.

Dataset	MeanGNN	GAT
Paris	27.10 $\pm$ 0.67	46.75 $\pm$ 0.50
Shanghai	28.64 $\pm$ 0.36	58.50 $\pm$ 0.75
LA	26.89 $\pm$ 0.15	53.36 $\pm$ 0.59
London	28.13 $\pm$ 0.25	47.72 $\pm$ 0.25

Appendix

Table 5: CityNetworks accuracy (%) for deep (

L=16

) MeanGNN and GAT trained directly on each dataset using the hyperparameter search described in Finkelshtein et al. (2025) . Results are mean

\pm

std over 4 training seeds with fixed data splits.

Dataset	#Nodes	#Edges	#Feature	#Classes	#Labeled Nodes	Diam.	Mean APSPD	Train/Val/Test Ratios (%)	Hetero- philic	Source
AirBrazil	131	1074	131	4	80	4	2.17	61.1/19.1/19.8		Ribeiro et al. (2017)
Cornell	183	554	1703	5	87	8	3.18	47.5/32.2/20.2	✓	Pei et al. (2020)
Texas	183	558	1703	5	87	8	3.02	47.5/31.7/20.2	✓	Pei et al. (2020)
Wisconsin	251	900	1703	5	120	8	3.25	47.8/31.9/20.3	✓	Pei et al. (2020)
AirEU	399	5995	399	4	80	5	2.32	20.1/39.8/40.1		Ribeiro et al. (2017)
AirUS	1190	13599	1190	4	80	—	—	6.7/46.6/46.6		Ribeiro et al. (2017)

Appendix

Table 6: Statistics for the 30 datasets used in this paper. APSPD is all-pairs shortest path (geodesic) distance.

Model	Dataset	$N$	Hparam search	Train / seed	Inference / seed
GOBLIN (zero-shot)	LA	240,587	—	$19.9\pm 0.3$ s	$15.8\pm 0.5$ s
	London	568,795	—	—	$10.2\pm 0.2$ s
	Paris	114,127	—	—	$4.5\pm 0.1$ s
	Shanghai	183,917	—	—	$18.0\pm 0.5$ s
GAT $L=2$	LA	240,587	$67.1$ s	$20.5\pm 0.2$ s	$15.1\pm 0.1$ ms
	London	568,795	$149.9$ s	$46.1\pm 0.4$ s	$34.9\pm 0.2$ ms

Appendix

Table 7: Wall-clock times (mean

\pm

std over 5 seeds, A10 GPU) on CityNetworks. GOBLIN’s train time (shown for LA only) is a one-time cost on Cora shared across all cities; inference includes the full BO operator search. GAT inference is a single forward pass; training is repeated per city per seed. The summary table gives total wall-clock across all 5 seeds and 4 cities, with and without GAT hyperparameter search (GOBLIN has no per-task search).

Dataset	$\rho_{\bar{W}}$	$\rho_{\text{B}}$	Mean geodesic distance	Val. Acc. (%)
AirBrazil	0.80	1.63	2.17	50.00
Cornell	0.80	3.22	3.18	71.19
Texas	0.80	2.79	3.02	74.14
AirEU	0.82	1.29	2.32	34.59
Squirrel	0.91	2.34	3.09	42.31
Wisconsin	0.80	3.18	3.24	62.50

Appendix

Table 8: Overall ranges (and for reference, validation accuracies), both fixed-

W

and black box, for 17 connected benchmark datasets. Computation of

\rho_{\text{B}}

uses 500 sampled nodes, or all of them, whichever is fewer. In most cases,

\rho_{B}

tracks mean geodesic distance fairly closely;

\rho_{\bar{W}}

provides a more accurate version of range—due to the fixed

\rho\leq 2

operators used, effective range of GraphAny on all tasks is

<1

. All ranges are computed on the checkpointed instantiation of GraphAny from Zhao et al. (2024) , trained on Wisconsin.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (131)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	1.36	0.30	0.37	0.43	0.37
$AX$	1.00	1.75	0.35	0.35	0.34	0.35
$A^{2}X$	1.61	1.84	0.35	0.28	0.23	0.28
$(I-A)X$	0.50	1.84	—	—	—	—
$(I-A)^{2}X$	0.87	1.77	—	—	—	—

Appendix

Table 9: Ranges and weights of GraphAny linear GNN components for the AirBrazil dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (183)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	2.98	0.30	0.34	0.35	0.37
$AX$	1.00	3.42	0.35	0.38	0.36	0.34
$A^{2}X$	1.48	3.23	0.35	0.29	0.30	0.29
$(I-A)X$	0.50	3.09	—	—	—	—
$(I-A)^{2}X$	0.86	3.18	—	—	—	—

Appendix

Table 10: Ranges and weights of GraphAny linear GNN components for the Cornell dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (183)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	2.82	0.30	0.32	0.33	0.34
$AX$	1.00	2.11	0.35	0.42	0.36	0.34
$A^{2}X$	1.50	3.89	0.35	0.25	0.31	0.31
$(I-A)X$	0.50	2.94	—	—	—	—
$(I-A)^{2}X$	0.87	3.02	—	—	—	—

Appendix

Table 11: Ranges and weights of GraphAny linear components for the Texas dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (251)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	2.94	0.30	0.34	0.34	0.36
$AX$	1.00	3.28	0.35	0.38	0.36	0.34
$A^{2}X$	1.48	3.32	0.35	0.29	0.30	0.30
$(I-A)X$	0.50	3.06	—	—	—	—
$(I-A)^{2}X$	0.86	3.11	—	—	—	—

Appendix

Table 12: Ranges and weights of GraphAny linear GNN components for the Wisconsin dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (399)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	0.36	0.29	0.40	0.42	0.48
$AX$	1.00	1.68	0.35	0.29	0.33	0.30
$A^{2}X$	1.71	2.11	0.36	0.31	0.25	0.22
$(I-A)X$	0.50	1.90	—	—	—	—
$(I-A)^{2}X$	0.91	2.29	—	—	—	—

Appendix

Table 13: Ranges and weights of GraphAny linear components for the AirEU dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	1.44	0.30	0.35	0.34	0.38
$AX$	1.00	2.64	0.35	0.31	0.33	0.31
$A^{2}X$	1.76	2.99	0.35	0.34	0.33	0.31
$(I-A)X$	0.50	2.38	—	—	—	—
$(I-A)^{2}X$	0.93	2.59	—	—	—	—

Appendix

Table 14: Ranges and weights of GraphAny linear components for the Squirrel dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	0.92	0.30	0.38	0.37	0.41
$AX$	1.00	2.38	0.35	0.33	0.34	0.33
$A^{2}X$	1.89	2.42	0.35	0.29	0.29	0.26
$(I-A)X$	0.50	2.37	—	—	—	—
$(I-A)^{2}X$	0.97	2.37	—	—	—	—

Appendix

Table 15: Ranges and weights of GraphAny linear components for the BlogCatalog dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	1.13	0.30	0.31	0.30	0.32
$AX$	1.00	2.79	0.35	0.40	0.35	0.34
$A^{2}X$	1.70	3.33	0.35	0.29	0.35	0.34
$(I-A)X$	0.50	2.47	—	—	—	—
$(I-A)^{2}X$	0.90	2.74	—	—	—	—

Appendix

Table 16: Ranges and weights of GraphAny linear components for the Chameleon dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	1.00	0.30	0.33	0.35	0.38
$AX$	1.00	2.39	0.35	0.30	0.33	0.31
$A^{2}X$	1.69	3.55	0.35	0.36	0.33	0.30
$(I-A)X$	0.50	2.46	—	—	—	—
$(I-A)^{2}X$	0.92	3.11	—	—	—	—

Appendix

Table 17: Ranges and weights of GraphAny linear components for the Actor dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	26.63	0.31	0.32	0.32	0.35
$AX$	1.00	30.65	0.36	0.34	0.34	0.33
$A^{2}X$	1.37	32.10	0.34	0.34	0.35	0.32
$(I-A)X$	0.50	34.24	—	—	—	—
$(I-A)^{2}X$	0.81	30.59	—	—	—	—

Appendix

Table 18: Ranges and weights of GraphAny linear components for the Minesweeper dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	2.02	0.30	0.33	0.32	0.35
$AX$	1.00	1.98	0.35	0.36	0.35	0.34
$A^{2}X$	1.82	2.39	0.34	0.32	0.32	0.30
$(I-A)X$	0.50	2.05	—	—	—	—
$(I-A)^{2}X$	0.95	2.05	—	—	—	—

Appendix

Table 19: Ranges and weights of GraphAny linear components for the Tolokers dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	2.21	0.30	0.34	0.31	0.34
$AX$	1.00	4.14	0.35	0.37	0.36	0.35
$A^{2}X$	1.54	4.73	0.34	0.29	0.33	0.31
$(I-A)X$	0.50	4.02	—	—	—	—
$(I-A)^{2}X$	0.87	4.41	—	—	—	—

Appendix

Table 20: Ranges and weights of GraphAny linear components for the CoCS dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	6.02	0.30	0.34	0.35	0.39
$AX$	1.00	5.63	0.35	0.34	0.35	0.33
$A^{2}X$	1.71	5.69	0.34	0.32	0.30	0.28
$(I-A)X$	0.50	5.83	—	—	—	—
$(I-A)^{2}X$	0.93	5.73	—	—	—	—

Appendix

Table 21: Ranges and weights of GraphAny linear components for the Pubmed dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	2088.70	0.30	0.33	0.35	0.39
$AX$	1.00	2212.81	0.35	0.26	0.29	0.28
$A^{2}X$	1.12	2166.40	0.35	0.40	0.36	0.34
$(I-A)X$	0.50	2173.21	—	—	—	—
$(I-A)^{2}X$	0.75	2179.69	—	—	—	—

Appendix

Table 22: Ranges and weights of GraphAny linear components for the Roman dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	16.10	0.31	0.32	0.31	0.35
$AX$	1.00	15.98	0.35	0.35	0.35	0.34
$A^{2}X$	1.39	16.06	0.34	0.33	0.34	0.32
$(I-A)X$	0.50	15.99	—	—	—	—
$(I-A)^{2}X$	0.80	15.81	—	—	—	—

Appendix

Table 23: Ranges and weights of GraphAny linear components for the AmzRatings dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (500)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	0.83	0.30	0.33	0.29	0.31
$AX$	1.00	3.36	0.35	0.39	0.38	0.37
$A^{2}X$	1.57	4.54	0.34	0.27	0.34	0.32
$(I-A)X$	0.50	3.05	—	—	—	—
$(I-A)^{2}X$	0.88	4.10	—	—	—	—

Appendix

Table 24: Ranges and weights of GraphAny linear components for the CoPhysics dataset.

LinearGNN	$\rho_{\bar{W}}$	$\rho_{\text{B}}$ (200)	$\alpha_{\text{Cora}}$	$\alpha_{\text{Wisconsin}}$	$\alpha_{\text{Arxiv}}$	$\alpha_{\text{Product}}$
$X$	0.00	3.34	0.30	0.32	0.32	0.35
$AX$	1.00	3.46	0.35	0.35	0.35	0.34
$A^{2}X$	1.82	4.07	0.34	0.33	0.33	0.31
$(I-A)X$	0.50	3.84	—	—	—	—
$(I-A)^{2}X$	0.96	3.82	—	—	—	—

Appendix

Table 25: Ranges and weights of GraphAny linear components for the Questions dataset.

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Graph foundation models (GFM) aim to acquire transferable knowledge by pre-training on diverse graphs, which can be adapted to various downstream tasks. However, domain shift in graphs is inherently two-dimensional: graphs differ not only in what they describe (topic domains) but also in how they are represented (format domains). Most existing GFM benchmarks vary only topic domains, thereby obscuring how knowledge transfers across both dimensions. We present a new benchmark that jointly evaluates topic and format gaps across the full GFM pipeline, including multi-domain self-supervised pre-training and few-shot downstream adaptation, and provides a timely evaluation of recent GFMs in the rapidly evolving landscape. Our protocol enables controlled assessment in four settings: (i) pre-training on diverse topics and formats, while adapting to unseen downstream datasets; (ii) same pre-training as in (i), while adapting to seen datasets; (iii) pre-training on a single topic domain, while adapting to other topics; (iv) pre-training on a base format, while adapting to other formats. This two-axis evaluation disentangles semantic generalization from robustness to representational shifts. We conduct extensive evaluations of eight state-of-the-art GFMs on 33 datasets spanning seven topic domains and six format domains, surfacing new empirical observations and practical insights for future research. Codes/data are available at https://github.com/smufang/GFMBenchmark.

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