Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

Li Sun; Zhenhao Huang; Silei Chen; Lanxu Yang; Junda Ye; Sen Su; Philip S. Yu

cs.LGFeb 28, 2026

Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

Authors: Li Sun, Zhenhao Huang, Silei Chen, Lanxu Yang, Junda Ye, Sen Su, Philip S. Yu

Organizations: Beijing University of Posts and Telecommunications, Beijing 100876, China · North China Electric Power University, Beijing 102206, China · University of Illinois Chicago, IL, USA

Abstract

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between model pre-training and domain adaptation. In this paper, we propose a fresh Riemannian geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then "glues" the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue's geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold. Codes are available at https://github.com/RiemannGraph/GraphGlue.

Figures & tables

Figure 1: An illustration of manifold gluing. The domains are distinguished by colors.

Figure 2: An Illustration of GraphGlue Framework.

Model	Node Classification						Link Classification		Graph Classification
	Arxiv		Computers		Reddit		FB15k_237		PROTEINS
	1-shot	5-shot	1-shot	5-shot	1-shot	5-shot	1-shot	5-shot	1-shot	5-shot
GCN	$12.6\scriptstyle{\pm 1.7}$	$27.6\scriptstyle{\pm 2.1}$	$33.8\scriptstyle{\pm 3.8}$	$65.7\scriptstyle{\pm 4.2}$	$11.1\scriptstyle{\pm 2.1}$	$28.3\scriptstyle{\pm 1.0}$	$32.1\scriptstyle{\pm 2.3}$	$52.4\scriptstyle{\pm 1.8}$	$50.1\scriptstyle{\pm 13.0}$	$55.0\scriptstyle{\pm 9.9}$
GraphSAGE	$14.6\scriptstyle{\pm 3.7}$	$26.1\scriptstyle{\pm 2.2}$	$35.4\scriptstyle{\pm 8.2}$	$66.7\scriptstyle{\pm 4.4}$	$14.6\scriptstyle{\pm 2.3}$	$22.2\scriptstyle{\pm 1.1}$	$35.7\scriptstyle{\pm 2.1}$	$58.9\scriptstyle{\pm 1.5}$	$58.9\scriptstyle{\pm 2.7}$	$60.4\scriptstyle{\pm 1.3}$
GIN	$11.2\scriptstyle{\pm 2.0}$	$26.0\scriptstyle{\pm 2.4}$	$44.7\scriptstyle{\pm 6.0}$	$69.5\scriptstyle{\pm 3.5}$	$18.5\scriptstyle{\pm 1.8}$	$29.0\scriptstyle{\pm 1.6}$	$38.2\scriptstyle{\pm 2.5}$	$63.7\scriptstyle{\pm 1.7}$	$54.2\scriptstyle{\pm 13.5}$	$58.8\scriptstyle{\pm 5.0}$
GCC	$12.6\scriptstyle{\pm 2.0}$	$26.8\scriptstyle{\pm 2.1}$	$34.8\scriptstyle{\pm 6.1}$	$62.6\scriptstyle{\pm 3.1}$	$54.7\scriptstyle{\pm 5.6}$	$65.2\scriptstyle{\pm 1.5}$	$47.8\scriptstyle{\pm 1.9}$	$73.6\scriptstyle{\pm 1.2}$	$59.2\scriptstyle{\pm 7.9}$	$64.2\scriptstyle{\pm 3.0}$

Table 1: Performance of cross-domain transfer on various downstream tasks, reported as mean

\pm

std over 10 runs. The highest result is bolded , and the runner-up is underlined .

Panel of Figure 3 — Figure 3: GTM vs Test Task Loss.

Figure 4: Effect of including distinct domains during pre-training.

Panel of Figure 5 — Figure 5: Geometric scaling law on (a) Computers and (b) Reddit datasets.

Figure 6: Visualization of the pre-trained manifold from 6 datasets.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Notation	Description
$\mathcal{M}$	A smooth manifold
${\bm{\mathsfit{G}}}$	A Riemannian metric tensor
${\bm{p}}$	A point in $\mathcal{M}$
$\mathcal{T}_{{\bm{p}}}\mathcal{M}$	The tangent space of point p on $\mathcal{M}$
$\|{\bm{G}}({\bm{p}})\|$	The volume element at ${\bm{p}}$
$(U,x^{1},...,x^{M})$	A coordinate chart of tangent space $\mathcal{T}_{{\bm{p}}}\mathcal{M}$

Appendix

Table 2: Notation and Description

Module	Computational complexity	Memory complexity
$(k,M)$ -Sparse Perturbation	$\mathcal{O}(k_{s}MB)$	$\mathcal{O}(BM(k_{s}+d))$
Adaptive Orthogonal Frame	$\mathcal{O}(B(\|V\|+\|E\|+M^{2})d)$	$\mathcal{O}(BMd)$
Matrix form of metric tensor	$\mathcal{O}(BMd)$	$\mathcal{O}(BM)$
$\mathcal{L}_{\text{holo}}$ and $\mathcal{L}_{\text{curv}}$	$\mathcal{O}(T_{s}M)$	$\mathcal{O}(T_{s})$
Riemannian prototypes and $\mathcal{L}_{\text{proto}}$	$\mathcal{O}(KBd+K(d+M))$	$\mathcal{O}(K(d+M))$
Riemannian MoE	$\mathcal{O}(KBd)$	$\mathcal{O}(KB)$

Appendix

Table 3: Computational and memory complexity of each module in GraphGlue.

Model	Pretraining	Adaptation (per graph sample)
PRODIGY	$\mathcal{O}(B\|V\|^{2}d)$	$\mathcal{O}((\|V\|+\|E\|)d+\|V\|^{2})$
GFT	$\mathcal{O}(B(\|V\|+\|E\|)d+BTh)$	$\mathcal{O}((\|V\|+\|E\|)d+Th)$
RAGraph	$\mathcal{O}(B(\|V\|+\|E\|)d+B\|E_{r}\|d)$	$\mathcal{O}((\|V\|+\|E\|)d+\|E_{r}\|d)$
SAMGPT	$\mathcal{O}(B(\|V\|+\|E\|)d+Bk_{s}d)$	$\mathcal{O}((\|V\|+\|E\|)d+k_{p}d)$
GCOPE	$\mathcal{O}(B(\|V\|+\|E\|)d+BK_{c}d)$	$\mathcal{O}((\|V\|+\|E\|)d+K_{c}d)$
MDGFM	$\mathcal{O}(B(\|V\|+\|E\|)d+B\|V\|^{2})$	$\mathcal{O}((\|V\|+\|E\|)d+\|V\|^{2})$

Appendix

Table 4: Comparison of computational complexity across graph few-shot learning methods.

Model	1	2	3	4	5	6
GCOPE	18.39	19.11	21.12	OOM	OOM	OOM
MDGFM	19.71	21.67	29.35	OOM	OOM	OOM
GraphGlue	12.53	15.07	15.73	16.87	28.67	29.21

Appendix

Table 5: Memory Cost. Lower values indicate better efficiency.

Domain	Dataset	Task	# Graphs	Avg. #Nodes	Avg. #Edges	# Classes
Citation	PubMed	Node	1	19,717	88,648	3
Citation	Arxiv	Node	1	169,343	1,166,243	40
Co-purchase	Computers	Node	1	13,752	491,722	10
Co-purchase	Photo	Node	1	7,650	238,162	8
Social Network	Reddit	Node	1	232,965	114,615,892	41
Social Network	FacebookPagePage	Node	1	22,470	342,004	4

Appendix

Table 6: Statistics of 12 datasets used in our experiment.

Table 13

	Variants	Arxiv	Computers	Reddit	FB15k_237	PROTEINS	HIV
1-shot	w/o EMA	15.46 $\pm$ 1.41	30.84 $\pm$ 9.50	7.43 $\pm$ 2.37	35.90 $\pm$ 17.40	58.48 $\pm$ 2.56	52.62 $\pm$ 2.41
	w/o L_proto	9.57 $\pm$ 4.56	31.24 $\pm$ 10.36	37.90 $\pm$ 9.34	43.59 $\pm$ 8.13	58.49 $\pm$ 2.60	54.10 $\pm$ 2.76
	GRAPHGLUE	29.73 $\pm$ 2.56	61.03 $\pm$ 7.13	68.42 $\pm$ 4.68	60.89 $\pm$ 2.11	69.12 $\pm$ 4.19	58.53 $\pm$ 8.20
5-shot	w/o EMA	16.08 $\pm$ 2.13	34.90 $\pm$ 7.77	11.53 $\pm$ 2.26	40.21 $\pm$ 12.07	59.85 $\pm$ 4.53	53.87 $\pm$ 2.43
	w/o L_proto	15.26 $\pm$ 9.91	36.63 $\pm$ 11.84	46.13 $\pm$ 14.14	64.56 $\pm$ 16.42	61.64 $\pm$ 6.28	55.50 $\pm$ 2.70
	GRAPHGLUE	39.98 $\pm$ 1.67	74.15 $\pm$ 2.38	84.89 $\pm$ 0.68	79.52 $\pm$ 1.75	73.94 $\pm$ 2.38	62.18 $\pm$ 2.50

Appendix

Table 13: Ablation study of GraphGlue’s key components.

Table 14: 1-shot results under different settings.

Table 15: 5-shot results under different settings.

	Method	Amazon-Ratings	Roman-empire	Texas	Wisconsin
1-shot	GCOPE	28.65 $\pm$ 5.82	11.44 $\pm$ 1.91	33.19 $\pm$ 6.62	31.22 $\pm$ 6.85
	MDGFM	29.53 $\pm$ 3.45	14.51 $\pm$ 2.08	34.63 $\pm$ 10.70	35.11 $\pm$ 10.53
	GraphGlue	31.16 $\pm$ 3.56	16.23 $\pm$ 3.00	35.16 $\pm$ 20.43	37.95 $\pm$ 10.91
5-shot	GCOPE	30.06 $\pm$ 5.11	16.00 $\pm$ 1.29	36.31 $\pm$ 10.14	38.21 $\pm$ 2.96
	MDGFM	30.42 $\pm$ 3.80	17.15 $\pm$ 1.66	48.33 $\pm$ 6.36	47.46 $\pm$ 4.86
	GraphGlue	32.17 $\pm$ 2.91	18.50 $\pm$ 1.07	50.88 $\pm$ 11.93	49.71 $\pm$ 8.00

Appendix

Table 16: Performance under different shot settings with pretrained on ogbn-arxiv, Reddit, Computers, FB15k_237, PROTEINS, and HIV.

	Method	Amazon-Ratings	Roman-empire	Texas	Wisconsin
1-shot	GCOPE	29.03 $\pm$ 4.17	13.14 $\pm$ 2.36	33.82 $\pm$ 7.39	30.08 $\pm$ 5.13
	MDGFM	27.01 $\pm$ 2.98	14.11 $\pm$ 2.14	36.02 $\pm$ 9.54	33.28 $\pm$ 8.76
	GraphGlue	34.12 $\pm$ 2.57	18.19 $\pm$ 2.51	38.65 $\pm$ 13.88	40.17 $\pm$ 10.09
5-shot	GCOPE	32.83 $\pm$ 3.26	16.98 $\pm$ 1.40	41.33 $\pm$ 9.85	43.74 $\pm$ 3.19
	MDGFM	32.54 $\pm$ 3.75	16.77 $\pm$ 1.92	48.10 $\pm$ 7.26	46.62 $\pm$ 4.16
	GraphGlue	36.26 $\pm$ 3.09	20.67 $\pm$ 1.34	52.60 $\pm$ 6.07	51.49 $\pm$ 7.97

Appendix

Table 17: Performance under different shot settings with pretrained on 8 datasets (including Amazon-Ratings and Roman-Empire).

Figure 7: Visualization of the pre-trained manifold from 6 datasets.

Model	Node Classification			Link Classification	Graph Classification
Model	Arxiv	Computers	Reddit	FB15k_237	PROTEINS	HIV
GCN	$12.61\scriptstyle{\pm 1.75}$	$33.89\scriptstyle{\pm 3.86}$	$11.15\scriptstyle{\pm 2.14}$	$32.11\scriptstyle{\pm 2.37}$	$50.11\scriptstyle{\pm 13.07}$	$52.56\scriptstyle{\pm 5.39}$
GraphSAGE	$14.68\scriptstyle{\pm 3.76}$	$35.47\scriptstyle{\pm 8.29}$	$14.69\scriptstyle{\pm 2.31}$	$35.74\scriptstyle{\pm 2.19}$	$58.99\scriptstyle{\pm 2.79}$	$56.78\scriptstyle{\pm 3.75}$
GIN	$11.20\scriptstyle{\pm 2.03}$	$44.77\scriptstyle{\pm 6.02}$	$18.53\scriptstyle{\pm 1.89}$	$38.25\scriptstyle{\pm 2.55}$	$54.22\scriptstyle{\pm 13.50}$	$52.63\scriptstyle{\pm 7.47}$
GCC	$12.65\scriptstyle{\pm 2.08}$	$34.82\scriptstyle{\pm 6.13}$	$54.78\scriptstyle{\pm 5.64}$	$47.84\scriptstyle{\pm 1.95}$	$59.20\scriptstyle{\pm 7.97}$	$52.63\scriptstyle{\pm 3.63}$
DGI	$13.32\scriptstyle{\pm 3.35}$	$35.26\scriptstyle{\pm 7.58}$	$60.08\scriptstyle{\pm 4.80}$	$42.50\scriptstyle{\pm 2.03}$	$53.18\scriptstyle{\pm 8.44}$	$52.80\scriptstyle{\pm 7.53}$

Appendix

Table 18: Performance of cross-domain transfer on various downstream tasks in the 1-shot setting, reported as mean

\pm

std over 10 runs. The highest result is bolded , and the runner-up is underlined .

Model	Node Classification			Link Classification	Graph Classification
Model	Arxiv	Computers	Reddit	FB15k_237	PROTEINS	HIV
GCN	$27.68\scriptstyle{\pm 2.13}$	$65.78\scriptstyle{\pm 4.20}$	$28.36\scriptstyle{\pm 1.01}$	$52.43\scriptstyle{\pm 1.87}$	$55.04\scriptstyle{\pm 9.98}$	$47.81\scriptstyle{\pm 3.91}$
GraphSAGE	$26.18\scriptstyle{\pm 2.21}$	$66.75\scriptstyle{\pm 4.45}$	$22.27\scriptstyle{\pm 1.17}$	$58.91\scriptstyle{\pm 1.52}$	$60.45\scriptstyle{\pm 1.39}$	$50.59\scriptstyle{\pm 0.75}$
GIN	$26.06\scriptstyle{\pm 2.42}$	$69.51\scriptstyle{\pm 3.50}$	$29.03\scriptstyle{\pm 1.66}$	$63.76\scriptstyle{\pm 1.73}$	$58.87\scriptstyle{\pm 5.05}$	$49.12\scriptstyle{\pm 4.95}$
GCC	$26.84\scriptstyle{\pm 2.14}$	$62.63\scriptstyle{\pm 3.16}$	$65.21\scriptstyle{\pm 1.56}$	$73.69\scriptstyle{\pm 1.24}$	$64.20\scriptstyle{\pm 3.09}$	$57.41\scriptstyle{\pm 1.73}$
DGI	$27.18\scriptstyle{\pm 2.33}$	$61.02\scriptstyle{\pm 3.20}$	$62.72\scriptstyle{\pm 2.21}$	$68.32\scriptstyle{\pm 1.46}$	$53.34\scriptstyle{\pm 6.27}$	$52.23\scriptstyle{\pm 8.49}$

Appendix

Table 19: Performance of cross-domain transfer on various downstream tasks in the 5-shot setting, reported as mean

\pm

std over 10 runs. The highest result is bolded , and the runner-up is underlined .

Model	Node Classification			Link Classification	Graph Classification
Model	Arxiv	Computers	Reddit	FB15k_237	PROTEINS	HIV
GCN	$12.61\scriptstyle{\pm 1.75}$	$33.89\scriptstyle{\pm 3.86}$	$11.15\scriptstyle{\pm 2.14}$	$32.11\scriptstyle{\pm 2.37}$	$60.11\scriptstyle{\pm 13.07}$	$52.56\scriptstyle{\pm 5.39}$
GraphSAGE	$14.68\scriptstyle{\pm 3.76}$	$35.47\scriptstyle{\pm 8.29}$	$14.69\scriptstyle{\pm 2.31}$	$35.74\scriptstyle{\pm 2.19}$	$68.99\scriptstyle{\pm 2.79}$	$56.78\scriptstyle{\pm 3.75}$
GIN	$11.20\scriptstyle{\pm 2.03}$	$44.77\scriptstyle{\pm 6.02}$	$18.53\scriptstyle{\pm 1.89}$	$38.25\scriptstyle{\pm 2.55}$	$64.22\scriptstyle{\pm 13.50}$	$52.63\scriptstyle{\pm 7.47}$
GCC	$12.65\scriptstyle{\pm 2.08}$	$34.82\scriptstyle{\pm 6.13}$	$54.78\scriptstyle{\pm 5.64}$	$47.80\scriptstyle{\pm 1.97}$	$59.20\scriptstyle{\pm 7.97}$	$52.63\scriptstyle{\pm 3.63}$
DGI	$13.32\scriptstyle{\pm 3.35}$	$35.26\scriptstyle{\pm 7.58}$	$60.08\scriptstyle{\pm 4.80}$	$42.56\scriptstyle{\pm 2.05}$	$53.18\scriptstyle{\pm 8.44}$	$52.80\scriptstyle{\pm 7.53}$

Appendix

Table 20: Performance of intra-domain transfer on various downstream tasks in the 1-shot setting, reported as mean

\pm

std over 10 runs. The highest result is bolded , and the runner-up is underlined .

Model	Node Classification			Link Classification	Graph Classification
Model	Arxiv	Computers	Reddit	FB15k_237	PROTEINS	HIV
GCN	$27.68\scriptstyle{\pm 2.13}$	$65.78\scriptstyle{\pm 4.20}$	$28.36\scriptstyle{\pm 1.01}$	$52.43\scriptstyle{\pm 1.87}$	$65.04\scriptstyle{\pm 9.98}$	$57.81\scriptstyle{\pm 3.91}$
GraphSAGE	$26.18\scriptstyle{\pm 2.21}$	$66.75\scriptstyle{\pm 4.45}$	$22.27\scriptstyle{\pm 1.17}$	$58.91\scriptstyle{\pm 1.52}$	$70.45\scriptstyle{\pm 1.39}$	$60.59\scriptstyle{\pm 0.75}$
GIN	$26.06\scriptstyle{\pm 2.42}$	$69.51\scriptstyle{\pm 3.50}$	$29.03\scriptstyle{\pm 1.66}$	$63.76\scriptstyle{\pm 1.73}$	$68.87\scriptstyle{\pm 5.05}$	$59.12\scriptstyle{\pm 4.95}$
GCC	$26.84\scriptstyle{\pm 2.14}$	$62.63\scriptstyle{\pm 3.16}$	$65.21\scriptstyle{\pm 1.56}$	$73.64\scriptstyle{\pm 1.25}$	$64.20\scriptstyle{\pm 3.09}$	$58.34\scriptstyle{\pm 2.19}$
DGI	$27.18\scriptstyle{\pm 2.33}$	$61.02\scriptstyle{\pm 3.20}$	$62.72\scriptstyle{\pm 2.21}$	$68.32\scriptstyle{\pm 1.47}$	$53.34\scriptstyle{\pm 6.27}$	$52.23\scriptstyle{\pm 8.49}$

Appendix

Table 21: Performance of intra-domain transfer on various downstream tasks in the 5-shot setting, reported as mean

\pm

std over 10 runs. The highest result is bolded , and the runner-up is underlined .

	Variants	Arxiv	Computers	Reddit	FB15k_237	PROTEINS	HIV
1-shot	w/o $\mathcal{L}_{\text{curv}}$	$22.33\scriptstyle{\pm 2.56}$	$49.63\scriptstyle{\pm 5.11}$	$64.38\scriptstyle{\pm 5.12}$	$53.12\scriptstyle{\pm 3.74}$	$51.21\scriptstyle{\pm 3.54}$	$50.34\scriptstyle{\pm 3.87}$
	w/o $\mathcal{L}_{\text{holo}}$	$27.14\scriptstyle{\pm 3.62}$	$56.39\scriptstyle{\pm 4.16}$	$65.93\scriptstyle{\pm 4.33}$	$54.85\scriptstyle{\pm 4.78}$	$53.23\scriptstyle{\pm 4.48}$	$54.83\scriptstyle{\pm 2.15}$
	GraphGlue	$\mathbf{28.88}\scriptstyle{\pm 5.22}$	$\mathbf{59.50}\scriptstyle{\pm 7.05}$	$\mathbf{67.12}\scriptstyle{\pm 3.39}$	$\mathbf{59.75}\scriptstyle{\pm 5.27}$	$\mathbf{55.87}\scriptstyle{\pm 4.85}$	$\mathbf{60.22}\scriptstyle{\pm 3.09}$
5-shot	w/o $\mathcal{L}_{\text{curv}}$	$29.17\scriptstyle{\pm 3.14}$	$66.85\scriptstyle{\pm 3.58}$	$74.13\scriptstyle{\pm 1.92}$	$69.33\scriptstyle{\pm 3.98}$	$58.77\scriptstyle{\pm 4.35}$	$57.13\scriptstyle{\pm 3.33}$
	w/o $\mathcal{L}_{\text{holo}}$	$35.77\scriptstyle{\pm 2.64}$	$67.16\scriptstyle{\pm 2.45}$	$79.11\scriptstyle{\pm 3.47}$	$74.02\scriptstyle{\pm 0.97}$	$58.74\scriptstyle{\pm 2.18}$	$54.12\scriptstyle{\pm 4.19}$
	GraphGlue	$\mathbf{37.02}\scriptstyle{\pm 2.33}$	$\mathbf{73.29}\scriptstyle{\pm 0.70}$	$\mathbf{85.05}\scriptstyle{\pm 1.17}$	$\mathbf{81.51}\scriptstyle{\pm 2.31}$	$\mathbf{65.32}\scriptstyle{\pm 2.45}$	$\mathbf{61.55}\scriptstyle{\pm 2.66}$

Appendix

Table 22: Ablation study of GraphGlue ’s key components.

Figure 8: Visualization of the pre-trained manifold from 6 datasets.

Graph Foundation Models

Graph Foundation Models are pretrained graph-learning systems designed to transfer across datasets, tasks, and domains with different structures and features.

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May 25, 2026

MDGMIX: Boundary-Aware Subgraph Mixing for Multi-Domain Graph Pre-Training

Multi-domain graph pre-training is a crucial step in constructing foundational graph models with cross-domain generalization capabilities. However, existing methods predominantly rely on jointly training all source domain graphs, resulting in high computational costs. Furthermore, it remains unclear whether all source domain graph data contribute equally to effective transfer. This paper empirically reveals significant data redundancy in multi-domain graph pre-training. Based on this finding, we propose the Multi-domain Graph Pre-training Framework, MDGMIX, which combines boundary-aware subgraph mixing with hierarchical discrimination. By selecting boundary nodes to construct challenging mixed-domain subgraphs, MDGMIX employs coarse-grained domain discrimination and fine-grained domain decomposition losses to decouple shared patterns from domain-specific patterns. During adaptation, MDGMIX employs a lightweight prompt weighting mechanism to transfer source domain knowledge. Extensive experiments demonstrate that MDGMIX consistently outperforms strong baselines in few-shot classification tasks while exhibiting superior time and memory efficiency. The code is available at: https://github.com/zhengziyu77/MDGMIX.

Ziyu Zheng, Yaming Yang, Ziyu Guan +2

School of Computer Science and Technology, Xidian University, Xi’an, China · School of Artificial Intelligence, Xidian University, Xi’an, China

Cross-Domain Generalization Cross-Domain Transfer Learning Graph Foundation Models

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Jun 16, 2026

Handling Feature Heterogeneity with Learnable Graph Patches

In recent years, the rapid development of foundation models and graph pre-training technologies has spurred increasing interest in constructing a universal pre-trained graph model or Graph Foundation Model (GFM). However, a significant challenge is that existing models are unable to address feature heterogeneity in graph data without textual information, which hinders the transferability of graph models across different datasets. To bridge this gap, we propose the concept of learnable graph patches, which we regard as the smallest semantic units of any graph data. We decompose the graph into learnable graph patches by unfolding the node features and constructing corresponding patch structures separately. We then design a framework that mines transferable information from graph data across domains. Specifically, after extracting graph patches, we propose a patch encoder to extract knowledge from each unit and a patch aggregator to learn how the units are combined into a whole. Due to its domain-agnostic nature, the model can be applied to downstream data across different domains. Furthermore, we analyze the connection between our method and existing graph models, as well as the transferability of the node embeddings it generates. Empirically, our method not only achieves the capability to use multi-domain graphs for pre-training, but also shows enhanced performance across various downstream datasets and tasks. Moreover, we observe consistent improvement in downstream performance as the volume of pre-training data increases.

Yifei Sun, Yang Yang, Xiao Feng +4

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Oct 10, 2026

More Domains, No Gains? FLO: Fast-Slow Reciprocal Learning for Multi-Domain Graph Pre-training

Inspired by the great success of foundation models in the development of artificial general intelligence, Graph Foundation Models (GFMs) have recently attracted significant attention and have the potential to advance graph intelligence. Exhibiting such intelligence requires effectively learning knowledge from large-scale, multi-domain graph data during pre-training. Increasing domain diversity during pre-training is expected to yield richer and more generalizable knowledge. Most existing methods pursue this goal by designing domain alignment strategies that help a single graph model learn from multiple domains. However, we observe that existing methods struggle to benefit from increasing domain diversity. Through empirical and theoretical analysis, we reveal two key limitations. Firstly, pre-training in most GFMs is confined to a single message-passing paradigm. Since propagation flattens relations among neighboring nodes, the graph model can hardly perceive the knowledge beyond propagation, namely the attribute-predictable component of these relations. Secondly, domain alignment strategies often rely on randomly initialized parameters that are jointly updated with the graph model using immediate loss feedback, leaving early knowledge acquisition vulnerable to cross-domain interference. To address these issues, we propose FLO, a Fast--sLow reciprOcal approach for multi-domain graph pre-training. Specifically, a propagation-free attribute branch predicts the graph model's relations without message passing and returns these predictions to refine the model. We further stabilize knowledge acquisition by pairing a fast process that adapts to the current domain with a slow process that integrates knowledge across domains. On 12 datasets, FLO benefits from increasing domain diversity and achieves the best average performance in cross-domain and cross-task transfer.

Yupeng Tong, Lianze Shan, Jitao Zhao +2

School of Computer Science and Technology, Tianjin University, Tianjin, China

Graph Foundation Models Cross-Domain Transfer Learning

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Model	Pretraining	Adaptation (per graph sample)
PRODIGY	$\mathcal{O}(B\|V\|^{2}d)$	$\mathcal{O}((\|V\|+\|E\|)d+\|V\|^{2})$
GFT	$\mathcal{O}(B(\|V\|+\|E\|)d+BTh)$	$\mathcal{O}((\|V\|+\|E\|)d+Th)$
RAGraph	$\mathcal{O}(B(\|V\|+\|E\|)d+B\|E_{r}\|d)$	$\mathcal{O}((\|V\|+\|E\|)d+\|E_{r}\|d)$
SAMGPT	$\mathcal{O}(B(\|V\|+\|E\|)d+Bk_{s}d)$	$\mathcal{O}((\|V\|+\|E\|)d+k_{p}d)$
GCOPE	$\mathcal{O}(B(\|V\|+\|E\|)d+BK_{c}d)$	$\mathcal{O}((\|V\|+\|E\|)d+K_{c}d)$
MDGFM	$\mathcal{O}(B(\|V\|+\|E\|)d+B\|V\|^{2})$	$\mathcal{O}((\|V\|+\|E\|)d+\|V\|^{2})$

Abstract

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