arXiv CSopen access

Empowering Heterogeneous Graph Foundation Models via Decoupled Relation Alignment

1

Empowering Heterogeneous Graph Foundation Models via Decoupled Relation Alignment

arXiv:2605.00731v1 [cs.SI] 1 May 2026

Ziyu Zheng, Yaming Yang, Zhe Wang, Ziyu Guan∗ , Wei Zhao

Abstract—While Graph Foundation Models (GFMs) have achieved remarkable success in homogeneous graphs, extending them to multi-domain heterogeneous graphs (MDHGs) remains a formidable challenge due to cross-type feature shifts and intradomain relation gaps. Existing global feature alignment methods (PCA or SVD) enforce a shared feature space blindly, which distorts type-specific semantics and disrupts original topologies, inevitably leading to "Type Collapse" and "Relation Confusion". To address these fundamental limitations, we propose Decoupled relation Subspace Alignment (DRSA), a novel, plug-and-play relation-driven alignment framework. DRSA fundamentally shifts the paradigm by decoupling feature semantics from relation structures. Specifically, it introduces a dual-relation subspace projection mechanism to coordinate cross-type interactions within a shared low-rank relation subspace explicitly. Furthermore, a feature-structure decoupled representation is designed to decompose aligned features into a semantic projection component and a structural residual term, adaptively absorbing intra-domain variations. Optimized via a stable alternating minimization strategy based on Block Coordinate Descent, DRSA constructs a wellcalibrated, structure-aware latent space. Extensive experiments on multiple real-world benchmark datasets demonstrate that DRSA can be seamlessly integrated as a universal preprocessing module, significantly and consistently enhancing the cross-domain and few-shot knowledge transfer capabilities of state-of-the-art GFMs. The code is available at: https://github.com/zhengziyu77/DSRA. Index Terms—Graph Foundational Model, Multi-Domain Graph Learning, Heterogeneous Graph, Graph Domain Generalization.

Homogeneous Graph

Heterogeneous Graph

Domain A

Domain A Paper Author

Inter-Domain Discrapancy Inter-Domain Multi-domain data Discrepancy (academic, movie)

Domain B

Intra-Domain Discrapancy Multi-Type Node (autor,paper) Multi-Type Relation(write,cite)

Domain B Movie Actor

How to Avoid Dependence on Metapaths

I. I NTRODUCTION Fig. 1: Multi-domain heterogeneous graph foundation models RAPH data, as a powerful paradigm for modeling com- exhibit significantly different negative transfer behaviors from plex entity relationships, has been extensively adopted the perspectives of meta-path-based homogeneous graphs and across diverse domains, including academic networks [1], raw heterogeneous relation graphs. recommendation systems [2], [3], and bioinformatics analysis [4]. In recent years, inspired by the success of largescale pre-training in the language [5] and vision fields [6], Graph Foundation Models (GFMs) [7], [8] have emerged as [13], [15]–[17], which assume uniform node and edge types a pivotal direction in graph representation learning. By pre- and merely require addressing inter-domain distribution shifts. training on multi-source graph data and adapting to downstream In contrast, extending this paradigm to multi-domain heterogetasks, GFMs aim to transfer generalizable knowledge across neous graphs remains a formidable challenge. Heterogeneous different scenarios. Recent studies [9]–[13] indicate that joint graphs exhibit not only cross-domain distribution shifts but also modeling over multi-domain graphs facilitates the acquisition complex intra-domain structures composed of multi-type nodes of universal structural patterns and semantic representations, and diverse relation semantics [18]–[22], which significantly thereby improving generalization under distribution shifts [14]. exacerbates the difficulty of cross-domain knowledge transfer. Despite remarkable progress, current research on multi- To investigate the impact of this dual-level discrepancy, we domain GFMs primarily focuses on homogeneous graphs [9]– conduct multi-domain pre-training using the ACM dataset [21] as the target domain. Employing the same pre-training strategy * Corresponding author on the source domains, we utilize meta-path graphs and raw Z. Zheng, Y. Yang, Z. Wang, Z. Guan, and W. Zhao are with the heterogeneous graphs as inputs, respectively. Experimental School of Computer Science and Technology, Xidian University, Xi’an, China 710071. E-mail: {zhengziyu@stu., zwang_01@stu., yym@, zyguan@, results reveal a pronounced negative transfer phenomenon ywzhao@mail.}xidian.edu.cn from both perspectives, which becomes even more severe

G

2

Challenge 1: Type Collapse

PCA

SVD

Challenge 2: Relational Confusion Movie-Director Movie-Actor Paper-Author Paper-Subject

P C A S V D Fig. 2: Multi-domain heterogeneous graphs face two fundamental challenges. Challenge 1 visualizes the node distributions on the ACM and IMDB datasets, where different colors represent node types from different domains. Challenge 2 illustrates the relation reconstruction errors after applying traditional feature alignment methods, with color intensity indicating the magnitude of the errors.

when relation aggregation is directly performed on the raw heterogeneous graphs. This finding indicates that the inherent intra-domain heterogeneity significantly exacerbates the difficulty of cross-domain alignment. Consequently, a critical research question naturally arises: How can we construct a universal foundation model for multi-domain heterogeneous graphs without relying on manually defined meta-paths? The core prerequisite for multi-domain pre-training is to overcome the incommensurability of input spaces across domains [23]. To achieve this, existing multi-domain GFMs designed for homogeneous graphs typically employ input-level global alignment techniques, such as Principal Component Analysis (PCA) [24] or Singular Value Decomposition (SVD) [25], to project multidomain node features into a unified dimensional space before pre-training. However, this strategy implicitly assumes that all node features, regardless of their intrinsic types and relation contexts, can be embedded within a shared metric space. This assumption is fundamentally violated in heterogeneous graphs, where different types of nodes possess fundamentally distinct semantic meanings and structural roles [26], [27]. To empirically validate this limitation, we conduct an analysis on two heterogeneous datasets: the academic network ACM and the movie network IMDB [28]. Specifically, by employing traditional alignment methods, we analyze the aligned features from these datasets. Visualizations of multi-

type node distributions and structural reconstruction errors reveal that: (1) Type Collapse: different node types exhibit pronounced distributional overlap post-alignment, rendering them indistinguishable; and (2) Relation Confusion: structural errors increase substantially, indicating that the alignment process disrupts original relation semantics. These phenomena demonstrate that coarse-grained global alignment not only distorts type-specific information but also overlooks the critical role of relation heterogeneity. The aforementioned analysis reveals a critical insight: unlike homogeneous graphs that merely need to address crossdomain distribution shifts, node semantics in multi-domain heterogeneous graphs are jointly determined by their attributes and cross-type relations. Relying solely on feature alignment leads to representation space mismatch. This indicates that an effective alignment mechanism must resolve the intradomain mismatch among multi-type nodes and heterogeneous relations. Consequently, the core challenge lies in tackling a dual-level distribution shift: ❶ Cross-type Feature Shift, where different node types possess feature spaces with varying dimensions and distributions; and ❷ Intra-domain relation Gap, where the mixed distribution formed by heterogeneous relations exhibits inconsistencies across different subspaces. Therefore, an effective cross-domain alignment mechanism necessitates the simultaneous modeling of feature semantics and relation structures. To tackle these challenges, we propose a novel plug-andplay relation-driven alignment framework, Decoupled relation Subspace Alignment (DRSA), which fundamentally rethinks the alignment mechanism in cross-domain heterogeneous graphs. Unlike conventional methods that enforce a unified representation within the feature space, DRSA decouples feature semantics from relation structures and achieves alignment at the level of a relation subspace by explicitly modeling cross-type interactions. Specifically, we introduce a dual-relation subspace projection mechanism that factors cross-type interactions into a shared low-rank subspace and captures relation dependencies via bilinear projections, thereby ensuring semantic consistency of relations within a unified latent space. In addition, we propose a feature–structure decoupled mechanism, where aligned features are decomposed into a semantic projection component and a structural residual term. This design enables the model to preserve feature consistency while adaptively capturing intra-domain variations induced by relation structures. To optimize the model, we adopt an alternating minimization strategy [29] , which progressively aligns relation structures and refines feature representations through a two-stage procedure. As each subproblem is convex and admits a closed-form solution, the overall optimization enjoys stable convergence. The main contributions of this work are summarized as follows: • We systematically analyze the structural origins of the neg-

ative transfer phenomenon in multi-domain heterogeneous graph pre-training, and reveal the fundamental limitations of traditional global feature alignment methods, which inevitably induce type collapse and relation confusion when handling multi-type nodes.

3

• We propose a plug-and-play relationly-driven alignment

framework, DRSA. By decoupling feature semantics from network topology and explicitly coordinating cross-type interactions within a relation subspace, DRSA effectively avoids the distortion of type-specific semantics. To the best of our knowledge, this is the first exploratory work that eliminates meta-path dependency and addresses textfree multi-domain heterogeneous graph foundation models. • Extensive experiments on multiple real-world benchmark datasets demonstrate that DRSA can be seamlessly integrated as a universal preprocessing module, consistently and significantly improving the cross-domain and few-shot knowledge transfer capabilities of state-of-the-art graph foundation models. II. R ELATED W ORK A. Heterogeneous Graph Self-Supervised Learning

structural discrepancies across graphs; MDGPT [40] incorporates domain tokens to enhance cross-domain discriminability; SAMGPT [9] employs structural tokens to align topological information. Furthermore, MDGFM [11] and SA2GFM [41] focus on robustness under domain shifts; BRIDGE [42] proposes alignment risk regularization with a mixture-of-experts mechanism; GRAVER [12] and RAG-GFM [13] improve generalization via substructure transfer and retrieval-augmented strategies. These methods typically perform input-level alignment (e.g., SVD or PCA) prior to pre-training. However, such global alignment implicitly assumes that nodes from different types share a common feature space, which is invalid in heterogeneous graphs. Given the intrinsic semantic disparity across node types, this coarse alignment inevitably induces metric collapse. The resulting distorted input further propagates through the pre-training, ultimately undermining the effectiveness of crossdomain knowledge transfer.

Heterogeneous graph self-supervised learning can be categorized into metapath-based and free-metapath methods. III. P RELIMINARIES AND P ROBLEM S TATEMENT Metapath-based methods transform into homogeneous graphs by predefined metapaths. DMGI [30] and HDMI [31] learn node A. Heterogeneous Graph consistency by maximizing mutual information between nodeA heterogeneous graph is formally defined as G = level and graph-level representations. HeCo [21] introduces (V, E, X , ϕ, ψ), where V and E represent the sets of nodes both network schema and meta-path views for contrastive learn- and edges, respectively. X = {X(t) }t∈T is the collection of ing, while HGMAE [32] reconstructs metapath-based edges feature matrices associated with each node type. The mapping and node features from a generative perspective. MUG [33] functions ϕ : V → T and ψ : E → R assign each node and achieves unified cross-domain input by leveraging a dimension- edge to its corresponding type, where T and R denote the sets aware module. These methods are primarily designed for single- of node and edge types, satisfying |T | + |R| > 2. For each domain settings and heavily depend on manually designed relation r ∈ R, the topological structure is represented by an metapaths. In multi-domain scenarios, each domain may involve adjacency matrix A(r) ∈ {0, 1}nsrc ×ndst . multiple metapath graphs, resulting in substantial computational overhead during pre-training. Meta-path-free methods aim to remove reliance on hand- B. Problem Formulation crafted priors. SHGP [18] introduces structural clustering-based Given a collection of K unlabeled source-domain heteropseudo-labeling in heterogeneous graphs. HERO [22] employs a geneous graphs Gs = {G1 , G2 , · · · , GK }, where each graph self-expression matrix to capture homophily in heterogeneous Gi originates from a distinct domain Di , our objective is to graphs, while SCHOOL [34] optimizes the affinity matrix pre-train a universal graph encoder fθ that generalizes to an via spectral clustering focusing on homophilic information. unseen target-domain heterogeneous graph. Given that graph RMR [35] introduces preservation, masking, and reconstruction data from different domains follow distinct feature distributions, mechanisms into relation subgraphs. RASH [19] models both the core prerequisite for multi-domain graph pre-training is homophily and heterophily from a relation perspective. Prompt- achieving alignment of node features. based methods further enhance downstream performance by Therefore, before applying the pre-training encoder fθ , it introducing type prompts and meta-path prompts [36], [37]. is imperative to construct a structure-preserving alignment However, in multi-domain heterogeneous settings, the structural mapping. For each domain Di and node type τ ∈ T , we aim discrepancies across node types and domains are significantly to learn an alignment operator Aligner(·) that projects the raw amplified, making it difficult for these methods to achieve features Xτ into a synchronized latent manifold Hτ ∈ Rnτ ×d effective knowledge sharing and alignment. (where d is the unified embedding dimension), while preserving the heterogeneous topological constraints: B. Multi-Domain Pre-trained Graph Foundation Models   H = Aligner X , {R } (1) τ τ r r∈R Recently, multi-domain graph foundation models have attracted increasing attention. These methods aim to pre-train on multiple source-domain graphs and transfer to unseen target Subsequently, the universal graph foundation model fθ is domains to evaluate generalization [7], [8]. Existing approaches optimized over the aligned graphs. typically follow a two-stage paradigm: multi-domain preK X training and cross-domain adaptation [17], [38], [39]. For min Lpre (Ĝi , fθ ) (2) θ example, GCOPE [10] introduces virtual nodes to mitigate i=1

4

Semantic Decoupling

Domain A

Multi-Domain Pretraing Unified Aligned Latent Space

Author

P Paper

X ⓧP

X

ⓧ

H

Domain B

Domain A

E Structural Residual

Domain B Movie

H

Paper

write

Author

� = ���

A

Actor

Cross Domain Finetune/Prompt

Relation Alignment

Relation-special interaction

ⓧ

H ⓧ

B

Pretrained Encoder

Target Domain

Alignment

Downstream Task

Fig. 3: Overview of the DRSA framework. DRSA decouples node features into semantic projections and structural residuals, aligns cross-type relations via a low-rank bilinear operator, and learns a unified latent space for multi-domain pretraining and downstream adaptation. It is a plug-and-play alignment module compatible with existing graph foundation models. where Ĝi represents the graph with aligned embeddings Hi . In this work, we remain agnostic to the specific choice of pretraining tasks Lpre , as our primary goal is to demonstrate that an effective decoupled relation alignment serves as a fundamental prerequisite for the transferability of graph foundation models. IV. M ETHODOLOGY In this section, we propose Decoupled relation Subspace Alignment (DRSA) to learn a unified latent space for multidomain heterogeneous graphs by jointly modeling feature semantics and relation structures. Instead of enforcing direct global feature alignment, DRSA formulates alignment as a structured latent representation learning problem, where cross-type interactions are captured via relation-aware bilinear operators, and node representations are decomposed into a semantic projection component and a structural residual term. This design enables the model to preserve transferable feature information while flexibly adapting to relation-induced variations. The overall objective is optimized through an alternating block coordinate descent procedure, which iteratively refines latent representations and feature projections with closed-form updates, ensuring stable convergence. The framework is shown in the Fig.3. A. Dual-relation Subspace Projection In heterogeneous graphs, nodes of different types are associated with type-specific feature spaces, and interactions

occur across heterogeneous domains. Relations between node types encode critical structural information. To capture crosstype interactions and achieve alignment of heterogeneous relationships, we introduce a dual-relation subspace projection mechanism. Instead of learning an independent, dense transition matrix for every relation type, which is highly prone to overfitting and ignores the shared characteristics of node types across different relations—we factorize the relation operator into type-specific bases. For each node type τ ∈ T , we assign two subspace projection matrices: an outgoing projection Aτ ∈ Rk×ρ and an incoming projection Bτ ∈ Rk×ρ , where ρ ≪ k. For a connected node pair with source type ϕs and destination type ϕd , the relation-specific interaction operator Mr is constructed via a bilinear composition: Mr = Aϕs B⊤ ϕd

(3)

Crucially, rather than optimizing Aτ and Bτ jointly with the node representations, we sample them from a Gaussian distribution (N (0, σ 2 )) and fix them as non-trainable random projections throughout the alignment process. Fixing Aτ and Bτ reduces the number of learnable parameters and simplifies the optimization, which helps avoid potential instability caused by the strong coupling between relation operators and latent representations in bilinear formulations. Moreover, random projections have been proven to approximately preserve geometric structures in high-dimensional spaces, providing a diverse set of projection directions [43]–[46]. As a result, the constructed operators Mr = Aϕs B⊤ ϕd can still capture heterogeneous

5

interactions effectively, without introducing additional trainable parameters. Given node latent aligned features Hϕs and Hϕd , the relation structure is reconstructed as: R̂r = Hϕs Mr H⊤ ϕd

(4)

where Mr is a relation-specific bilinear operator bridging different node types. This formulation enables efficient modeling of heterogeneous interactions within a unified latent space.

and relations within the domain, we further inject the complex multi-relation structural information of heterogeneous graphs into the feature alignment process. This decomposition method provides a flexible alignment mechanism to prevent node type collapse and relation confusion caused by aligning heterogeneous graphs across multiple domains. C. Optimization

The proposed unified objective involves multiple coupled variables {Hτ , Pτ , Eτ }, which makes joint optimization comB. Decoupled Latent Feature putationally expensive and unstable. Therefore, we adopt a twoThe dual-relation subspace projection effectively aligns stage alternating optimization scheme, which can be interpreted heterogeneous topological structures; the learned node repre- as a Block Coordinate Descent (BCD) method. 1) Structure-Driven Target Estimation: In the first stage, sentations must also preserve the intrinsic semantic information encoded in the original features. However, in real-world we update the latent aligned feature Hτ using only relation heterogeneous graphs, feature semantics and relation topology information, while fixing all other variables. Specifically, for each node type τ ∈ T , we solve the following subproblem: often reside in inherently different spaces. X A naive formulation that enforces a rigid linear projection 2 2 min ∥Rr − Hϕs Mr H⊤ (7) ϕd ∥F + β∥Hτ ∥F Hτ = Xτ Pτ is therefore overly restrictive, as it implicitly Hτ r∈R assumes that complex relation dependencies can be fully explained by feature transformations alone. In practice, this where the above subproblem denotes the relatoion structural leads to an undesirable trade-off between feature fidelity and error across all heterogeneous relations connected to node type structural consistency, limiting the expressiveness of the learned τ . This is a convex quadratic problem with respect to Hτ , which leads to the following normal equation: representations. To overcome this limitation and endow the model with the Cτ H⊤ (8) τ = Bτ flexibility to capture structure-specific variations, we introduce a feature–structure decoupled representation. Specifically, we To rigorously handle directed heterogeneous graphs, we split the r decompose the target-aligned feature of each node type into a relation aggregation into outgoing edges (t − → t′ ) and incoming ′ r ⊤ semantic component and a structural residual: edges (t − → t). Let Σt′ = Ht′ Ht′ denote the second-order statistics of the neighbor representations. The operators are Hτ = Xτ Pτ + Eτ (5) explicitly defined as: nτ ×dτ dτ ×k Let Σϕ = H⊤ where Xτ ∈ R is the raw feature matrix, Pτ ∈ R ϕ Hϕ denote the second-order statistics. The is a type-specific semantic projection operator that maps raw operators are analytically defined as: The matrices Cτ and Bτ features into the shared latent space, and Eτ ∈ Rnτ ×k is are defined as: X X is a residual term capturing structure-specific variations from Cτ = βIk + Mr Σϕd M⊤ M⊤ (9) r + r Σϕs Mr linear projection. This formulation is inspired by decompositionr r τ− →ϕd ϕs − →τ based representation learning, where semantic and structural X X ⊤ ⊤ ⊤ components are explicitly separated. Bτ = (Rr Hϕd Mr ) + (R⊤ (10) r Hϕs Mr ) r r Instead of jointly optimizing all variables, we adopt a **twoτ− →ϕd ϕs − →τ phase strategy: ⊤ The updated representation is obtained as Hτ = (C−1 τ Bτ ) . • Phase 1: Estimate a structure-driven aligned feature Hτ This stage is purely structure-driven and does not involve using only relation information. feature-dependent terms. It enforces consistency across hetero• Phase 2: Project features into the learned structural subspace and absorb realtion inconsistencies into the geneous relations and constructs a unified structural embedding space. residual term. 2) Feature Decomposition: Given the updated latent aligned This decomposition prevents feature signals from interfering feature Hτ , we update the feature projection and residual by with structural alignment. The overall objective can be formalsolving: ized as: X min ∥Hτ − Xτ Pτ − Eτ ∥2F + β∥Eτ ∥2F + γ∥Pτ ∥2F (11) min ∥R − H M H⊤ ∥2 {H,P,E}

r

ϕs

r

Pτ ,Eτ

ϕd F

r

+

X

∥Hτ − Xτ Pτ − Eτ ∥2F

(6)

τ

+β

X τ

∥Eτ ∥2F + γ

X

∥Pτ ∥2F

τ

Unlike earlier graph foundation models that solely rely on feature pre-alignment while neglecting heterogeneous nodes

This subproblem admits closed-form analytical solutions. We first update the semantic projection matrix via Ridge Regression, and then compute the structural residual: −1 ⊤ Pτ = (X⊤ Xτ (Hτ − Eτ ) τ Xτ + γI) 1 Eτ = (Hτ − Xτ Pτ ) 1+β

(12) (13)

6

Algorithm 1 Decoupled relation Subspace Alignment (DRSA) Require: Features {Xτ }, Relations {Rr }, Hyperparams {k, γ, β}, Iterations {T } Ensure: Aligned representations {Hτ } 1: Initialize Hτ , Pτ , Eτ 2: Initialize projections Aτ , Bτ 3: for iter = 1 to T do 4: // Stage 1: Structure-driven update 5: for each node type τ do 6: Compute Στ ′ = Hτ⊤′ Hτ ′ 7: Cτ ← βI, Bτ ← 0 8: for each relation r : τ → τ ′ do 9: Mr ← Aτ Bτ⊤′ 10: Cτ ← Cτ + Mr Στ ′ Mr⊤ 11: Bτ ← Bτ + (Rr Hτ ′ Mr⊤ )⊤ 12: end for 13: for each relation r : τ ′ → τ do 14: Mr ← Aτ ′ Bτ⊤ 15: Cτ ← Cτ + Mr⊤ Στ ′ Mr 16: Bτ ← Bτ + (Rr⊤ Hτ ′ Mr )⊤ 17: end for 18: Hτ ← (Cτ−1 Bτ )⊤ 19: end for 20: // Stage 2: Feature decomposition 21: for each node type τ do 22: Pτ ← (Xτ⊤ Xτ + γI)−1 Xτ⊤ (Hτ − Eτ ) 1 23: Eτ ← 1+β (Hτ − Xτ Pτ ) 24: Hτ ← Xτ Pτ + Eτ 25: end for 26: end for 27: return {Hτ } This stage ensures that the learned feature remains consistent with the feature space while preserving structural variations. The residual term Eτ provides the flexibility to capture domainspecific variations and relation topological noise that cannot be fully explained by a linear feature projection. Based on Equation 5, we further update the latent alignment features Hτ for different node types from a feature perspective. The above two stages are performed iteratively until convergence. This procedure can be interpreted as a Block Coordinate Descent method. Although the overall problem is non-convex, each subproblem is convex with respect to its variables, ensuring that the objective value monotonically decreases during optimization.This design integrates structural information from different relation during the feature alignment process while maintaining compatibility across feature spaces of different node types. The overall procedure is summarized in Algorithm 1.

TABLE I: Summary of datasets and their details. Datasets

Node Type

Relation

Target

Classes

DBLP

Author (A): 4057 Paper (P): 14328 Conference (C): 20 Term (T): 7723

P-A: 19645 P-C: 14328 P-T: 85810

Author

4

ACM

Paper (P): 4019 Author (A): 7167 Subject (S): 60

P-A: 13407 P-S: 4019

Paper

3

IMDB

Movie (M): 4278 Director (D): 2081 Actor (A): 5257

M-D: 4278 M-A: 12828

Movie

3

Aminer

Paper (P): 6564 Author (A): 13329 Reference (R): 35890

P-A: 18007 P-R: 58831

Paper

4

YELP

Business (B): 2614 User (U): 1286 Service (S): 4 Rating Levels (L): 9

B-U: 30383 B-S: 2614 B-L: 2614

Business

3

A. Experimental Setup Datasets. To evaluate the model’s performance, we used six publicly available benchmark datasets: DBLP, ACM, IMDB, Aminer, Freebase, Yelp, DBLP [47] and ACM [28], Aminer is a heterogeneous graph dataset of academic papers, IMDB [28] comes from a movie dataset, and Yelp [48] is a commercial heterogeneous graph dataset. Baselines. To comprehensively validate the superiority of DRSA, we benchmark it against ten representative state-of-theart models, categorized by their distinct pre-training methodologies: Metapath-based Methods: Metapath2Vec(MP2V) [49], HeCo [21], and HGMAE [32]. These models address heterogeneity through meta-path-guided neighborhood aggregation. Metapath-free Methods: RMR [35], HetGPT [36] and HGPrompt [37]. These approaches explicitly account for the multiple node types and edge types in heterogeneous graphs without requiring conversion to homogeneous graphs. Graph Foundation Models: GCOPE [10], MDGPT [40], and SAMGPT [9]. This category encompasses the latest research explorations in multi-domain pre-training for homogeneous graph structures. Since DRSA is designed as a plug-and-play input alignment module, we integrate it with representative models from the latter two categories, resulting in variants such as RMR + DRSA and GCOPE + DRSA. This setup allows us to isolate and quantify the contribution of DRSA.

Evaluation Protocol. We evaluate the model’s cross-domain generalization capability to unseen target domains, treating each dataset as a distinct domain. In a leave-one-out fashion, one dataset is designated as the target domain for evaluation, V. E XPERIMENT while the remaining datasets are utilized for multi-domain In this section, we conduct extensive experiments to evaluate pre-training. the effectiveness and transferability of our proposed DRSA For methods primarily designed for single-domain scenarios, framework. We compare DRSA, integrated with various cutting- we employ Singular Value Decomposition for feature alignment edge graph foundation models, against a comprehensive set of across different domains, unifying the alignment dimension baselines on challenging multi-domain heterogeneous graph to 50. To facilitate the learning of universal knowledge benchmarks. across diverse domains, we utilize a parameter-sharing encoder

7

TABLE II: Node classification performance comparison. The results of the base models coupled with our DRSA module are highlighted with a blue background, and the corresponding absolute improvements are presented in the subsequent row with a pink background. ACM

Method

DBLP ACC

AUC

AMiner F1

AUC

F1

MP2V

32.61±0.99

50.21±0.56

32.61±0.99

HeCo

62.47±12.44 82.94±7.60 61.05±11.63 55.47±10.43 81.46±6.84 53.17±10.28 26.73±5.77 51.54±2.18 21.90±3.02 33.57±2.57 50.25±1.78 30.61±2.92

HGMAE

67.22±12.96 89.23±5.01 61.91±14.88 63.36±9.09 92.62±3.38 59.09±9.99 23.99±16.28 51.46±3.84 13.44±6.08 34.58±3.89 54.61±3.49 28.06±5.41

24.65±0.98 50.01±0.45 23.97±0.93

ACC

AUC

IMDB

ACC

F1

ACC

AUC

F1

24.30±2.57 50.20±0.55 21.66±1.44 33.44±0.92 49.85±0.76 32.80±0.73

RMR

50.88±14.82 60.75±13.29 47.63±14.84 30.03±5.07 55.85±5.43 24.18±4.27

+DRSA

65.07±11.33 76.26±11.96 61.40±11.01 82.71±9.06 96.69±3.22 81.97±9.82 41.20±8.94 64.97±5.57 37.36±7.23 36.78±2.52 52.15±2.59 32.73±4.48

Impro.

+14.19%

+15.51%

+13.77%

+52.68%

+40.84%

+57.79%

HGPrompt 56.07±9.73 77.63±11.17 55.42±10.29 36.67±7.02 63.82±6.61 33.90±6.96 +DRSA

25.92±4.27 52.74±3.00 22.15±2.89 34.48±2.73 51.65±2.64 32.09±3.56 +15.28%

+12.23%

+15.21%

+2.30%

+0.50%

+0.64%

37.60±8.49 62.83±6.99 33.67±7.29 33.08±2.82 49.99±1.13 27.71±3.95

70.90±11.51 85.14±11.04 69.62±11.88 63.43±11.02 85.21±5.88 61.31±10.98 43.33±9.82 67.48±8.04 38.57±8.22 34.73±3.55 53.25±3.21 29.09±4.47

Impro.

+14.83%

+7.51%

+14.20%

+26.76%

HetGPT

55.91±8.57

71.87±5.69

53.98±6.84

32.44±5.95 59.37±5.45 26.18±5.71

+DRSA

64.83±8.12 75.58±6.01 62.82±6.54 75.72±9.62 90.27±5.87 73.49±10.28 43.67±15.77 56.85±9.15 37.63±8.26 37.94±5.56 56.04±5.93 34.91±5.36

Impro.

+30.90%

+27.41%

+47.31%

+5.73%

+4.65%

+4.90%

+1.65%

+3.26%

+1.38%

32.39±4.99 56.56±3.54 27.64±3.52 34.82±3.13 52.97±4.07 31.72±4.35

+8.92%

+3.71%

+8.84%

GCOPE

49.02±7.42

68.08±5.79

46.43±6.63

+DRSA

80.48±11.26 93.74±5.77 80.91±10.42 79.59±7.05 93.41±3.40 78.03±7.90 42.59±7.77 68.46±5.88 39.10±7.03 38.76±3.97 57.10±5.30 36.14±4.45

Impro.

+43.28%

+21.39%

42.83±5.50 68.36±4.89 41.33±5.67

+9.99%

+3.12%

+3.07%

+3.19%

33.12±6.49 59.80±6.05 29.86±5.00 35.32±2.35 52.90±2.48 32.49±2.61

+25.66%

+34.48%

+36.76%

MDGPT

47.40±5.66

66.67±5.69

46.61±5.58

32.19±2.69 57.59±3.32 31.57±3.05

+DRSA

76.99±11.08 91.42±5.87 77.18±10.39 77.70±10.10 93.12±6.03 76.74±10.43 41.70±6.12 67.17±4.85 38.04±4.77 37.99±5.18 56.11±6.98 35.66±5.91

+8.66%

+9.24%

+3.44%

+4.20%

+3.65%

25.14±2.81 50.21±0.95 22.24±1.34 33.41±3.42 52.57±3.18 28.03±3.66

+24.75%

+30.57%

+45.51%

SAMGPT

46.34±4.82

65.32±4.89

45.57±4.66

31.82±3.31 57.72±3.82 31.29±3.53

+DRSA

76.34±12.49 90.42±5.50 76.32±11.58 80.58±8.29 93.92±4.53 79.20±9.25 43.23±9.69 68.11±6.51 39.44±8.19 37.20±4.81 55.62±6.41 35.32±5.00 +30.00%

+25.10%

+30.75%

+48.76%

+36.20%

+45.17%

+9.47%

+29.59%

Impro.

+35.53%

+36.70%

+0.29%

+31.46%

Impro.

+25.05%

+11.28%

+47.91%

+16.56%

+16.96%

+15.80%

+4.58%

+3.54%

+7.63%

25.16±2.05 50.82±1.57 22.56±1.29 35.10±2.46 53.35±2.73 34.24±2.73 +18.07%

+17.29%

+16.88%

+2.10%

+2.27%

+1.08%

architecture. Specifically, HeCo and HGMAE adopt a HAN [20] encoder, RMR employs a GAT [50] encoder, and all other methods leverage a GCN [51] encoder. The hidden layer dimension for all encoders is consistently set to 256. In the downstream evaluation, we assess the effectiveness of DRSA on two distinct tasks: few-shot node classification and few-shot link prediction [52]. For few-shot node classification, k labeled instances per class are sampled for training, with the remainder used for testing. For few-shot link prediction, categories are defined based on different edge types to evaluate whether distinct types of nodes maintain their heterogeneous relation structures. Each k-shot setting is repeated 20 times, with different label sampling for each run. We employ three widely-used evaluation metrics for classification tasks: classification accuracy (Acc), average AUC-ROC (AUC), and average F1-score (F1), reporting their means and standard deviations across these runs. All implementations were executed on an NVIDIA RTX 5090 GPU with 32GB memory.

can deliver significant performance improvements for such single-domain models. Notably, RMR combined with DRSA achieved a 52.68% absolute accuracy improvement on the DBLP dataset, while HGPROMPT saw a 13.87% increase on the ACM dataset. Recently emerging graph generation models are primarily designed for homogeneous graphs. When directly applied to multi-domain heterogeneous graphs, these methods suffer from severe performance degradation. This is mainly attributed to their reliance on crude global feature alignment techniques. By integrating DRSA as a preprocessing alignment module, DSRA significantly enhances the performance of state-of-the-art graph foundation models, including GCOPE, MDGPT, and SAMGPT, yielding gains of 20%-30% across multiple datasets. This indicates that existing graph foundation models (GFMs) are largely constrained by suboptimal input alignment. By providing a well-calibrated latent space, DRSA effectively enables cross-domain generalization.

B. Performance Comparison

Edge Classification. To evaluate DSRA’s ability to capture heterogeneous relation, we evaluated edge classification performance in Table III. The results confirm the superiority of our proposed dual-relationship subspace projection mechanism; across all datasets, the DSRA-enhanced models consistently outperformed their baseline versions. Notably, on Yelp—a highly complex and sparse business dataset—SAMGPT+DRSA achieved a significant 21.66% increase in accuracy. This indicates that DSRA effectively coordinates heterogeneous interactions while aligning node semantics, thereby avoiding the

Node Classification. For node classification, we observed that models specifically designed for heterogeneous graphs also exhibit shortcomings in cross-domain scenarios. Metapath-based methods such as HeCO and HGMAE outperform meta-path-free methods in multi-domain scenarios; meta-pathfree methods like RMR and HetGPT, which rely solely on the aggregation of heterogeneous relationships, exhibit more pronounced negative transfer. Table II demonstrates that DRSA

8

TABLE III: Edge classification performance comparison. The results of the base models coupled with our DRSA module are highlighted with a blue background, and the corresponding absolute improvements are presented in the subsequent row with a pink background. Yelp

Method

DBLP

AUC

F1

ACC

AUC

F1

ACC

AUC

F1

RMR +DRSA Impro.

37.89±9.85 44.26±7.46 +6.37%

52.58±2.20 56.80±2.83 +4.22%

25.79±4.06 29.78±3.21 +3.99%

46.42±11.38 50.84±12.40 +4.42%

58.28±4.92 65.21±6.26 +6.93%

34.46±5.84 38.43±7.74 +3.97%

51.77±8.27 57.88±8.16 +6.11%

51.15±1.76 52.64±1.62 +1.49%

46.59±4.01 49.16±3.76 +2.57%

GCOPE +DRSA Impro.

54.50±8.67 81.42±7.70 +26.92%

70.00±3.38 87.42±4.11 +17.42%

37.30±3.91 56.00±4.42 +18.70%

33.64±13.44 41.07±12.34 +7.43%

58.25±4.29 61.88±5.17 +3.63%

29.87±6.96 32.38±6.03 +2.51%

47.35±6.55 54.10±3.12 +4.85%

49.81±1.45 54.10±3.72 +4.29%

44.44±4.19 48.48±4.44 +4.04%

MDGPT +DRSA Impro.

56.32±11.29 79.29±7.53 +22.97%

72.09±3.77 84.72±3.31 +12.63%

38.95±5.56 54.11±4.55 +15.16%

38.59±13.64 42.82±9.12 +4.23%

53.46±2.71 54.05±4.74 +0.59%

30.21±6.49 32.92±4.42 +2.71%

47.74±8.97 51.77±7.54 +4.03%

49.91±1.16 54.04±3.39 +4.13%

44.15±5.30 47.90±4.51 +3.75%

SAMGPT +DRSA Impro.

57.57±12.01 79.23±7.35 +21.66%

71.58±2.85 85.36±3.16 +13.78%

38.94±5.68 53.78±4.15 +14.84%

34.41±14.15 44.30±12.14 +9.89%

53.73±3.14 54.38±4.80 +0.65%

28.06±7.07 32.84±5.07 +4.78%

48.34±7.09 51.38±7.76 +3.04%

49.61±1.51 53.56±2.63 +3.95%

44.97±4.66 47.55±4.37 +2.58%

relationship confusion caused by traditional alignment methods. The results in Tables II and III demonstrate that DSRA consistently improves the performance of all backbone models across all datasets and evaluation metrics. This confirms that DSRA is a general-purpose and effective input-level alignment module suitable for multi-domain heterogeneous graphs, and it also indicates that the input alignment problem is a primary bottleneck in existing methods.

  

'05$RXUV *&23( 505



+*0$( +H&R

$FFXUDF\

$FFXUDF\



 

IMDB

ACC

  '05$RXUV *&23( 505



      



1XPEHURIVKRWV (a) ACM



      

1XPEHURIVKRWV (b) DBLP





+*0$( +H&R

low-shot (K ∈ {1, 3, 5}), where the DRSA-enhanced model demonstrates substantial performance gains. As the number of labeled samples increases, the performance gap between DRSA and the baselines gradually narrows. Nevertheless, DRSA maintains a consistent advantage across all shot settings. In addition, we observe that DRSA exhibits smoother and more stable performance curves compared to baseline methods, suggesting that the learned representations are more robust and less sensitive to sampling variability. This advantage can be attributed to the input-level alignment mechanism of DRSA. By constructing a unified latent space that preserves both feature semantics and relation consistency, DRSA enables more effective generalization under limited labeled data. These results further validate the effectiveness of the proposed decoupled alignment strategy. D. Ablation Study

$FFXUDF\

$FFXUDF\

Components Ablation. To investigate the contributions of individual components within DRSA, we conduct an ablation study, as illustrated in Fig. 5a. Specifically, we compare the   full model (ALL) with three variants: removing the structural '05$RXUV +*0$( '05$RXUV +*0$( *&23( +H&R *&23( +H&R residual (w/o residual), removing the feature term (w/o feature),  505 505 and removing the dual-relation operator (w/o M). (N) represents                   1XPEHURIVKRWV 1XPEHURIVKRWV the node classification task, and (E) represents the edge (c) Aminer (d) IMDB classification task. When the structural residual is removed, the aligned feature Fig. 4: Impact of shots number analysis. degenerates to Hτ = Xτ Pτ . This leads to a significant performance drop across all datasets, indicating that E is essential for capturing structure-specific variations beyond C. Performance on Few-Shot Classification linear feature projection. In heterogeneous graphs, features and To further evaluate the cross-domain generalization capability relation structures reside in distinct semantic spaces. Enforcing of DRSA under limited supervision, we conduct few-shot node a rigid mapping forces the model to overfit the feature space classification experiments with varying numbers of labeled while neglecting relation inconsistencies. samples. We adopt GCOPE+DRSA as our representative model. Removing the feature term also results in noticeable degraThe results are shown in Figure 4. Overall, DRSA consistently dation, suggesting that relation structural information alone is outperforms all baseline methods across all datasets and shot insufficient to capture full semantics. Moreover, eliminating settings. The advantage is particularly pronounced in extremely feature decomposition disrupts the two-stage optimization 



9

$//

ZRUHVLGXDO

ZRIHDWXUH

7\SH0

ZR0



  







     



5HODWLRQ0

  











'%/3(

,0'%1































 





















)XOO5DQN0





$FFXUDF\

 

*OREDO0

'%/31  ,0'%(  $&01  

     

 

 



ZR0

'%/31

$&01

,0'%1

$PLQHU1

<HOS(

'%/3(

<HOS(

,0'%(

(a) Ablation experiments of different components on four datasets.

$PLQHU1

(b) Ablation experiments on variants of different M .

Fig. 5: Ablation experiments.

Accuracy (%)

Accuracy (%)

Accuracy (%)

Accuracy (%)

mechanism. Structure-driven estimation provides a stable target, erogeneity, while Full Rank M is prone to overfitting and while feature projection regularizes the solution and enforces reduced optimization stability. Type M and Relation M, on consistency with the input space. This highlights the comple- the other hand, exhibit two competitive parallel strategies, each mentarity between structural and feature information, proving with unique advantages in specific tasks. Specifically, Type that decoupling their optimization is crucial for achieving stable M performs exceptionally well in the node classification task and effective alignment. because decomposition using a node type basis better preserves Removing the dual-relation operator causes the most severe and emphasizes the node-specific semantics during alignment. degradation. As a relation interaction operator, M maps features Conversely, Relation M demonstrates stronger capabilities in of different node types into a shared relation subspace. Omitting edge classification tasks because its edge-type-centric approach M implicitly assumes a unified space across node types, which more clearly captures finer-grained topological interaction contradicts the heterogeneous nature of the data and leads to patterns. indistinguishable cross-type interactions. Furthermore, we observe consistent degradation trends in 82 80 80 edge classification tasks when ablating these components. 85 85 75 78 80 80 Since edge classification fundamentally relies on cross-type 76 75 70 75 70 74 interactions, removing the dual-relation operator (w/o M) 65 70 72 65 60 65 55 leads to the most drastic performance drop, as the model 70 60 50 60 68 1.0 1.0 0.2 0.2 fails to map distinct node types into a shared structural 0.8 0.8 0.4 0.4 66 0.6 0.6 0.6 0.6 0.4 0.4 0.8 0.8 space. Similarly, removing the structural residual (w/o residual) 0.2 0.2 1.0 1.0 noticeably impairs the model’s ability to preserve domain(a) ACM (b) DBLP specific topological semantics. the results demonstrate that edge classification is more sensitive to structural modeling, 44 38.5 further highlighting the necessity of the dual-relation design. 48 42 43 38.0 46 40 Overall, the results demonstrate that the three components 44 37.5 42 38 42 37.0 40 are complementary and mutually reinforcing: the residual term 36 41 38 36.5 34 36 captures structural variations, the feature decomposition ensures 40 36.0 34 32 1.0 1.0 0.2 0.2 35.5 0.8 0.8 39 semantic consistency, and the relation operator M models 0.4 0.4 0.6 0.6 0.6 0.6 0.4 0.4 0.8 0.8 0.2 0.2 heterogeneous interactions. Together, they form a unified 1.0 1.0 framework that effectively addresses feature type collapse and (c) Aminer (d) IMDB relation confusion. Fig. 6: Sensitivity of the structural residual penalty β and the Variants of different M. To validate our relation operator feature projection regularization γ across different datasets. design, we compare the node type-based dual projection (Type M) with several variants in Fig. 5b: the removal operator (w/o M), all relations sharing a single matrix (Global M), applying full-rank projection (Full Rank M), and a parallel E. Hyperparameter Analysis low-rank strategy constructed from a relation perspective: M = In this section, we investigate the sensitivity of the DRSA Aψ(s,d) B⊤ (Relation M). framework to its core hyperparameters: the structural residual ψ(d,s) Global M performs poorly due to ignoring relation het- penalty β and the feature projection regularization γ. Figure 6

10

ACM-p ACM-a

ACM-s IMDB-m

IMDB-d IMDB-a

DBLP-a DBLP-p

(a) ACM (raw)

(b) ACM (Ours)

(c) ACM (PCA)

(d) ACM (SVD)

(e) IMDB (raw)

(f) IMDB (Ours)

(g) IMDB (PCA)

(h) IMDB (SVD)

DBLP-c DBLP-t

Fig. 7: Multi-domain node visualization.

Fig. 8: Relation structure error on ACM(paper-author) and IMDB(movie-actor).

VII. C ONCLUSION In this paper, we systematically investigate the "negative transfer" phenomenon in multi-domain heterogeneous graph Structural Residual Penalty (β): The parameter β determines pre-training and reveal the fundamental limitations of trathe model’s tolerance for structural variations. As shown in ditional global feature alignment, which inherently induces Figure 6, setting β to an extremely small value degrades type collapse and relation confusion when handling multi-type performance, causing the residual term Eτ to dominate during nodes. To address this bottleneck, we introduce Decoupled optimization. This results in the model absorbing excessive relation Subspace Alignment (DRSA), a universal, plug-anddomain-specific topological noise, thereby weakening the play input alignment framework. By innovatively employing a generalization ability of the learned features. Conversely, when dual-relation subspace projection alongside a feature-structure β is too large, the residual term is excessively suppressed. decoupled representation mechanism, DRSA effectively untanThis forces the model to rely entirely on linear feature gles semantic features from relation topologies. This allows projections, causing it to lose the flexibility needed to capture the model to harmonize heterogeneous interactions within a inconsistencies in heterogeneous relation, which confirms that unified latent space without sacrificing type-specific semantic a balanced residual is crucial for decoupling semantic and integrity. Extensive empirical evaluations across diverse multistructural signals. domain benchmarks confirm that DRSA successfully overcomes Feature Regularization (γ): The parameter γ controls the dual-level distribution shifts. When integrated with existing complexity of the semantic projection matrix Pτ . Specifically, state-of-the-art graph foundation models, it delivers substanthe performance remains relatively stable under different values tial and consistent performance gains in both cross-domain of γ, indicating that the model is not overly sensitive to the generalization and few-shot adaptation tasks. Ultimately, our strength of feature regularization. This suggests that the feature work provides a highly effective and text-free paradigm for projection term primarily serves as a stabilizing constraint advancing multi-domain heterogeneous graph learning without rather than a dominant factor, making the model less prone to the reliance on manually crafted meta-paths. overfitting. ACKNOWLEDGMENTS VI. V ISUALIZATION This work was supported in part by the National NatuTo evaluate the aligned features, we visualized node embed- ral Science Foundation of China under Grants 62425605, dings(Fig. 7) and relation reconstructions(Fig. 8). Compared 62133012, and 62303366, in part by the Key Research and to traditional alignment methods, DRSA generates clearly Development Program of Shaanxi under Grants 2025CYseparated clusters across node types and domains, effectively YBXM-041, 2022ZDLGY01-10, and 2024CY2-GJHX-15, and mitigating type collapse. Semantically distinct nodes remain in part by the Fundamental Research Funds for the Central distinguishable within a shared latent space. We further visual- Universities and the Postgraduate Innovation Fund of Xidian ized the reconstructed heterogeneous relation patterns. DRSA University under Grant YJSJ26014. significantly reduces reconstruction errors, particularly across R EFERENCES type relations, and is highly consistent with the true relation space, indicating that the learned latent space maintains relation [1] Y. Yang, Z. Guan, J. Li, W. Zhao, J. Cui, and Q. Wang, “Interpretable and efficient heterogeneous graph convolutional network,” TKDE, 2021. consistency. These results confirm that DRSA simultaneously [2] S. Wu, F. Sun, W. Zhang, X. Xie, and B. Cui, “Graph neural networks maintains semantic distinguishability and structural fidelity, in recommender systems: a survey,” ACM Computing Surveys, vol. 55, thus avoiding type collapse and relation confusion. no. 5, pp. 1–37, 2022. illustrates the one-shot classification accuracy across different datasets as β and γ vary.

11

[3] M. Yan, H. Huang, Y. Liu, J. Zhao, X. Gao, C. Xu, Z. Guan, and W. Zhao, “Truthsr: Trustworthy sequential recommender systems via user-generated multimodal content,” in Database Systems for Advanced Applications. Singapore: Springer Nature Singapore, 2025, pp. 180–195. [4] P. Reiser, M. Neubert, A. Eberhard, L. Torresi, C. Zhou, C. Shao, H. Metni, C. van Hoesel, H. Schopmans, T. Sommer et al., “Graph neural networks for materials science and chemistry,” Communications Materials, vol. 3, no. 1, p. 93, 2022. [5] G. Paaß and S. Giesselbach, Foundation models for natural language processing: Pre-trained language models integrating media. Springer Nature, 2023. [6] M. Awais, M. Naseer, S. Khan, R. M. Anwer, H. Cholakkal, M. Shah, M.-H. Yang, and F. S. Khan, “Foundation models defining a new era in vision: a survey and outlook,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025. [7] J. Liu, C. Yang, Z. Lu, J. Chen, Y. Li, M. Zhang, T. Bai, Y. Fang, L. Sun, P. S. Yu et al., “Graph foundation models: Concepts, opportunities and challenges,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025. [8] ——, “Towards graph foundation models: A survey and beyond,” arXiv preprint arXiv:2310.11829, 2023. [9] X. Yu, Z. Gong, C. Zhou, Y. Fang, and H. Zhang, “Samgpt: Text-free graph foundation model for multi-domain pre-training and cross-domain adaptation,” in Proceedings of the ACM on Web Conference 2025, 2025, pp. 1142–1153. [10] H. Zhao, A. Chen, X. Sun, H. Cheng, and J. Li, “All in one and one for all: A simple yet effective method towards cross-domain graph pretraining,” in Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2024, pp. 4443–4454. [11] S. Wang, B. Wang, Z. Shen, B. Deng, and Z. Kang, “Multi-domain graph foundation models: Robust knowledge transfer via topology alignment,” arXiv preprint arXiv:2502.02017, 2025. [12] H. Yuan, Q. Sun, J. Shi, X. Fu, B. Hooi, J. Li, and P. S. Yu, “Graver: Generative graph vocabularies for robust graph foundation models finetuning,” arXiv preprint arXiv:2511.05592, 2025. [13] H. Yuan, Q. Sun, J. Tao, X. Fu, and J. Li, “Overcoming in-memory bottlenecks in graph foundation models via retrieval-augmented generation,” arXiv preprint arXiv:2601.15124, 2026. [14] A. Sicilia, X. Zhao, and S. J. Hwang, “Domain adversarial neural networks for domain generalization: When it works and how to improve,” Machine Learning, vol. 112, no. 7, pp. 2685–2721, 2023. [15] Z. Liu, X. Yu, Y. Fang, and X. Zhang, “Graphprompt: Unifying pretraining and downstream tasks for graph neural networks,” in Proceedings of the ACM web conference 2023, 2023, pp. 417–428. [16] Z. Zheng, Y. Yang, Z. Guan, W. Zhao, X. Huang, and W. Lu, “Beyond single-granularity prompts: A multi-scale chain-of-thought prompt learning for graph,” in Proceedings of the ACM Web Conference 2026, 2026, pp. 547–558. [17] T. Fang, Y. Zhang, Y. Yang, C. Wang, and L. Chen, “Universal prompt tuning for graph neural networks,” Advances in Neural Information Processing Systems, vol. 36, pp. 52 464–52 489, 2023. [18] Y. Yang, Z. Guan, Z. Wang, W. Zhao, C. Xu, W. Lu, and J. Huang, “Self-supervised heterogeneous graph pre-training based on structural clustering,” Advances in Neural Information Processing Systems, vol. 35, pp. 16 962–16 974, 2022. [19] Z. Zheng, Y. Yang, Z. Guan, W. Zhao, and W. Lu, “Enhancing homophilyheterophily separation: Relation-aware learning in heterogeneous graphs,” in Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2, 2025, p. 4050–4061. [20] X. Wang, H. Ji, C. Shi, B. Wang, Y. Ye, P. Cui, and P. S. Yu, “Heterogeneous graph attention network,” in The World Wide Web Conference, 2019, pp. 2022–2032. [21] X. Wang, N. Liu, H. Han, and C. Shi, “Self-supervised heterogeneous graph neural network with co-contrastive learning,” in Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, 2021, pp. 1726–1736. [22] Y. Mo, F. Nie, P. Hu, H. T. Shen, Z. Zhang, X. Wang, and X. Zhu, “Self-supervised heterogeneous graph learning: a homophily and heterogeneity view,” in The Twelfth International Conference on Learning Representations. [23] C. Chen, W. Xie, W. Huang, Y. Rong, X. Ding, Y. Huang, T. Xu, and J. Huang, “Progressive feature alignment for unsupervised domain adaptation,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2019, pp. 627–636. [24] H. Abdi and L. J. Williams, “Principal component analysis,” Wiley interdisciplinary reviews: computational statistics, vol. 2, no. 4, pp. 433–459, 2010.

[25] G. W. Stewart, “On the early history of the singular value decomposition,” SIAM review, vol. 35, no. 4, pp. 551–566, 1993. [26] C. Zhang, D. Song, C. Huang, A. Swami, and N. V. Chawla, “Heterogeneous graph neural network,” in Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, 2019, pp. 793–803. [27] Z. Hu, Y. Dong, K. Wang, and Y. Sun, “Heterogeneous graph transformer,” in Proceedings of the web conference 2020, 2020, pp. 2704–2710. [28] X. Fu, J. Zhang, Z. Meng, and I. King, “Magnn: Metapath aggregated graph neural network for heterogeneous graph embedding,” in Proceedings of the web conference 2020, 2020, pp. 2331–2341. [29] P. Tseng, “Convergence of a block coordinate descent method for nondifferentiable minimization,” Journal of optimization theory and applications, vol. 109, no. 3, pp. 475–494, 2001. [30] C. Park, D. Kim, J. Han, and H. Yu, “Unsupervised attributed multiplex network embedding,” in Proceedings of the AAAI conference on artificial intelligence, vol. 34, no. 04, 2020, pp. 5371–5378. [31] B. Jing, C. Park, and H. Tong, “Hdmi: High-order deep multiplex infomax,” in Proceedings of the Web Conference 2021, 2021, pp. 2414– 2424. [32] Y. Tian, K. Dong, C. Zhang, C. Zhang, and N. V. Chawla, “Heterogeneous graph masked autoencoders,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 37, no. 8, 2023, pp. 9997–10 005. [33] L. Shan, J. Zhao, D. He, Y. Huang, Z. Feng, and W. Zhang, “Mug: Metapath-aware universal heterogeneous graph pre-training,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 40, no. 30, 2026, pp. 25 260–25 268. [34] Y. Mo, Z. Lu, R. Yu, X. Zhu, and X. Wang, “Revisiting self-supervised heterogeneous graph learning from spectral clustering perspective,” Advances in Neural Information Processing Systems, vol. 37, pp. 43 133– 43 163, 2024. [35] H. Duan, C. Xie, and L. Li, “Reserving-masking-reconstruction model for self-supervised heterogeneous graph representation,” in Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2024, pp. 689–700. [36] Y. Ma, N. Yan, J. Li, M. Mortazavi, and N. V. Chawla, “Hetgpt: Harnessing the power of prompt tuning in pre-trained heterogeneous graph neural networks,” in Proceedings of the ACM Web Conference 2024, 2024, pp. 1015–1023. [37] X. Yu, Y. Fang, Z. Liu, and X. Zhang, “Hgprompt: Bridging homogeneous and heterogeneous graphs for few-shot prompt learning,” in Proceedings of the AAAI conference on artificial intelligence, vol. 38, no. 15, 2024, pp. 16 578–16 586. [38] X. Fu, Y. He, and J. Li, “Edge prompt tuning for graph neural networks,” arXiv preprint arXiv:2503.00750, 2025. [39] M. Sun, K. Zhou, X. He, Y. Wang, and X. Wang, “Gppt: Graph pretraining and prompt tuning to generalize graph neural networks,” in Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2022, pp. 1717–1727. [40] X. Yu, C. Zhou, Y. Fang, and X. Zhang, “Text-free multi-domain graph pre-training: Toward graph foundation models,” arXiv preprint arXiv:2405.13934, 2024. [41] J. Shi, Q. Sun, H. Yuan, and X. Fu, “Saˆ 2gfm: Enhancing robust graph foundation models with structure-aware semantic augmentation,” arXiv preprint arXiv:2512.07857, 2025. [42] H. Yuan, Q. Sun, J. Shi, X. Fu, B. Hooi, J. Li, and P. S. Yu, “How much can transfer? bridge: Bounded multi-domain graph foundation model with generalization guarantees,” in Forty-second International Conference on Machine Learning. [43] E. Bingham and H. Mannila, “Random projection in dimensionality reduction: applications to image and text data,” in Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining, 2001, pp. 245–250. [44] A. Rahimi and B. Recht, “Random features for large-scale kernel machines,” Advances in neural information processing systems, vol. 20, 2007. [45] W. B. Johnson, J. Lindenstrauss et al., “Extensions of lipschitz mappings into a hilbert space,” Contemporary mathematics, vol. 26, no. 189-206, p. 1, 1984. [46] M. Eliasof, K. S. I. Mantri, B. Bevilacqua, B. Ribeiro, and C.-B. Schönlieb, “Bridging input feature spaces towards graph foundation models,” in The Fourteenth International Conference on Learning Representations. [47] J. Zhao, X. Wang, C. Shi, Z. Liu, and Y. Ye, “Network schema preserving heterogeneous information network embedding,” in International joint conference on artificial intelligence (IJCAI), 2020.

12

[48] C. Shi, Y. Lu, L. Hu, Z. Liu, and H. Ma, “Rhine: Relation structure-aware heterogeneous information network embedding,” IEEE Transactions on Knowledge and Data Engineering, vol. 34, no. 1, pp. 433–447, 2020. [49] Y. Dong, N. V. Chawla, and A. Swami, “metapath2vec: Scalable representation learning for heterogeneous networks,” in SIGKDD. ACM, 2017, pp. 135–144. [50] P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Lio, and Y. Bengio, “Graph attention networks,” arXiv preprint arXiv:1710.10903, 2017. [51] T. N. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” arXiv preprint arXiv:1609.02907, 2016. [52] M. Ren, E. Triantafillou, S. Ravi, J. Snell, K. Swersky, J. B. Tenenbaum, H. Larochelle, and R. S. Zemel, “Meta-learning for semi-supervised few-shot classification,” arXiv preprint arXiv:1803.00676, 2018.