Towards Graph Foundation Models: Training on Knowledge Graphs Enables Transferability to General Graphs
Authors: Kai Wang
Siqiang Luo
Caihua Shan
Yifei Shen
Venue: NeurIPS 2025 poster ()
Keywords: Knowledge Graph
Graph Foundation Model
Graph Message Passing
Primary area: deep_learning

Abstract: Inspired by the success of large language models, there is a trend toward developing graph foundation models to conduct diverse downstream tasks in various domains. However, current models often require extra fine-tuning to apply their learned structural and semantic representations to new graphs, which limits their versatility. Recent breakthroughs in zero-shot inductive reasoning on knowledge graphs (KGs), offer us a new perspective on extending KG reasoning to general graph applications. In this paper, we introduce SCR, a unified graph reasoning framework designed to train on knowledge graphs and effectively generalize across a wide range of graph tasks and domains. We begin by designing the task-specific KG structures to establish a unified topology for different task formats. Then we propose semantic-conditioned message passing, a novel mechanism addressing the inherent semantic isolation in traditional KG reasoning, by jointly modeling structural and semantic invariance patterns in graph representations. Evaluated on 38 diverse datasets spanning node-, link-, and graph-level tasks, SCR achieves substantial performance gains over existing foundation models and supervised baselines, demonstrating its remarkable efficacy and adaptability.

Towards Graph Foundation Models: Training on Knowledge Graphs Enables Transferability to General Graphs
Caihua Shan', Yifei Shen", Nanyang Technological University 'Microsoft Research Asia "aai wang ntu. edu.sg, siqiang. luo edu.edu.sg caihuasshan @ microsoft.com, yifeishen microsoft.com
Kai Wang', Siqiang Caihua
Abstract
Inspired by the success of large language models, there a trend toward developing graph foundation models to conduct diverse downstream tasks in various domains. However, current models often require extra fine-tuning to apply their learned structural and semantic representations to new graphs, which limits their versatility. Recent breakthroughs in zero-shot inductive reasoning on knowledge graphs (KGs), offer new perspective extending KG reasoning general graph applications. In this paper, we introduce SCR, a unified graph reasoning framework designed train on knowledge graphs and effectively generalize across wide range of graph tasks and domains. We begin by designing the task-specific KG structures to establish unified topology for different task formats. Then propose semantic- conditioned message passing, a novel mechanism addressing the inherent semantic isolation in traditional KG reasoning, by jointly modeling structural and semantic invariance patterns in graph representations. Evaluated on 38 diverse datasets spanning node-, link-, and graph-level tasks, SCR achieves substantial performance gains over existing foundation models and supervised baselines, demonstrating remarkable efficacy and adaptability. Our source code is available on https //github. com/ KyneWang/SCR,
Introduction
In pursuit of artificial general intelligence, graph foundation models (GFMs) designed to pretrain on large-scale graph data, learn generalizable representations, and adapt them to wide range of downstream tasks [39 36). However, most GFMs still face challenges, including format mismatches between pretraining objectives and downstream tasks, and semantic discrepancies between source and target datasets. As result, extensive fine-tuning is often required.
In contrast to homogeneous or heterophilic graphs, which define single relation among nodes, knowledge graphs capture complex, multi-relational connections among entities. The most common task KG reasoning, which involves learning embeddings of entities and relations infer missing components in triples (head entity, relation, tail entity)
[[54] Moving beyond traditional transductive knowledge graph (KG) reasoning, recent work [7] explores zero-shot inductive reasoning. This paradigm learns relation and entity representations conditioned the graph structure, enabling generalization to unseen KGs and the inference of entirely new entities and relations without any fine-tuning. [66].
Inspired by these breakthroughs, we improve the topological transferability of GFMs from novel perspective: pre- pre-training on knowledge graphs using inductive reasoning as the training objective,
The Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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and then transferring to other graph domains, such as citation and molecular graphs, to perform downstream tasks like node and graph classification. Nevertheless, developing such GFM faces two significant problems. (1) Cross-Task Transferability: It is challenging to generalize the KG reasoning format across diverse graph tasks and transfer learned representations to general graphs effectively. (2) Semantic Transferability: Semantic features in graphs, such as node features and textual attributes, capture domain sppeciff knowledge beyond the graph's topology. Integrating semantic features into the inductive reasoning process remains largely unexplored.
To tackle the cross-task transferability, we first design task -ask-specific KG structures to transform general graphs and their tasks into KG formats. As shown in Figure[] we introduce two new entities, "label [", and "super graph A", and define three new relations, "node O is attributed with label D", "node O belongs to super graph A", "super graph A is attributed with label D".. These definitions allow us to reframe classification tasks as KG reasoning, predicting the tail entity based on a given relation and head entity. For example, in a citation network, performing node classification is analogous to reasoning edges between papers and labels.
The semantic transferability problem in inductive KG reasoning manifests as a semantic isolation issue. Existing models prioritize graph structure at the expense of domain semantics, and attempts to integrate semantics (e.g., via feature initialization) often compromise topological generalization. To resolve this dilemma, we propose a novel Semantic Conditional Message Passing (SCMP) framework. SCMP moves beyond simple feature injection by explicitly conditioning the message- passing mechanism on both local semantic neighbors and global semantic contexts. By leveraging knowledge pretrained from diverse sources (e.g., textual descriptions and ontological axioms), our framework enhances reasoning performance while simultaneously preserving robust generalization across both semantic and topological dimensions.
In summary, we propose the Semantic Conditional Reasoner (SCR), a novel graph reasoning frame- work that leverages inductive KG reasoning to advance graph foundation models. To the best of our knowledge, this the first work to employ KG reasoning as pretraining objective for graph foundation models. We conducted extensive experiments on link prediction, node classification, and graph classification tasks across 38 datasets from diverse domains. The results demonstrate performance improvement over existing foundation models and supervised baselines, underscoring the transferability of our approach.
2 Related Works
Transferability is key to the success of graph foundation models. Here we describe current studies by clarifying how they address differences between source and target datasets and bridge gaps
across task formats [29 85 37 51]. OFA (33] and ZeroG (29) leveraged pre-trained language models to encode node/class features as text, creating unified feature space across diverse datasets. Meanwhile, OpenGraph [74] adopted masked autoencoding, and AnyGraph (73) used link prediction loss during pretraining on multiple graphs, enabling direct application to conduct node classification and link prediction tasks on new graphs. GraphAny [85] designed a novel architecture to tune model parameters through an analytical solution, allowing
fit unseen graphs for node classification tasks. All these methods claim to work on both in in-domain and cross-domain datasets.
Beyond designing model architectures and pretraining objectives, graph prompt learning is also popular to employ lightweight prompts, aiming to align pre-training with downstream tasks [89]. Depending on different unsupervised pre-training and prompt learning strategies employed, current notable approaches include GPPT (52), All-in-one (53), GPrompt [22), and GPF-plus [15). Typically, their source and target datasets are the same graph dataset.
The existing foundation models in KGs study the transferability across different KGs g 66 For example, ULTRA [77 learned transferable graph representations by conditioning relational interactions, enabling generalization to unseen KGs.
We provide detailed version of related works in Appendix N Unlike all the prior studies, our method SCR explores a novel scenario, training solely on common-sense KG datasets while achieving transfcrability across wide range of general graphs and tasks without the need for extra fine-ture men-tuning.

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3 Background
Let knowledge graph be represented as G {E, R, T3 where & is the of entities and R the set of relations. The factual triples in the KG are denoted by T {{e,, r, e,) EA, E & E Rj. where each triple consists of a head entity eg, relation r, and a tail entity e,. Given a query (eq: Ta). where ey E & is the query entity and rq E R is the query relation, the goal of KG Reasoning is to identify the correct entity eo &, such that either (g. Ce) or (Ee. gg. Cg) forms valid triple in g. In addition, we define feature matrix X' E R where each row represents feature vector of dimension do for the corresponding entity in the set E. Now, consider model trained on a knowledge graph Gr = {En. Ry, J. The task of zero-shot inductive reasoning on knowledge graphs is to test the model on new inference graph Gin = {Enf, Rinf, Tims), where both entities and relations are completely unseen during training. The whole notation used are listed in Appendix A
CMP-based Backbone Model: For inductive KG reasoning. recent studies utilize graph neural
networks based on Conditional Message Passing (CMP) represent KG triples (87) X
88
67
Traditional message passing neural networks, such as GCN (26). GAT [6]], and GraphSAGE: 23 compute unary node representations and lack the ability to model interactions in a node set (such as edges) [8]. Differently, for a KG 9 and trainable relation embeddings R, CMP- model
Mg = CMP G, R.) calculates the triple representations h, for each entity ey conditioned on the query Tg):
h INIT(Eq: Cvs Ta) Le,=e, *Tg.
h e AGO g (Mso(h (1) r)] ew E NN,(e,), T ER)),
(2)
h (1+1) = UPD(h!) h!").
At initialization of INIr() function, only the query entity ey carries information: its hidden state (0) is set to a non-zero vector determined by rg R(rg], while all other entities are zeroed out. During message passing, this signal propagates outward, and each target entity e, ultimately learns an embedding h. that reflects how it is viewed from the perspective of (Eq, ra). MSG() is differentiable message function that integrates two types of information: the aggregated paths between e, and ew as R.rr.. The representations iteratively updated over
(1) and the edge connecting eu C2 layers through AGG() and UPD() functions. The final representation (L.) is then used to predict the plausibility of triples (cg, Co) in KG reasoning.
These conditional representations are theoretically expressive 25 and practically effective [77 Using a specific initialization function INIr)), CMP-based models rely solely on KG structures and relation embeddings, enabling inductive reasoning on new KGs. Moreover, CMP supports parallel learning of h. for all e, E, reducing computational costs.
4 Methodology
We propose SCR, a novel graph learning framework, to achieve zero-shot reasoning across general graph tasks (node//ink/graph-lee and diverse domains beyond Knowledge Graphs. The framework structured around three core contributions:
We define format that reformulates standard node classification and graph classification into inductive KG reasoning tasks, enabling cross-task transferability.
Unified Reasoning Format (Section 4.1)
We introduce SCMP to enhance the utilization of semantic features while preserving topological expressive power.
Semantic Conditional Message Passing (SCMP) (Section 4.2):
Inductive Training and Reasoning (Section 4.3) This section details the complete workflow for handling unseen KGs with arbitrary types. While we focus on node features this work, the framework is readily extendable to explicit edge features using SCMP.
As present Figure [ the training workflow operates via a query-conditional reasoning process. After preprocessing graph features and constructing the relation graph, SCR uses base CMP module to derive relation representations. Our proposed SCMP module then leverages this information to compute triple representations, which are ultimately scored for training. In the inference phase,
3

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KG Inductive Reasoning Task
Unifted Reasoning Format for Diverse Graph Tasks
Link Prediction
Node Classification
Gruph Classification
Textual Embeedding
Node Features
Graph Embeddings
Query: (ej, I
Query: (ep 1t)
Query: (gi+
C
C2
Cj
Training on KG Datasets
Reasoning on Generul Gruphs
SCR: Semantic Conditional Reasoner
Uniified Features
Semantic Features
Query
Hu
MLP Decoder
RS
CMP Encoder
SCMP Encoder
Candicite Scores
Knowledge Graph
Relation Graph
Relation
Entity Level
Task Output
Graph Data Preprocessing
Query-Conditionll Reasoning
The proposed framework SCR transforms diverse graph tasks into inductive reasoning on knowledge graphs with semantic features.
Figure 1:
SCR adapts to general classification tasks by transforming the graph into KG format. This unified approach enables the learned reasoning patterns to be directly transferred for entity labeling without fine-tuning, demonstrating strong inductive generalization.
4.1 Unified Graph Reasoning Format
Here we aim to develop a unified framework that addresses node-level, edge-level, and graph-level tasks simultancously. First, KG reasoning be considered specialized form of link prediction focused on a specific relation, making straightforward to apply. Because node and graph classifica- tion tasks draw labels from finite set, reformulate them using the following task-specife KG structure (Definition 4.1,. thereby transforming labeling tasks into KG reasoning.
Definition 4.1. (Task-specific KG Structure) For given graph task on dataset D (X,Y) the task-specific knowledge graph is constructed as follows:
G = { is attribbted_ ys (x,, 9:) E DD
where Tx includes all original edges present within X.
The examples are illustrated Figure In node classification tasks, a unique "label D" entity is introduced for each label type, with defined relation "node O is attributed with label D" connecting nodes to their corresponding labels. The original node connections are preserved, and the input node features also retained as semantic features for entities. For graph classification, we integrate individual graphs into a KG structure by adding "super graph 2 entities linked to their nodes via the relation "node O belongs super graph A." We then aggregate semantic features for each graph entity and add "semmntically-nearee task-specific KGs are given in Appendix
edges between super graph nodes. The detailed procedures for
Therefore, an ideal, fully trained CMP-based graph model that generalizes across various knowledge graphs can simultaneously handle node and graph classification tasks. Knowledge graphs often contain numerous "n-to-1" relations, such as "person-to-gentee to-gender" or "movic-to-ss torie-tt-genr,"" which are closely related to labeling tasks (9]. This relationship enables KG reasoning models to achieve strong performance in the new relation "is attributed with". Furthermore, this unified KG reasoning format eliminates the need to Iearn separate parameters for each label class, enabling support for unseen labels during inference.
4.2 Semantic Conditional Message Passing (SCMP)
Semantic Isolation Issue: Due to the specific design for topological generalization, CMP-based models cannot effectively utilize node semantic features general graph tasks, named as the semantic isolation issue.

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Some simple attempts even worsen performance. In the first attempt, we directly apply node semantic fea- tures into the INIT() function (Eq. T
MBR
ULTRAPS
MRR
WNNvV FBvl NL.V!
0.6
-Ber
#Otherituee
to initialize node representation h similar to standard GNNs. How- ever, as shown in Figure Aa.. the performance degrades after inject- ing features ("+Berr") and even af- ter fine-tuning with such initialization ("+BertTune"). This is because the core target node distinguishaaiiiity as-
0.2
0.4
0.2 The Number
0.0
WKvv1
3
10 30
Results with Initial Features
(b) Results with KNN Edges
Figure 2: Preliminary results of the baseline ULTRA. "+Bert" denotes using BERT-encoded features as initialization. We also fine-tune the BERT- -enooeedd ULTRA ("+BertTune") followed by reasoning with features from the other source ("+OtherTune"). Higher MRR is better.
sumption of CMP is violated [23). which requires, for all Tg E R and ey * eq E, the condition
(NI cgz r4) o INIT(eq, Cu, (4)) must hold 81 Similar declines are observed when embeddings from other language models used ("+OtherTunne"
The second attempt is to introduce semantic feature similarity into the graph structure. We construct a k-nearest neighbor (KNN) graph based on the similarity of node features, and add new triples with the relation "is wwwantic siiranttissmillrrrreeee to" into the knowledge graph. As illustrated in Figure increasing k reduces the performance of ULTRA. This is due to the added edges diluting local information and causing distant nodes to lose their distinctiveness. The resulting dense topology either amplifies compresses embeddings unevenly, leading to over-smoothing and decline in link prediction performance.
Although these attempts fail, they offer insights for improving CMP from three aspects. First, we adapt a semantic unifier to preprocess node features. We then design the new semantic-injecter INTT function satisfying the assumption of target node distinguishability. Finally, we use the parameter- frozen CMP to embed the semantic node features directly.
Semantic Feature Unifier: To handle semantic diversity across domains, the semantic unifier employed to preprocess node features without additional training. Given the feature matrix X' R R we utilize singular value decomposition (SVD) in extracting important latent features:
X LayerNorm (UVA), (U,A,V) = SVD(X,
(4)
where LayerNorm(-) represents the layer normalization function, ensuring numerical stability. min(do, [E]) is smaller than d, SVD will use reduced rank decompose X, with the remaining dimensions zero-padded to reach d. Such that, the unitied features X' IR Elxd maintain consistent dimensionality d across different graph data. Besides, the relative spatial distances between nodes are preserved in the unified features due to the nature of SVD. For scalability, we employ randomized truncated SVD to ensure linear complexity.
cemantic-injecter INIT Function: Given query q Tg). first recall the initialization function in CMP: INIT(Eg, Cv, Pg)) = Te, rg. Instead of using the original semantic features, we inject the semantic neighbor labels into the entity initialization. The improved initialization function defined as follows:
INIT (eg, = *
Le,Es., *
(5)
where Se, represents the semantic neighbors of eg. These neighbors are determined by selecting the top A spatially nearest entities in the semantic space based on pairwise similarities, while excluding direct topological neighbors. In addition, Va denotes a trainable vector, randomly initialized and shared for all semantic neighbors in Sr.- In this schema, the initial representations of these neighbor entities are not all-zero vectors, enabling them to propagate effective high-order messages at the beginning of the CMP process. Note that, according the theoretical study of CMP [25], if we assume * Va and neither of them contains zero entries (Appendix H shows the assumption generally holds.), INIT? function satisfies the target node distinguishability assumption. Specifically, for all ry E R and for any e, # eg E E, holds that INIT2(eg, Eg:: rq) # INIT2(e,, Ge, Pq))
Although the new initialization function captures high-level semantic relationships among entities, the original semantic features remain excluded
Non-parametric Semantic Representation:
5

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from the computation process. To address this, we still use semantic features to initialize all the entities, but keep CMP parameters frozen. This setup is similar SGC [72), non-parametric adaptation of traditional GNNs that relies on repeated graph propagation for representation learning. Finally, an MIPP is employed to merge the semantic representation Hg with the original CMP-based representations based on the specific query.
H CMP, R, H CMP (q.Po(q.3 9, R2,) + ML,(HHg,,
where H X
(6)
(7)
where the parameters of both CMP instances are shared. The empty set used in Eq. 6 means that this CMP is query-in inry--independen,, and we do not need to input the query. Besides, R. and Rg are two parts of relation representations, which will be described in Sec. 4.3 Notably, H.g can be precomputed and seamlessly integrated into the computation process of query-specific CMP, enabling SCMP to preserve time and space complexities compared to CMP.
4.3 The Whole Process of SCR
Here we describe the entire process of training SCR on multiple KG datasets. As illustrated in the lower part of Figure D the first step is to preprocess the graph data. For each KG G. we apply the semantic feature unifier to process node features, followed by the construction of the relation graph G,. The second step is snveryconnitionall reasoning. Given a query apply CMP to learn the relation representation Rg via the relation graph Gr. Based on the relation representations Rq. further use our proposed SCMP to learn the triple representation h, for (eg, Tgg Gv). These representations are passed through an MLP to compute the scores for the existence of triples. We use cross-entropy loss train the model for classifying positive and negative triples.
(Cg. rg) on G, first
As for the inference phase, SCR unifies classification tasks as KG inductive reasoning by transforming general graph into a KG. Thereby, the learned reasoning patterns in SCR can be adapted to label the entity without fine-tuning corresponding samples.
Build the Relation Graph G,= Given a KG G. a relation graph G, is constructed following UL- TRA [17], to connect unseen relation types in 9 with four types of relation-level interactions (i.e.. "head-to-head", "tail-to-taill, "head-to-taill, and "tail-to-head"). Please refer to Appendix C for further details.
Learn the Relation Representation Rg: We then learn the relation embeddings via G,-, Specifically, given a query q = (eg, Tg), the calculation process is follows:
Rg = CMP (0. 9r, P) Ry = CMPa(q.9. P)
where
(0) =
(8)
where P denotes the learnable embeddings corresponding to four types of interactions in the relation graph Gy. For the query q. the query-conditional relation representations R. are generated using
CMP on G.. Alternatively, when no query is provided and the initialized embedding R. (0) is set as an
all-ones vector, the query-independee representations Ry are computed and utilized in Eq. 6
Query Conditional Reasoning: Based on R2 and Rg, we utilize our proposed SCMP model to learn the entity representation given the query q (g):
H SCMP ((. 9, X. R.g. Rg),
(10)
p(g, ev) MLP(h
(11)
where hy E H denotes the final entity representation of the entity e.. To evaluate the plausibility of the triple Tq: ). an MLP is employed to compute a score, where a higher value indicates a greater likelihood of the triple being valid in G.
Model Training: KG inductive reasoning models are typically trained by minimizing the binary cross-entropy loss over positive and negative triples. To handle semantic features across domains, we train one SCR model with multiple types of semantic features on diverse KG datasets. Specifically, we employ the BERT [0] sentence encoder to generate semantic features. We also incorporate ontology features and explore non-feature scenario during model training, as presented in Appendix [D] Note that, we focus node semantics in this work, edge semantics can be supported with trivial

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Table 1: Performance KG inductive reasoning datasets. "(3g)" means training with three KGs, and "SCR-X" refers to results obtained using different types of semantic features (e.g.. "One" means all-ones features). The best results are in bold.
IndE(FB)
IndE(WN)
IndE(NL)
IndER(FB)
IndER(WK)
IndER(NL)
Total AVG
Methods
#1
Hits@10
Hits
Hits010
Hav@
Hise
Hits@
Supervised SOTA
0.477
0.636
0.640
0.734
0.464
0.654
0.166
0.296
0.152
0.244
0.296
0.481
0.366
0.507
ULTRA(3g)
0.486
0.667
0.517
0.678
0.561
0.742
0.386
0.599
0.254
0.405
0.393
0.561
0.433
0.608
ULTRA(4g)
0.491
0.670
0.387
0.598
0.415
0.398
0.627
(1TTRA(50g)
0.493
0.664
0.558
0.664
0.590
0.777
0,382
0.585
0.251
0.406
0.397
0.582
0.445
0.613
ProLINK(3g)
0.494
0.684
0.553
0.690
0.546
0.759
0.372
0.591
0.234
0.393
0.400
0.590
0.433
0.618
SCR (3g)
0.495
0.688
0.576
0.703
0,592
0.791
0.392
0.611
0.251
0.407
0.403
0,599
0,451
0.633
SCR-One
0.491
0.678
0.569
0.688
0.581
0.773
0.390
0.604
0,250
0.399
0.388
0,578
0.445
0.620
SCR-MPNet
0.495
0.688
0.578
0.704
0.589
0.788
0.392
0.611
0.250
0.406
0.403
0.451
0.633
SCR-MiniLM
0.496
0.687
0.576
0.702
0,585
0.788
0.392
0.611
0.250
0.406
0,405
0.604
0.451
0.633
SCR BeR-DistilBeert
0.495
0.688
0.576
0.706
0.584
0.788
0.392
0.610
0,250
0.407
0.401
0.601
0.450
0.633
SCR Ontology
0.489
0.684
0.570
0.679
0.575
0.772
0.387
0.605
0.230
0.395
0.391
0.584
0.440
0.620
modifications to our framework. At predefined mini-batch intervals, the feature type is reselected to help the model adapt to diverse input features and improve its generalization ability. The total pretraining loss is computed as follows:
L=
Σ NEF
- llggplq calx)
1 Σ n i=1
log(1 - p(q,ee))))
Here, p(g. Cal-t) is the score for a positive triple in KG G with the node features X' while ((q,)))22) contains negative samples created by corrupting the target entity.
Although the training objective is link prediction, it learns the neighborhood connectivity and therefore captures local neighborhoods and community structures. Global semantics are retained via our non-parametric semantic representation, which aggregates all original node features in the CMP process. Together, these components enable representations learned during KG training transfer to downstream node- and graph-level tasks that rely on local structures and semantic cues.
We analyze the expressive power of our proposed SCR in Appendix F and discuss the computational complexity and scalability Appendix
5 Experiments
We evaluate our method on 38 diverse datasets across three-level tasks. In particular, we wish to answer the following research questions: RQ1: How effective is SCR in inductive reasoning across distinct knowledge graphs? RQ2: To what extent does SCR generalize across diverse feature spaces on the same KG? RQ3: How well does SCR generalize across variety of graph-related tasks? RQ4: What is the impact of the main components on the performance of SCR? ? RQ5: How does the reasoning performance change when adjusting the key hyperparameters? Due to the space limitation, discussions about RQ5 are detailed in Appendix G
5.1 Experimental Setup
We pre-train SCR on three commonly-used KG datasets, WNISRR FBI FB15k237 59 and
CodexM The CMP follows NBFNet with non non-parametric DistMult 78 message function and a simplified PNA aggregation function [67] For semantic features, we employ the BERT [TO] sentence encoder to generate pre-training features. Hyperparameters are selected through grid search based on the metrics from the validation set without fine-tuning for each dataset. Implementation details and hyperparameter configurations are provided in Appendix Three graph learning tasks are used evaluate: link-level KG inductive reasoning and node-fgraph-level classification on general graphs, across 38 real-world datascts. The details of tasks and datasets described in Appendix B
7

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Table 2: The accuracy results on node classification datasets. GraphAny(X) or AnyGraph(X) indicates pertaining on the X dataset. SCR-20% uses 20% of the "node-label" edges from the training set, while SCR-5 includes five edges per class. The best results are bolded.
Learning Paradigm
Methods
Cora
Citeseer
Pubmed
Wisconsin
Texos
Actor
Avg.Rank
MLP
48.42+00.3
44.40=044
69.50 69.50=1.79
66.67+3.51
48.65+44.01
33.95+00.00
8.83
Full-Shot Truining
GCN
81.40.0.70
63.40...63
76.60_0032
37.25
12.35
28.5510068
7.33
GAT
81.70
69. 19.10=1.59
77.30=060
52,94
54.05:241
27.30+0:22
5.67
StaphAny(Producte
79.3610.21
67.94.0.29
76.54_0334
65.8912.25
13.92
28. 28.9911061
5.00
Graph Pre- Pre-TTrainng
Full-Shot Analytical
ComphAny(Ariiv)
79.38:20116
68. 23
76. 17
65.10
22
72.97
28. 21
5.50
Tuning
CraphAAn(Wiscomee
77.82+1.15
67.50=0044
77.46-033
71.77=5.88
13.51+1.21
29.51+0055
4.33
GraphAny(Cora)
80.1810.13
68.90=0007
76.60=031
61.1815.08
71.891148
10.91
5.17
Graph Pre Training
No Tuning
AnyGruph(Linkl)
OpenGraph
80.65+0.99
58.57.1782
51.93-66.44
69.99=0.33
62.75
80.15=1.2 zN
24.42+5.64
1.57
21.78+6632
0.57
16.7445.8
1.49
12.83
7.33
AnyGruphiLLink2)
69.0514471
45.52:2426
78.02=1.46 46
1.29910.44
0.81=000
5,562021
11.00
KG Pre-Training
ULTRA(3g)
79.401...00
67.40..0000
77.90-0000
49.02.1..00
56.7610.00
22.61
7.50
No Tuming
SCR (3g)
81.80
71.33=0027
82.93_0.55
14.91
67.6411044
23.26:10.56
3.67
SCR-20%
73.62+2.78 56. 3.:53
71,94=023
50.59#3.14
64.32+3.59
22.78++0.4
9.00
Few-Shot Labeling
SCR-5
54.48.11.96
32.38
50.38_6.17
28.6318.82
58.3814439
19.00
11.67
Table 3: The accuracy results on graph classification datasets. SCR-20% and SCR-5 are two few-shot labeling variants of SCR. The best results are bolded.
Learning Parddigm
Methods
IMDB-B
COLLAB
PROTEINS
MUTAG
ENZYMES
COX2
B2R
DD
Avg. Rank
Wull-Shot Training
GIN
67.75s2.50
18:20
64.72a054
75,50a574
21,88:055
77.90:1.57
81,79-1.4
70,59a081
3.13
One Shot Training
Prnetin&FFnnttuee
GCN
57,3020Ms
$7.75
48,10:5025
47.231u01
56.361297
63,448384
65.20::.0
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22:21=219
20.58:200
76.19:541
27.08:195
25:80
34,69=850
55.33
57,154432
7.25
GPPT
50.151075
47.181595
60.92.247
60.40
21,29
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59. 59.32.11.2 2n
57.69.6 59
8.50
Graph Pre Training
One-Sho Shot Tuning
GPrompt
GPF
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51.6611366
48:25
63.91
66.49.1676
19.171:1125
79.87.8.
68.40:55.0
73.60:4.1
13.96.11445
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12.29
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55.43
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13.78
71.17.1440
57.6211242
7.25
Pre Training
ULTRA(3))
(9.25=0000
58:09:0000
63,33=0000
=5:21
77.75=000
79.32-003
13.52+000
No Tuning
SCR (3g)
61.83:1 (00
65.45
68.54:1477
85.33-2.11
22.92:2200
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46.05
02.14444
7.38
5.2
Main Experimental Results (RQ1)
All 24 inductive KG reasoning datasets are used in RQI: the first 12 datasets from GralL 58 with test graphs containing only unseen entities (termed as "IndE"), and the remaining 12 datasets from InGram (28 featuring both unseen entities and relations (termed as "IndER"). Notably, eight datasets in IndE//ndER(NL) come from NELL-995 (excluded from training). introducing new semantic features for each method. This setting prevents data leakage by dynamically generating entity representations based the unique structure of each KG during training and inference. Even if a triple appears in both the pre-training and test datasets, the different structures around it ensure distinct representations, thereby mitigating memorization.
We compare SCR with two KG reasoning baselines (ULTRA and ProLINK pre-trained on different sizes of KGs) and one supervised SOTA. Two evaluation metrics are used: Mean Reciprocal Rank (MRR) and Hits N, where higher scores indicate better performance 1 58). For semantic fea- tures, we generate entity-level embeddings from available textual descriptions using BERT sentence encoders.
We report the average performance for cach benchmark and the results are summarized in Table [ comprehensive evaluation on more than 50 transductive and inductive KG datasets is provided in Appendix M Overall, SCR outperforms all existing zero-shot models as well as the supervised model in the total average metrics, demonstrating its effectiveness. For individual benchmarks, we observe that SCR surpasses ULTRA(3g)) ProLINK. and supervised results in most metrics. Although UL4RA(4g) and (LTRA(50g) achieve better performance on some metrics, they are pre-trained on more diverse KGs (including NELLL-995) and still show poorer performance on the IndER(FB) and IndE(WN) benchmarks. Furthermore, compared to IndER(X) benchmarks, SCR shows substantial performance gains on IndE(X) benchmarks beneficial from node semantic features.
8

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5.3 Generalizing Across Semantic Spaces (RQ2)
To address the cross- domain challenge, we explore the generalizability of SCR across different semantic feature spaces, and verify that SCR is not restricted to graphs with textual features. Specifi- cally, we select five types of semantic features as input to the pre-trained SCR (within BERT-encoded semantic space). In Table "MPNet", "MiniL.M", and "DistilBERT" refer to three popular sentence encoders based on language models, while "One" and "Ontology" utilize all-ones features and ontology features derived from relation type counting, respectively. The results show that SCR variants using different sentence encoders achieve performance nearly identical to the original SCR, despite the encoders producing embeddings with varying dimensions. This consistency underscores the effectiveness of our unified semantic space. Although SCR (One) and SCR (Ontology) perform slightly worse than SCR on some metrics, they still outperform baselines such U3TRA(3g). indicates that SCR is not constrained by access to textual features and exhibits generalization capabilities across diverse feature sources, even all-ones features. The semantic content of IndE(NL) and InLER(NL) was not included in the pre- pre-training KGs. Despite this, the performance improvement still demonstrates the robustness of SCR unseen domains semantic inputs. The key lies in the pre-training design of SCR: it systematically trains the model to handle diverse scenarios-fioe KGs with rich semanties (text/ontology) to those with input features. SCR learns reason over KGs with diverse semantics rather than depending on auxiliary textual data.
5.4 Generalizing Across Graph Tasks (RQ3)
In this section, verify the performance of SCR on classification tasks across diverse general graphs. Following prior studies [89]. we employ six node classification datasets, including homophilic graphs (Cora, Citeseer, PubMed) 49 41 and heterophilic graphs (Wisconsin, Texas, Actor) [42 (66. We utilize eight graph classification datasets from various domains, covering social networks (IMDB-B, COLLAB) [77). biological (ENZYMES, PROTEINS, DD) [1I 3 69], and small molecule datasets
(MUTAG, COX2, BZR) [7 44. The experimental results of prediction accuracy are shown in Table Comprehensive results can be found in Appendix O
2 and Table 3
For node-level tasks, SCR significantly outperforms existing foundation models on three homophilic graphs and shows superior performance over ULTRA, OpenGraph, and AnyGraph three het- crophilic graphs. However, SCR lags behind GraphAny on heterophilic graphs, as GraphAny utilizes training labels to tune the model parameters through an analytical solution. Such task-specific tuning in GraphAny and graph prompt methods is powerful but limits their versatility as graph foundation models. To improve robustness on heterophilic graphs, several promising strategies can be explored, such as pre-training or fine-tune see-tuning on heterophilic structures, or replacing standard aggregation functions with operators more suitable for heterophilic settings. Enhancing SCR on heterophilic graphs will be our future work.
Table shows the experimental results for graph-level tasks. Following the experimental setup from ProG [89] 80% of graph samples are divided into the test set and only a few labeled graphs are transformed into the task-specific KG. We observe that SCR outperforms existing graph models using one-shot training or prompt tuning. Further, SCR is competitive with the fully-trained GIN using the same training set, while GIN requires extra training time and SCR directly infers the task-specific KG. Existing zero-shot foundation models such as OpenGraph, AnyGraph, and GraphAny are not suitable for graph classification tasks. This limitation underscores the value of SCR across diverse graph tasks. In addition, the fact that performance gains are achieved on IMDB-B and COLLAB, which lack node features, demonstrates that the improvement beyond ULTRA is not exclusively dependent on semantic features.
5.5 Ablation Studies (RQ4)
To assess the impact of the key techniques, we conduct ablation experiments for multiple pre-trained variants. The results are illustrated in Figure 3
The two variants, excluding Semantic-Augmented Relation Graph ("w/o SARG") and Semantic-Ineected Entity Initialization ('w/o INTT2"), utilize the original relation graph and initialization function of ULTRR((3)) to omit semantic neighbor information. Across three tasks, the observed performance declines underscore the effectiveness of our semantie-injection techniques. The new INIT2 function has relatively larger contribution, especially in graph-level tasks.
(1) Semantic Neighbors:

---

CSCR
Kio
W/
ULTRAN3
(2) Non-parde non-parametric Semantic Representa- tion: The non-parann con-paametric semantic encoding in SCMP directly handles semantic features, with the reduced performance of "wo NPSR" empha- sizing its essential role in leveraging semantic diversity. However, except for IndE datasets, the observation that "w/o NPSR" outperforms the original ULTRA most tasks suggests that the post-merging approach effectively preserves the functionality of CMP.
Mite
0.45
0.55
0.35
0.4
0.30
IndE IndER AVG. Nod: Graph
Figure 3: The ablation study results of SCR vari- ants. "w/o SARG" denotes using the relation graph without semantic neighbors, the latter two have semantic-injected initialization and global seman- tic encoding, respectively. "w/o RelDiff" denotes using identical relation embeddings in SCMP.
(3) Relational Condition: The variant "w/o RelDiff" utilizes the average vector of R, as substitute for each individual vector in Rgg- effectively removing the influence of relation type differences entity-level inference. Despite the presence of only few relation types in node/graph-Ievel graph structures, the observed performance decline highlights the essential role of relational information. Notably, in graph-level tasks, relation-specific embeddings play vital role in distinguishing rare graph-label relations from semantic and topological edges.
(4) Few-Shot Labeling: We evaluate the performance of SCR in scenarios where the 'node/graph- label' edges are sparse within the graph. "SCR-20% uses 20% of the "node-label" edges from the training set, while "SCR-5" includes five edges per class. Both variants have no fine-tuning process, but utilize different scopes of "label information" when inference on the pre-trained model. As shown in Table and Table reducing the number of labels in the task sasc-specific KG leads to a decline in reasoning performance. However, "SCR-200 and "SCR-5" still obtain better accuracy than some baselines, which highlights the effectiveness of our method. In a few small-scale datasets, such as MUTAG and ENZYMES, the performance "SCR-20%" " lower than "SCR-5" due to the former having fewer accessible label edges.
6 Conclusion
In this paper, we take the first successful step toward generalizing inductive KG reasoning in graph foundation models. The proposed method. SCR, conducts semantic conditional message passing on multi-relational graphs, effectively integrating semantic features with structural information while addressing node-level, edge-level, and graph-level tasks simultancously. Extensive experiments demonstrate that SCR achieves strong generalizability across diverse graph domains and tasks. We further discuss the limitations of our work Appendix [L] Our future research agenda will prioritize two key objectives: (1) extending the applicability of this approach to broader graph-bace bapp- tasks across diverse domains, and (2) systematically validating the scaling principles that govern large-scale model architectures.
Acknowledgments
This research supported by the National Research Foundation, Singapore, under its Frontier CRP Grant (NRT-F-CRP-2224-0005) and under its AI Singapore Programme (AISG Award No: AISG3-RP-2024-034 Any opinions, findings, and conclusions or recommendations expressed in this material those of the author(s) and do not reflect the views of the National Research Foundation, Singapore.
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Appendix
A
Notations and Definitions
The notations used in this paper and their descriptions are summarized in Table
Table 4: Summary of the major notations in this paper.
Symbol
Description
G
A knowledge graph (KG)
T
The set of triples in KG
&,
The entity and relation set in KG item number specific set An entity (e) or a relation (r) in a KG A query with an entity and relation The ground-truth entity of a query node/entity feature matrix
[T1.1E).1R)
e,
q = (eq, rq)
x
d' d.d.
Dimension of features and embeddings The training KG and inference KG
Gur, Gue
CMP(
conditional message passing module
h.
The representation of e, conditioned Relation-level interaction representations Query-independent relation representations
R.
R,
Relation representations conditioned on g Query-independent entity representations
H,
H.
Entity representations conditioned
INIT(q, ev)
The initialization function CMP
MsG()
The message passing function of CMP
AGG(, UPD()
The aggretation and update functions
N-(ee)
The direct neighbors of connecting via
plg,ee)
for the triple The unified feature matrix
The plausibility
X
Gr
The relation graph corresponding to
Rond
The interaction types in the relation graph
The triples the relation graph
Se..
The semantic neighbors of e,
1 (g = v)
The indicator function
L
The loss function of SCR
F
The set of diverse features for training
B Tasks and Datasets
B.1 Task-Specific Datasets
Link-level KG Reasoning: We conduct inductive KG reasoning experiments on 24 datasets. Half of them are derived from the GralL. work (58), which are constructed from commonly-used KG benchmarks, including WN18RR (2), FB15k237
[59] and NELL-995 [75]. In these datasets, the train graphs and the test graphs share the same relation types. To evaluate performance in the full context of inductive reasoning, we also employ datasets used the InGram work 28 The InGram datasets were derived from three real-world KG benchmarks: FB 15k237 [59], Wikidata68K [21). and NELL--995 (75). There are four datasets in each series with different proportions of triplets with new relations 100%, 75%, 50%, and 25%. Note that, there other KG datasets where

---

textual descriptions are not easily accessible; we leave the evaluation of such datasets for future work. Structural statistics for these datasets can be found in Table TO]
To evaluate the adaptability of our method across various types/domains of graph tasks, we conduct experiments on 14 datasets involving both node-level and graph-level classification tasks. Following prior studies [89], we employ six commonly-used node classification datasets, including homophilic graph datasets (Cora, Citeseer, PubMed) [49 41] and heterophilic graph datasets (Wisconsin, Texas, Actor) [2
Node/Graph-Ievel Classification:
56]. Furthermore, we considered eight graph classification datasets from various domains, such as social networks (IMDB-B, COL- LAB) [77], biological datasets (ENZYMES, PROTEINS, DD)
[ 3 69], and small molecule More detailed information on these datasets can be found
datasets (MUTAG, COX2. BZR) 27 44
in Table I
Table 5: Statistics of pre-training KG datasets.
[Trl
Dataset
|&
[Ra,
#Train
#Validation #Test
WNI8RR
40.9k 11
86.8k
3.0k
3.1k
FB 15k-237
14.5k
237
272.1k
17.5k
20.4k
CodexMedium
17.0k
51
185.5k
10.3k
10.3k
Table 6: Statistics of Bert-based text encoder.
Method
Dim
Model Name
Bert
768
bert faas--ni-mmaanttoeen
MPNet
768
all 1il-mpeettbase-22
MiniLM
384
paraphrase-MinniMM-666
DistilBert
512
dbsiiuu-bbas-mmltiiggul--aeel
B.2 Task-Specific Data Preparation
To evaluate the generalizability of SCR foundational graph reasoning engine, reformulate various task data into a unified KG reasoning format, which includes a multi-relational graph structure and semantic node features. We illustrate the task-specific data forms in Figure
For graph structure, KG triples can be directly represented as multi- relational graph structure. For semantic features, we generate entity-level embeddings from available textual descriptions using BERT-based sentence encoders. To simulate different feature spaces, we employ four classical language models as sentence encoders, including BERT [0], MPNet (50), MiniLM 770) and DistilBERT 47.. MiniL. and DistiIBERT have different embedding dimensions compared to BERT and MPNet. Details of textual encoders are provided in Table Gi the Appendix.
Link-level KG Reasoning:
For semantic features, we directly utilize the provided input node features. In terms of graph structure, we augment the original homogeneous graph by introducing "label classes" as distinct nodes. Edges with a "labeling" relation type are added to connect nodes with training labels to their corresponding class nodes. Consequently, the augmented graph contains two relation types and two entity types (nodes and labels). This approach eliminates the need to learn specific parameters for each class, enabling support for new nodes or labels through zero-shot classification paradigm. Prior work [73 74] adopted a similar format but in a homogeneous graph, lacking the relation distinguishability between original edges and labeling edges.
Node-level Classification:
Graph-level Classification: Unlike node-level classification, graph classification tasks aim to predict the category of an entire graph. The graphs in the training set have no direct connections to the test graphs, which presents a challenge to the CMP reasoning process. To address task requirements, both the graph structure and the semantic feature format are specifically designed. First, we integrate all individual graphs into a single disconnected large graph, adding "graph" node representing each graph, which connects to its corresponding nodes via a new relation type. Next, we perform global semantic encoding of SCR on this large graph to obtain the global representations of each graph node, and then capture semantically similar edges among graph nodes. This allows us to convert the task into a node-level task, where the global representations serve as semantic features and reasoning occurs on an augmented graph encompassing all graph nodes and labels.
25

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C Semantic-Augmented Relation Graph
CMP-based models eliminate the necessity for learning unique embeddings for each entity. Instead, they depend on trainable relational representations to facilitate relation-specific message functions.
To accommodate varied relational vocabularies in new KGs, recent research 200 86 18] emphasizes
the importance of identifying the "invariance" present in the KG relational structure, thereby enabling any new relation type to be represented using a predefined set of parameters.
Drawing from insights in prior research [7]. we construct a relation graph G. (R, Rfndd Tr h. where the nodes represent the relations in 9, and the edges Reaud capture four types of interactions between relations: "head-to-head", "tail-to-tail", "head-to-taill, and "tail-to-head". For instance, if two triples (e1:71;'0 r1;
and (e2; r2, 63) are linked tail-to-head, an edge (r1: "t-h", ,t=h" would be added to Tr. Since these four interaction types are inherently derived from the triple structure in knowledge graphs, the pre-trained embeddings of these interaction types can be universally shared across KGs, allowing for the parameterization of any unseen relations.
In SCR framework, refine the relation graph by supplementing the original triple data T with additional edges obtained through semantic augmentation. Specifically, we derive semantic interactions among entities from the unified features X. For each entity e,, we identify the top spatially nearest entities in the unified feature space via pairwise similarities, while excluding its direct topological neighbors. The set of semantic neighbors Se,, is defined as follows:
S.,. (es E | J& co: k, et E Ne..)
(12)
Here, fa(+) represents the similarity function, No., fez E E (.).,)))TTT E R2 refers to the topological neighbor set of e,. The hyperparameters k and ó refer to the number of neighbors and the similarity threshold, respectively. The semantic interaction between e, and each element S., is regraded an additional relation type r.. Finally, the construction rules for the relation graph Gr can be formalized as follows:
Dee E E,, E R:
Be E eN N = (11,4112,, (n). E TT:
Dee Se, n.C = (1,4-19,,)) (re, THim)) E Tr,
Se, 00 E N + ra). (r., (h-41,)) E TT:
where 4 E ('h', } denotes the side of the relation (head or tail), Mt. C & represents the set of entities connected to relation r2 on the 4 side, Ta is newly introduced relation in the semantic space, and the final node set of G, is equal to (R U {ra}).
In classification tasks, although there are a few relation types in the relation graph, it still follows strict topological rules. For example, label edges only link from nodes to their labels, while original edges connect among nodes. This creates meaningful asymmetric constraints, i.e. there are no "t-h" and "t-t" interactions from the label edge type to the original edge type. By learning how different relation interactions interact topologically across the graph, our model derives transferable reasoning capabilities that generalize beyond explicit relation semantics.
D Implementation Details
87 we We introduce the statistics of pre-training KGs in Table Following previous work 82
augment the triples in each G with reverse and identity relations. The augmented triple set T is defined as: T = =T= {(e,, r r (en))((n,, ex) E T U ((eer",,))) E &), where the relation r is the reverse relation of relatiionnono r, the relation r' refers to the identity relation, and the number of augmented triples is | = T + (E).
We employ the ULTRA(3g) 17 model as the major baseline, utilizing the released checkpoint pre- pre-trained on three knoglwedge graphs. We evaluate OpenGraph [74] and AnyGraph [73 across diverse nove-level datasets using their publicly released pre-trained model weights. The metric results of GraphAny are referred to its official paper 85), and some node-level and graph-level results for graph prompt learning models are from the ProG work [89] Although there are some previous KG
reasoning baselines [16] 45 58 with no semantic features involving in, we ignore them in our more
challenging generalized reasoning tasks.
26

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We train SCR with three commonly-used KG datasets. WNI8RR 2]. FB15k237 [59, and CodexM 46). following the hyperparameter settings of ULTRA(3g). Concerns about potential rela- tion leakage during pre-training can be ignored because neither our method nor ULTRA learns relation- specific parameters. Specifically, the CMP module follows NBFNet [87] with non con-parmettric DistMult [78] message function and simplified PNA aggregation funcition 77.. which leverages only two uubaaggreaations MEAN and STD. The number of layers L for both CMP and SCMP is set to
with the hidden dimension configured at 64, The relation encoder utilizes randomly initialized edge embeddings for Ruund. In contrast, (CMP(.) initializes the embeddings of edge types using the relative relation embeddings Rgg. We suggest consulting the ULTRA paper [17 for further details.
We introduce two common types of node semantic features in knowledge graphs for model training.
Textual Embeddings are vector representations of textual information associated with entities in KG, typically generated using models like BERT [10 or Word2 [40]. Textual embeddings are broadly applicable across different KGs, as most KGs contain some form of textual metadata. However, the richness and variety of text data across KGs-such as short labels or multilingual content-can introduce diversity in how these embeddings are utilized, requiring models to generalize across various linguistic and domain-specific contexts.
Ontology Features refer to structured representations of entities within formalized schema, such as |R|-length vector that counts the relation types associated with each entity. These features offer global understanding of an entity's ' role in the graph by capturing its relational context. Common across various domains, they provide a simplified view of an entity's interactions. However, the diversity of relation types and their distribution can vary significantly across KGs, which affects how well these features generalize.
Hyperparameters are selected through grid search based on the metrics from the validation set. The similarity threshold ō and the number of neighbors k were not fine-tuned for individual datasets. Specifically, we set 8=0.9 for all node/graph-level datasets. For the neighbor number k, all six node- level datasets share k=2, while graph-level datasets use either k=1 k=3, depending on their domain. SCR maintains robust performance across datasets with a single task-level configuration, preserving its sero-shot capability. All experiments are performed on Intel Xeon Gold 6238R CPU 2.20GHz and NVIDIA RTX A30 GPUs (four for pretraining and one for evaluation), and are implemented in Python using the PyTTrcc framework. Our source code is implemented based on ULTRA? which is available under the MIT License. All employed KG datasets are open and commonly used.
E Task-specific KG Structure
Node Classification Task: We first define the unified reasoning format from the view of node classification. Suppose G = (V, E) is graph in D whose nodes in V must be classified by labels in a finite label set L. We construct the new, heterogeneous graph G = (V, E') as follows.
Let V V L be the of all nodes in the new graph, where each é L is viewed as a distinct "label node". Retain every original edge from E in G, so that if (v, u) E E in the original graph G, the same (possibly typed) edge is preserved in G. Furthermore, introduce a designated relation type Naael connecting nodes e to label nodes f C, i.e.:
Ejabel = { (v, Flabel, 2) V,
and v is assigned training lahel f in D)-
(13)
Then let the edge set E E Endel This completes the construction of the heterogencous graph G E).
Node classification in G bijectively map to link prediction in G, observe that assigning a label to a node e in the original problem becomes the presence of an edge (v, Flabel, E) in G. First, assume a labeling function f V - 2 is given. Each instance e + l that appears in I corresponds to including (w, Tlabel. 2) E Fraeel- Hence the labeling of G completely specifies the set of label-links in
G. Conversely, given link (v, Mabell, E) E É, one uniquely recovers the statement that v is labeled
27

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by é in the original classification problem. This one-to-one correspondence implies that any function assigning labels to nodes in G bijectively maps to set of label-links in G.
Graph Classification Task: Let {G1, G2 ................................ GM } be collection of graphs, where each G; is to be assigned one or more labels from a finite label set C = {fi..... fx J. Suppose each graph G2 in has node set V; and edge set E,. We aim label each G, with one or more labels from L. An extended graph G is constructed as follows.
:
Step 1: Introduce a new graph node s; for each graph G,, which will represent the entire graph G, as single entity in G.
Step 2: Include in G all original nodes from each G, That is, take Vaul U V, and add these re-indexed nodes G along with their internal edges Eall U E,
Step 3: For each u E Vi, add an edge (s;, Tnode-gruph: v) to indicate that e is member of the graph
G. The relation Fnode gragh is designated edge type (e.g.. "belongsToGrraph",
Step 4: For labeling, add a node for each label E Let these form the set of label nodes in G. To encode the classification of G; with label f, add an edge (s;, Flabel, E) whenever G; is assigned label Let Fiabel be the set of all such edges.
Step 5: For edges between graph nodes, add an edge (s;, Taimilar: 8j) whenever the graph embedding vector of G, is close that of Gj. Let Esimitar be the set of all such edges.
Hence, the heterogeneous graph is merged as follows:
G (Vall fsi....., SMM U.,
Eall U Enode-graple U Elabel Esimilar).
(14)
Similar to the claims about node classification, labeling G3 with in the original problem is exactly equivalent the statement that (st, Plahel. f) an edge in G. Because every valid assignment G₃ corresponds bijectively to an edge (st, Mlabel: f).
F Expressive Power
We formally analyze the expressive power of SCR by comparing with ULTRA [77. Following the theory of the Weiseeiler-Leman test, measure expressivity via a method's ability to distinguish non-isomorphic subgraphs in knowledge graphs.
Firstly, we show that SCR is at least as expressive as ULTRA. For any non-isomorphic graphs distinguishable by ULTRA, there exists a parameter configuration of SCR that achieves identical distinguishability..
We establish this through architectural reduction. Let (k,, WMLP) denote SCR's key hyperparam- eters where & controls semantic neighborhood size and WMLP the MLP weights from Eq. (7). When 8o (0, 0). SCR reduces to ULTRA through three key simplifications:
1. The augmented relation graph G, collapses to ULTRA's original structure by removing the semantic relation type Ts;
The INIT function (Eq. (5)) reduces to ULTRA's initialization by eliminating the na term;
3. The representation fusion becomes identity because MLP(H,,) 0;
Under Og. the message passing dynamies of both architectures become isomorphic. Therefore, ULTRA constitutes a proper subspace of SCR's parameter space.
Secondly, we indicate that there exists a class of non-isomorphic triples distinguishable by SCR but not by ULTRA, provided that semantic features contain discriminative information beyond graph topology.
Consider two candidate entities c1, e2 E E with identical topological signatures relative to query entity eg:
Vp E Tpahh SULTRA (Cy. e1) = fULTRA (cg, 62)
(15)
where 1path denotes relational paths and f the path encoding function.
28

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IndE MRR
IndER
0.350
30
0.345
10
10
0.50
0.335
0.330
0.48
0.325
0
0.8
6:8
0.8
0.5
IndE: Hiis10
IndER Hits10
50
50
0.540
30
30
0.70
10
10
0.530
0.66
0.525
0.520
0.8
0.5
Figure 4: Comparison of performance metrics under different hyperparameter settings (k and ō) for semantic neighbor selection. (a) Average MRR results. (b) Hits@ 10 results. Darker colors indicate higher values.
ULTRA cannot distinguish (Eg, Tap ei) from (Eqs Tgg e2) since their topological embeddings coincide. However, the semantic features satisfy:
min (e,)
|
min VEN
||ses
iol12
(16)
where Nr, (ey) are Tg neighbos of eg. then SCR's 's semantic proximity measure induces divergent embeddings:
[ - 1011 2 2 0
(17)
The separation constant y persists through MLP fusion (Eq. (7)) by the Lipschitz continuity of neural networks. Thus, SCR distinguishes the triplets while ULTRA cannot.
This analysis reveals SCR's enhanced expressiveness stems from its semantic-topologicall fusion mechanism. By jointly optimizing structural and semantic proximity measures during pre-training the model learns disentangled yet complementary representations that strictly subsume purely topological approaches like ULTRA.
G Hyperparameter Sensitivity (RQ5)
Furthermore, we evaluate the impact of hyperparameters and 8 on the selection of semantic neighbors. Here, & specifies the number of neighbors, while 8 determines the minimum similarity threshold. illustrated in Figure variations in these hyperparameters slightly affect prediction performance. Different choices of & show similar performance across the IndE benchmarks, but for IndER datasets, & 10 clearly outperforms other values. When k > 10, the influence of becomes more pronounced, as a lower å includes more dissimilar neighbors, negatively affecting model performance.
H Assumption in SCR
we claim that the target node distinguishability assumption holds for the INIT function, if lq and neither of them contains zero entries. This assumption usually holds because of the distinction between r (relation representations outputted by CMPs) and v, (trainable vector parameters) is inherently preserved through their distinct initialization and optimization mechanisms.
In Section 4.2
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Empirically, we conducted parameter analysis on our pre-trained SCR model and observed that: All Vn parameters maintained non-zero magnitudes 0.5511); Fq oulputs on six datasets showed no exact zero entries or equality to Va- While theoretical equality is possible, it would require exact parameter convergence to zero or identical gradient updates- statistically implausible in practice.
I Complexity and Scalability Analysis
Given a knowledge graph 9 = R., T), we have that |8], [R], [T| represent the size of entities, relation types, and triples, respectively. g. (R. fund - T,) denotes the relation graph G. X Rd the input feature matrix, is the hidden dimension of the model, and the number of layers in the model. In the preprocessing stage, unifying semantic features requires time complexity of (((E)dd)) for the SVD low-rank approximation. Our adoption of "torch. Jowrank(X, q=d, niter=2)" leverages randomized truncated SVD, avoiding the O(E)))) complexity of the full SVD, Constructing relation graphs involves extracting the top K most similar neighbors for each entity, with time complexity of O(E (d log K)), which simplifies to ((E)?d) d > log K. Therefore, the overall complexity is O(dd, + (d)).
In terms of the CMP module, shown in Zhu et al. 87, the time complexity for a forward pass to compute one query reasoning. The runtimes of CMP and SCMP are comparable because SCMP's global encoding is shared across all queries. resulting in only linear overhead. Combining the CMP calculations on Gr, the total complexity is (([T] + +TT,I) + (LE) + Ld.). Because CMP-based reasoning calculates | candidate triples at the same time, resulting in an amortized complexity is better than traditional relational pesssage-passing models, such RGCN [48], CompGCN 660 and GralL (58).
on 9 is (IT(TTd + [
Regarding scalability, SCR exhibits comparable scalability and running time to ULTRA. To ease the concern, we conducted additional experiments in Appendix Mon all transductive KG datasets mentioned in UITTRA, including large-scale datasets with over 100k triples, such as YAGO310. We acknowledge that both methods face practical limitations when applied to KGs with millions or billions of triples. Specifically, the time cost of subgraph extraction and message passing becomes non-trivial compared to traditional embedding-basee models. This limitation is inherent to subgraph- based inductive frameworks but does not preclude SCR 's applicability to typical large-scale KGs. We will prioritize this in future work. For large-scale KGs, recent acceleration techniques like TIGER [63] (enabling efficient subgraph extraction for inductive reasoning on Freebase) are critical. While SCR 's current implementation does not yet integrate these optimizations, its framework is compatible with such methods.
Impact of Feature Dimension
In terms of the impact of the dimension gap between semantic features and node features. conduct additional experiments with 50-dimensional Glove Features (with zero-padding), Clipped 64-dimensional Bert features, random features, and all-ones features. The results in Table indicate that using node features with closer dimensions still invokes the performance drop. Additionally, we test the variant using the semantic features of the query node in INIT () in Huang et al. [25]. There still exists a performance drop compared with the original ULTRA on most datasets. These results indicate that the semantic isolation issue still holds when setting the dimension of the node features closer to the dimension of the semantic features and using /TT fusion.
K Impact of Long-range Dependency
It is worth noting that unlike conventional GNNs, Graph Foundation Models are still in their early stages, and many associated challenges remain open. Over-smoothing and over-squashing are known issues in message-passing based models, especially in long-range dependency tasks.
Over-smoothing typically occurs in deep architectures, where repeated message passing leads to uniform node embeddings. In our model, however, message propagation occurs over relatively shallow subgraphs (3-6 layers), which mitigates this risk. Furthermore, our message passing is source- conditioned: only the source node e, is initialized with non-zero embedding, and information
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Table 7: Performance of ULTRA with different semantic features.
FB vl
WN_vl vl
NE_vl
ULTRA
0,486
0.593
0.716
+Bert
0.163
0.014
0.580
+All One(64d)
0.227
0.024
0,684
+Random(64d)
0.218
0.015
0.658
+Bert(Clip64)
0.200
0.013
0,593
+Glove(50d)
0.160
0.007
0.609
+Bert+INIT3
0.483
0.549
0.648
INI03
0.483
0.524
0.720
Table Performance on the long-range Pascal dataset.
Method
Macro F1
ULTRA (full labeling)
0.039
SCR (full labeling)
0,053
GCN (full training)
0.101
GraphTransfommertuull training)
0.121
SCR (20% labeling)
0.051
GCN (20% training)
0.046
Graphhrranffommer2226 training)
0,052
flows outward. Thus, each node's embedding is view from Egg, not a globally shared representation, preserving diversity. Over-squashing. caused by bottlenecks in aggregating long-range messages into fixed-size vectors, may arise due to dense multi-hop paths. To address this, we employ the expressive PNA aggregator and set the hidden dimension to 64, balancing representational capacity with computational efficiency, while also accommodating both BERT-based textual features and common graph-domain features.
To further validate SCR's performance deep extreme-range tasks, we employed a subset of PascalVOC-SP (685K nodes, 5M edges) in the LRGB benchmark [[3]. While LRGB assumes fully- supervised training on very large graphs, our proposed SCR was designed for zero-shot generalization. SCR only saw the label information during inference but no any fine-tuning on them. As shown in Table 8 SCR delivers a substantial gain over ULTRA, but under full supervision, it still trails GCN and GiraphTranfformer We believe that large-scale training enhances the performance of GCN and TranSorras To mitigate the effect of training, we use a few-shot setting. GCN and GraphTransformet are trained on 20% samples, while SCR remains strictly zero-shot, merely seeing those labels at inference. Under this setting, SCR matches GraphTransformer and outperforms GCN, demonstrating that it retains long-range ability even without specific training.
While these are well-known challenges, our current focus is to investigate the semantic and structural transferability of KG pre-training to diverse graph tasks core goal in the emerging Graph Foun- dation Model paradigm. Our work takes step forward by focusing on cross-task and cross-graph transferability, which we believe is largely orthogonal to the over-smoothing, over-squashing, and long-range issues. We consider these important directions for future work.
L Limitations
Here, discuss two limitations of this work. First, the training data for SCR confined three popular KGs. There is room for improvement by training with more diverse graphs, particularly on challenging tasks like those involving heterophilic graphs. Second, the scalability of SCR on larger- scale graphs remains to be verified in future work. The expectation is positive, given the recent efforts focused on accelerating KG reasoning through system and algorithmic optimizations [3 65).
Third, this paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here. In this work, the LLM is used only for writing and editing.
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Table Per-dataset and average performance of ULTRA and SCR on 54 KG datasets.
ULTRA(3g)
SCR(3g)
KG Datasets
MRR
Hits@ 10
MRR
Hits@10
0.242
0.305
0.182
0.312
WikiTopicsMMT/hhellt
0.279
0.332
0.265
0.410
WikiTopiccMMT2:org
0.083
0.145
0.078
0.139
WikiTopicsMMT::sii
0.258
0.348
0.245
0.354
WikiTopicsMTI<aart
0.251
0.414
0.244
0.407
WikiTopicaMT3::nfrrr
0.622
0.779
0.635
0.781
WikiTTopicsM11::cii
0.293
0,455
0.256
0.461
WikiToppiesMT4hhcattth
0.557
0.707
0.615
0.753
Metafam
0.330
0.821
0.246
0.560
FBNELL
0.473
0.653
0.480
0.676
ILlc2022:smal
0.296
0,441
0.285
0.443
ILPC2022:large
0.297
0.423
0.285
0.419
HM:lk
0,079
0.150
0.055
0.097
HM:33
0.063
0.120
0.047
0.083
HM:5k
0.055
0.101
0.041
0.072
HM-indigo
0.436
0.649
0.425
0.631
YAGO310
0.480
0.658
0.488
0.666
NEL.L995
0.437
0.575
0.456
0.608
CoDExSmall
0.472
0.668
0.436
0.653
CoDExLarge
0.333
0.461
0.329
0.458
Hetionet
0.261
0.382
0.289
0.402
ConceptNet1000k
0.061
0.117
0.115
0.218
DBpedia100k
0.397
0.565
0.401
0.573
Ar
0.183
0.262
0.227
0.349
WDssigger
0.370
0.488
0.371
0.498
NELL23K
0.241
0.406
0.234
0.402
FB15k237
0.159
0,272
0.155
0.265
FB FB15k237 20
0.183
0.309
0.179
0.305
FB #B15k237_50
0.230
0.396
0.222
0.389
FB FB152237
0.369
0.562
0.344
0.533
WN18RR
0.369
0.533
0.444
CedExmedium
0.374
0.527
0.350
0.498
Inductive e.r (23 graphs)
0.342
0.510
0.338
0.516
Inductive (18 graphs)
0.416
0.568
0.433
0.582
Transductive (13 graphs)
0.293
0.428
0.300
0.445
Total AVG (54 graphs)
0.355
0,510
0.361
0.521
Pretraining (3 graphs)
0.371
0.541
0.379
0.534
M Evaluation on More KG Datasets
We rigorously test all 54 datasets and the pre-training graphs referenced in ULTRA's frame- that SCR outperforms ULTRA across the majority
work [77.. The results shown in of metrics when evaluated under identical conditions (PyG-based implementation and pre-training data).
N Related Work
N.1 Knowledge Graph Reasoning
Traditional transductive KG reasoning models, such as TransE M. DistMult
78 RotatE [54].
RGCN [48]. and CompGCN [60], represent entities and relations within knowledge graph using
continuous vector embeddings 668 64]. These models, however, assume that all entities and relations
in the KG are known beforehand, which limits their ability to generalize to unseen entities within same graph or across different KGs [63
4 In contrast, inductive KG reasoning approaches [87 address this limitation by enabling generalization to KGs with previously unseen entities or relations. Most existing inductive methods [76]
S employ query-conditional MPNNs to generate
"relative" entity embeddings by extracting local structural features from a subgraph induced by the
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Table 10: Inductive KG datasets used in the experiments. "Triples" refers to the number of edges in the graph used for training, validation, or testing. "Valid" and "Test" refer to the triples that need to be predicted in the validation and test sets, respectively, within the corresponding graphs.
Training Graph
Validation Graph
Tost Graph
Group
Datasct
Eatities
Rels
Triples
Entities
Rels
Triples
Valid
Eatities
Rels
Triples
Test
FB:vl 58
1594
180
4245
1594
180
4245
489
1093
180
1993
411
IndE(FB)
FR:v2
53
2608
200
9739
2608
200
9739
1166
1660
200
4145
947
FB:v3
3668
17986
3668
17986
2194
215
1731
FR:y4
S8
4707
219
27203
4707
219
27203
3352
305
219
11714
2840
WNvv
2746
5410
2746
5410
1618
373
IndE(WN)
WN.v2
58
6954
10
15262
6954
15262
1838
2757
10
4011
852
WN.v3
12078
11
25901
12078
25901
3097
5084
11
6327
1143
WN:v4
3861
7940
3861
7940
934
7084
12334
2823
NLv1
3103
14
4687
3103
4687
414
225
14
833
201
VL
2564
8219
2564
8219
2086
88
4586
935
IndF(NI.)
3L 58
4647
142
16393
4647
142
16393
1851
3566
142
8048
1620
NL.v4
2092
7546
2092
75446
876
2795
76
7073
1447
FB-25 2X
5190
163
91571
4097
216
17147
5716
4097
216
17147
5716
IndER(FB)
FB.50
5190
85375
205
3879
FR-75 2X
4689
134
62809
2792
186
9316
3106
2792
186
9316
3106
FB-100
4659
134
62809
2624
6987
2329
2624
77
6987
2329
WK-25 28
12659
47
41873
3228
3391
1130
3228
74
3391
1131
IndER(WK)
WK.50
12022
72
82481
9328
9672
3224
9322
93
9672
3225
WK-75 28
6853
52
28741
2722
3430
1143
2722
65
3430
1144
WK-100 2X
9784
67
49875
12136
37
13487
4496
12136
37
13487
4496
NL-25
4396
17578
2146
2230
120
744
IndER(NL)
NL-50 28
4396
106
17578
2335
119
2576
859
2335
119
2576
859
NL-75
2607
11058
1578
116
1818
606
1578
116
1818
607
NL-100
28
1258
55
7832
1709
2378
793
1709
53
2378
793
Table 11: Statistics of node/graph classification datasets.
Dataset
Graphs
Nodes
Edges
Feature Dims
Classes
Node-level Task
Cora
2.708
5,429
1,433
7
Homophilic Node Classification
CiteSeer
1
3,327
9,104
3,703
6
Homophilic Node Classilication
Pubmed
19,717
88,648
500
Homophilic Node Classification
Actor
I
7600
30,019
932
5
Heterophalic Node Classification
Wisconsin
251
515
1,703
5
Heterphilicc Node Classification
Texas
183
325
1703
5
Heteropillic Node Classification
Graphs
Avg. Avg.nodes
Avg.edges
Dims
Classes
Graph
IMDB -IBBBBIARY
1,000
19.8
96.53
2
Social Network Classification
COLLAB
5,000
74.5
2457.8
3
Social Network Classification
PROTEINS
1,113
39.1
72.8
2
Protein Graph Classification
ENZYMES
600
32.6
62.1
6
Protein Graph Classification
DD
1,178
284.1
715.7
89
2
Protein Graph Classification
MUTAG
188
17.9
19.8
2
Small Molecule Classification
COX2
467
41.2
43.5
2
Small Molecule Classification
BZR
405
35.8
38.4
2
Small Molecule Classiication
query entity. GralL (58), for example, extracts an enclosing subgraph between the query entity and each candidate entity, but this approach suffers from high computational costs. Other models, such as NBFNet [87] and RED-GNN (82] propagate query features through the L-hop neighborhood subgraph of the query entity. To improve computational efficiency, recent works have focused on
optimizing algorithms, including path-pruning techniques during the GNN propagation process [33
88 67.. In the direction of building foundation model for KG reasoning. ULTRA [17] utilizes four basic interaction types of the KG relational structure to perform inductive reasoning on entirely novel KGs. Building on ULTRA, ProLINK (66) harnesses the power of large language models (LLMMs) to enhance reasoning performance for few-shot relation types on low-resource KGs. Nevertheless, these inductive methods face challenges in generalizing wide variety of graph tasks and feature spaces, as their reasoning capabilities remain primarily confined to topological structures.
N.2 Graph Foundation Models
Graph foundation models are increasingly recognized for their ability to manage diverse graph- structured data across various tasks. Traditionally, model fine-tuning offers simple method to adapt
33

---

these models to downstream tasks 80 31 30]. However, significant diserepancies between tasks can lead to negative transfer and catastrophic forgetting 43 An alternative to fine-tuning graph prompt learning, which reformulates input graph data to better align with the pretext task 6 55 22].
In this context, GPF utilizes a prompt token by adding supplementary features to the base graph. Building on this, GPF-plus [5] trains multiple independent basis vectors and integrates them through attentive aggregation facilitated by several learnable linear projections. GPPT [52) introduces graph prompts as additional tokens comprising task-specific and structural elements, aiding in node tasks and link prediction pretext alignment. Gprompt (38] incorporates prompt vectors into graph pooling through element -wise multiplication. Other research considers graph prompts additional graphs [19 24]. The All-in-one model [53], for instance, integrates token graphs as prompts within the original graph, linking tokens directly with the original graph elements. Although these graph prompt learning methods achieve good performance in various graph tasks, they require an additional learning phase for task-specific parameters.
Recently, several foundational models for specific graph tasks have been proposed to adapt to diverse unseen data without model tuning. ULTRA [7] and KG-ICL [8] are pre-trained on multiple KGs to obtain the capability of reasoning on new KGs. PrOLINK [66] and TRIX (84) further expand on ULTRA with prompt graphs from LLMs and iterative updates of relation/entity embeddings. GraphAny [85] addresses inductive node classification by formulating inference as an analytical solution to a linear GNN architecture, while attention module fuses predictions from multiple models, ensuring scalability. Models like InstructGLM [79] and HiGPT [57] leverage large language models (LLMs), using natural language prompts to guide graph learning and handling heterogencous graphs without downstream fine-tuning, broadening the applicability of foundation models to diverse graph tasks. Building a general graph foundation model is not trivial; the major challenges to overcome are related to structural and feature heterogeneity. OpenGraph [74] proposes a zero-shot graph learning framework with a unified graph tokenizer and a scalable graph transformer, allowing the model to handle unseen graph data, aided by LLM-based data augmentation. AnyGraph [73 extends this by addressing structural and feature heterogeneity through a Graph Mixture-of-Experte architecture, supporting fast adaptation and scaling efficiently. RiemannGFM [1 incorporates diverse vocabulary geometries via a novel product bundle and learns structural representations in Riemannian manifolds through stacked Riemannian layers, enabling cross-domain transfcrability. OMOG (37 trains dataset-specific expert models and dynamically integrates them via adaptive gating functions for unseen graphs, optimizing prior knowledge transfer while suppressing negative interference. Research on Graph Foundation Models still in its early stages, and current methods often struggle to match the competitive performance of task-specific supervised methods [71 36 14]
34
Several recent methods also incorporate semantic features into the graph reasoning framework. The initializer INIT in Huang al. [25] incorporates the semantic feature of the query node u. but ignores the semantics of other nodes in the neighborhood. As a result, using I IN INIT(( would not significantly drop the performance of ULTRA, because it still cannot exploit the full range of node semantics. This is also one of the motivations we propose the semantic isolation issue. Liu (35 employs PL.M-based textual embeddings as the input node feature of GNN, and alternates the training of GNN and PLM within a single dataset. This method cannot handle our zero-shot GFM settings, especially for non-textual semantic features in general graphs. Additionally, the performance drop reported in their experiments when directly using pre-trained PLM embeddings indicates the necessity of re-training a PLM for enhanced text representation. A contemporaneous work 112 achieves semantic injection for KG foundational reasoning, but it focuses solely on text embeddings derived from a single semantic space (i.e., an LLM). Consequently, their pretraining approach cannot process zero-shot features originating from different semantic spaces. We note that their late fusion between query-conditioned structural encoding and global structural semantic encoding is similar to our proposed strategy, indirectly confirming the feasibility and rationale of our design choice. In summary, these recent methods cannot effectively integrate multi-source zero-shot features. Consequently, none of these approaches provides a viable alternative to our method within GFM.
0 Additional Experimental Results
34

---

Table 12: Accuracy results on node classification datasets where 90% samples are divided into the test set.
Learning Paradigm
Methods
Cora
Citeseer
Pubmedd
Wisconsin
Texas*
Actor
One-Shot Training
GCN
26.5615555
21.78:17.32
39.37
41 1..60113.10
37.97
20.57:1-447
Pre-train Fine-Tune
40.40
35.05
44.74
40.69
47.66
20.74:4.12
GPPT
43.15:9944
37.26::.17
48.31
30.4026.81
31,81
22.58
All-in-one
52.39:10.17
40,41:2250
45.17:16.15
78.24:116.8
65.49:17.0
2:.61
Graph Pre- Pre-Training
Gprimpe
16.66-2:1.22
13.21
15.74
83.80:2.44
33.25-240.1
25.26+1.10
One-Shot Tuning
GPF
38.57:541
31.16:8.05
49.99
88.67:5578
87,40+3340
28.70+3.35
GPF-plus
55.77:10.30
59.67:11.87
18.94
91.03:1.111
95.83:14.19
29.32:3.56
KG Pre-Truining
SCR (3g)
76.182009
50.40:ons
72.76=20
46.67:10.28
24.15
23.5220014
SCR-20% SCR-5
58.814274
36.62:162
67.94:20.6
45.42:1147
52,68+083
21.81:1066
No Tuning
56.80+355
32.164385
51.63+5.46
45.60+2.06
56.59+071
2..68+1.09
Table 13: Fl results node classification datasets where 90% samples are divided into the test set.
Learning Paradigm
Methods
Cora*
Citescer
Puhmed
Wisconsin*
Texas*
Actor
GCN
16.60
10.81
35.23 48
26.342:.01
24.05=5.12
11.56:3300
Onc-Shot Training
Pre-train & Fine-Tune
35.92+4.06
30.78+391
41.03++3.36
27.43+4.47
29.53+6644
15.91
GPPT
38.99
33.00:6649
16.43
23.74
25.64
19.62+0.%
All-in-one GPrompt
46.58:18.22
30.20144.44
38.05
67.684100.3
43.37416.01
16.05
Graph Training
One-Shot Tuning
46.28++8.46
11.45
19.46
77.03-16.40
29,20+:3.62
22.00+
GPF
23.799.5.19
18.63317.34
15.36:115:8
82.97:16.10
78.43-19.19
31.6915447
GPF-plus
53,28::1146
56.22.+13999
19.08
85.24
86.22+10.29
24.56
KG Pre-Training
SCR (3g)
73.06+0.11
50.02++0.5
10.79
17.82
17.51
19.64
SCR-20% SCR-5
55.81
36.27:1343
64.92:10:0
17.14 14:106
16.05
19.14:0.52
No Tuning
55.56:2229
28.1043.12
47.1946..3
27.41
23.7340077
18.74:1064
Table 14: Fl performance on node classification datasets.
Methods
Cora
Citesocr
Pubmed
Wisconsin
Texas
Actor
GCN
16.60.1.54 35.9244406
10.81
15.43
26.3414.01
24.05
11.56-3.08
One-shot Training
Pre-train & Finc-tune
30.78=391
41.03
26.74
29.53
15.91=099
Graph Prearrinn
OpenGraph AnyGraph (Link1)
79.85
67.52.1075
17.741165
15.45
17.78.15.07
9,84
60.5
49.81=5518
58 28.444428
1.332034
0.40
4.98:10.27
No Tuning
AnyGruph (Link2)
68.513.16
43.47:13.44
1..91
1,27:1022
0.68
4.93.0031
KG Pre- Training
ULTRA(33)
78.40:20.00
64.68:2000
76.152000
25.71
19.81
14.62-0.0
Tuning
(3g)
80.92:1061
69.24:1110
13.
29.03:1366
28.73
20.29=0:41
Sho-Shot Labeling
SCR-20% SCR-5
71.98:2.95
$3.48=2.54
69.09-004
23.62 30
26.7447.10
19.45-0.57
14.08
32.35
47.19+4.45
19.76#284
37.2946.9
18.19=091
Table 15: Fl performance graph classification datasets.
Methods
IMDB-B
COLLAR
PROTEINS
MUTACI
ENZYMES
COX2
B7R
DDD
Shot Training
GCN
55.24e1.00
54 54.62,111
41.7120.7
59.73e134
63,70:532
22.7811006
33.12=1.45
23.71
GPYT
44.16:a4
42,87e1.0
47.07
53.15e.432
19.872200
44.68:117
49.00=141
51, 31.5026354
Graph Pre Training
Qhi-SSlet Tuning
GPF
All-in-oee
Girrmpt
$2.10=1101
56 22223. 17
56 58.88
43.35
14.14100
47.7860.10 10
58.30:1015
64.68:535
57.01 1574
71 71.38:344
78.57:493
63.001405
19,52:136
17.34
19.562311
49.62 19.6221042
43.08.1.
46.26:1514
44.81=5775
62. 60.11
48. 48.83_1100
48. $2
52 90:330
56 7.22
GPF-plus
63.2011311
Pro-Troining
ULTTRA/3))
38.871000
23.041000
37.48 (00)
3.84
44.23_.0m
No Tuning
SCR
60.9142.18
57.71
13.23
84.23-190
21.77
24:4455555
$1.09
69 85:85
Few Shot Labeling
SCR-5 5
SCR-20%
51.29:441
49 04
46.074577
46.3544438
57.921221
57 18
24.01
79,33:531
21.566::18
9. 9.38 49
51.06:2036
45.80:3341
45. 45.39
40.2::144
70.27:4431
68 85-85
35

---

Table 16: Per-dataset results of performance on zero-shot KG inductive reasoning.
Dutasets
Supervised SOTA
MRR
Hise I0
MRR
ULTRA(3g)
Hins8
MRR
SCR
His 10
MRR
SCR (One)
Hise 10
MRR
SCR (MPNet)
Hise 10
SCR (Ontologs) MRR
His@ 10
MRR
SCR (4g)
Hise t0
FR
0.457
0.589
0.486
0.657
0.496
0.684
0.489
0.670
0.496
0.684
0.493
0.681
0.499
0.657
0.604
0:511
0.507
0.718
0.713
0.509
FB:v3
0,476
0.485
FB:v4
0,496
0.645
0.477
0.671
0.485
0.083
0,481
0.678
0.485
0.682
0.481
0.679
0.489
0.676
WNNv1
0.741
0.825
0.593
0.779
0.661
0.795
0.641
0.772
0.663
0.799
0.658
0.750
0.640
0.796
WN:v2
0.701
0.798
0.620
0,752
0.650
0.785
0.657
0.765
0.650
0.783
0.653
0.755
0.645
0.788
WNiv
0.452
0.399
0.387
0.400
0.532
0.594
0.592
NLav
0.637
0.866
0.715
0.861
0.783
0913
0.743
0.861
0.771
0.908
0.764
0.898
0.745
0.858
NLvv2
0.419
0.601
0.525
0.719
0.538
0.761
0.533
0.750
0,540
0.760
0,516
0.739
0.552
0.753
NL.v3
0,436
0.594
0.511
0.687
0.554
0.750
0.553
0.750
0.552
0.751
0,544
0.740
0.556
0.753
NL.v4
FR:25
0.389
0.388
0.641
0.389
0.645
0.387
F8:50
0.117
0.218
0.330
0.536
0.341
0.548
0.335
0.537
0.341
0.549
0.336
0.541
0.340
0.543
FB:75
0.189
0.325
0.391
0.554
0.400
0.611
0.399
0.003
0,400
0.610
0.395
0.603
0.397
0.00
10:100
0.223
0.371
0.438
0.611
0.437
0.612
0.438
0.636
0.438
0.610
0.431
0.637
0.439
0.642
WK:25
0.301
0.068
0.296
0.160
0.159
0.299
0.173
WK:75
0.247
0.362
0.373
0.519
0.365
0.532
0.368
0.522
0.365
0.531
0.342
0.514
0.375
0.536
WK:100
0.107
0.169
0.178
0.289
0.186
0.302
0.176
0.283
0.186
0.302
0.142
0.289
0.188
0.309
NL-25
0.354
0.501
0.367
0.538
0.392
0.90
0.359
0.562
0.394
0.604
0.376
0.566
0.404
0.612
0.375
0.261
0.527
0.349
0.350
0.519
0.350
0.540
0.360
NL:100
0.309
0.506
0.442
0.631
0.475
0.695
0.468
0.692
0,473
0.693
0.464
0.678
0.476
0.687
36


Reviews:
[{"review_id": "fdQLNyYzV2", "reviewer": "Reviewer_cmwp", "summary": "This paper introduces SCR, a novel graph foundation model designed to address the challenge of transferring knowledge from knowledge graphs (KGs) to general graph domains and tasks without requiring extra fine-tuning. Inspired by recent advances in zero-shot KG reasoning, SCR unifies diverse graph tasks (node, link, and graph classification) into an inductive KG reasoning framework. The authors propose a task-specific KG transformation that reframes general graph problems as KG reasoning, and introduce Semantic Conditional Message Passing (SCMP), which integrates both structural and semantic information to overcome the \"semantic isolation\" problem in traditional KG models. Extensive experiments on 38 datasets across multiple domains demonstrate that SCR achieves strong zero-shot and few-shot generalization, outperforming existing graph foundation models and supervised baselines on a range of inductive reasoning and classification tasks. The paper provides detailed ablations and discussions on the impact of semantic features, model components, scalability, and limitations.", "questions": "Please see weaknesses.", "limitations": "Yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "- Strengths\n  - The paper provides a comprehensive empirical evaluation across 38 datasets spanning node-level, link-level, and graph-level tasks. This broad experimental scope convincingly demonstrates the generalizability and robustness of the proposed approach across a wide range of domains and graph types.\n  - The motivation for bridging knowledge graph reasoning and general graph foundation models is well-articulated, and the paper offers a thorough description of the SCR framework and its components. The unified transformation of graph tasks into KG reasoning is clearly presented, and the introduction of Semantic Conditional Message Passing (SCMP) is well-explained. Most methodological details are accessible, with only minor sections that could benefit from further clarification.\n\n- Weaknesses\n  - The main figure intended to illustrate the SCR framework does not significantly aid understanding of the method. As presented, it lacks clarity and does not effectively convey the model’s workflow or the intuition behind key components, which could hinder readers’ comprehension.\n  - The main innovation appears to be a practical and effective integration of node semantic information based on the ULTRA framework. The introduction of virtual nodes to convert various tasks into reasoning tasks on graphs primarily serves this integration, which to some extent reduces the novelty of this work.\n  - The largest performance gains are observed in graph classification tasks. However, it remains unclear to what extent the improvement is attributable to the introduction of semantic information. If such ablation studies have not been conducted, additional experiments isolating the effect of semantic features on graph classification would strengthen the claims. Additionally, did SCR (3g), ULTRA (3g) and ProLINK(3g) consistently use the same KGs?\n  - The methodology section could be better organized. Currently, the lack of an initial high-level overview of the entire approach makes it difficult for readers to grasp the core ideas before delving into technical details. This affects the overall readability and the depth at which readers can understand the method.", "was_revised": true, "final_justification": "N/A", "rebuttal": "We thank the reviewer cmwp for the insightful and valuable comments. We sincerely hope that our rebuttal adequately addresses your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know if you have further concerns, and we will continue actively responding to your comments.\n \n > **1. W1: The main figure lacks clarity and does not effectively convey the model’s workflow.**\n \nWe sincerely thank you for this comment. Because external figure links are not permitted during the rebuttal phase, we describe the points we plan to revise. First of all, we will redraw all the arrows and reorganize the two bottom subfigures, so that the workflows for pre‑training on KGs and reasoning on general graphs are shown clearly. Besides, we also modify the caption to clarify the role of each component. The updated figure will be added in the revised version.\n\n\n > **2. W2: The main innovation appears to be a practical and effective integration of node semantic information based on the ULTRA framework. The introduction of virtual nodes to convert various tasks into reasoning tasks on graphs primarily serves this integration, which to some extent reduces the novelty of this work.**\n \n\nThank you for raising this point. We agree that the use of virtual nodes is a common design choice, but it remains essential to unify different graph tasks. The novelty of our work is to generalize the inductive KG reasoning method within the ULTRA framework to handle diverse tasks on general graphs, providing a practical recipe for building graph foundation models.\n\n\n > **3. W3: Additional experiments isolating the effect of semantic features on graph classification would strengthen the claims. Additionally, did SCR (3g), ULTRA (3g), and ProLINK(3g) consistently use the same KGs?**\n \n\nWe sincerely appreciate these valuable comments.  \n\n\nIn Section 5.5, we conducted ablation studies to verify the impact of semantic features on node/graph classification. As shown in the right figure of Figure 3, the reduced performance of “w/o NPSR” emphasizes its important role in leveraging semantic diversity. Meanwhile, the Semantic-Injected Entity Initialization and Relation Representations also play essential roles. Additionally, in Table 3, two graph classification datasets we evaluated (IMDB-BINARY, COLLAB) are featureless, which indicates that the performance gain is not only derived from semantic features. \n \n\nThe three compared methods (SCR, ULTRA, ProLINK) use identical underlying topological graphs. The critical distinction is that only SCR incorporates semantic features to construct additional semantically-similar edges, while ULTRA and ProLINK rely solely on raw graph structures.  \n \n > **4. W4: The methodology section could be better organized. An initial high-level overview of the entire approach is needed.**\n \n\nWe sincerely appreciate this constructive suggestion. To improve clarity, we will relocate the workflow description currently in Section 4.3 to the beginning of Section 4, serving a high-level overview of the entire approach accompanied by Figure 1. This will provide readers with a clear roadmap before delving into implementation details."}, {"review_id": "nz86cKoKwM", "reviewer": "Reviewer_wV6S", "summary": "The paper introduces **SCR (Semantic Conditional Reasoner)**, a framework that leverages *inductive knowledge graph (KG) reasoning* as a foundation for general-purpose graph learning. Instead of pretraining on general graphs directly, the authors propose transforming diverse graph tasks (like node or graph classification) into KG reasoning problems using task-specific KG structures. A key challenge they address is the *semantic isolation problem*, where existing KG reasoning models struggle to integrate node features effectively. To overcome this, SCR introduces **Semantic Conditional Message Passing (SCMP)**, which combines structural and semantic information via a new initialization scheme and non-parametric semantic encoding. The framework supports semantic generalization by using feature-agnostic unification and modular pretraining with various semantic sources. By training exclusively on KGs, SCR can perform zero-shot inference across multiple graph domains and tasks without fine-tuning.", "questions": "1. Section \"CMP-based Backbone Model\" is crucial in understanding the paper, but it is not carefully written. Could the author elaborate more, such as what is \"conditioned on the query\" or the initialization process of $h_v$ ?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**  \n1. The paper proposes a unified framework that reformulates multiple graph tasks as inductive link prediction problems on knowledge graphs (KGs), offering a different angle on generalizing Graph Foundation Models (GFMs).  \n2. The method demonstrates competitive results across standard benchmarks.\n\n**Weaknesses**  \n1. Graph-level and node-level tasks often require modeling local neighborhoods, community structures, or global graph semantics—factors not typically present in KG link prediction tasks. Without pretraining on such structures, it is unclear how the learned representations transfer effectively.\n2. The comparison with ULTRA is potentially unfair. ULTRA is trained solely on KGs and not designed for general graph tasks. In contrast, the proposed method is designed a broader range, giving it a task diversity advantage. \n3. The model performs better on homophilic graphs than heterophilic ones, suggesting it relies heavily on feature similarity or local neighborhood consistency. This raises concerns about its robustness across structural regimes, which are common in real-world graphs.  \n4. Over-smoothing and over-squashing are known issues in message-passing-based models, especially in deep architectures or long-range dependency tasks. The paper does not provide any discussion or evaluation on these issues. Benchmarks like LRGB or synthetic long-range tasks would help assess whether the model is scalable in such settings.", "was_revised": true, "final_justification": "The paper proposes a new approach toward graph foundation model by transforming diverse graph tasks (like node or graph classification) into KG reasoning problems using task-specific KG structures. Throughout the rebuttal phase, the authors have provided further explanation and experiments that mostly resolve my concerns.", "rebuttal": "We thank the reviewer wV6S for the insightful and valuable comments. We sincerely hope that our rebuttal adequately addresses your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know if you have further concerns, and we will continue actively responding to your comments.\n \n> **1. W1: Graph-level and node-level tasks often require modeling local neighborhoods, community structures, or global graph semantics—factors not typically present in KG link prediction tasks. Without pretraining on such structures, it is unclear how the learned representations transfer effectively.**\n \n\nThank you for highlighting this concern. Here we transform these two tasks into KG formats by introducing two extra entities, “label□” and “super graph△”, and a new relation, “is attributed with”, to predict the labels for a node or a graph. We believe that many KG relations (e.g., \"person → hasGender → gender\") are **functionally similar to classification tasks** (\"is_attributed_with\"), as they map numerous nodes/graphs to shared attributes. \n\nAlthough the pre‑training objective is link prediction, it learns the neighborhood connectivity and therefore captures local neighborhoods and community structures. Global semantics are retained via our non‑parametric semantic representation, which aggregates all original node features in the CMP process. Together, these components enable representations learned during KG pre‑training to transfer to downstream node‑ and graph‑level tasks that rely on local structures and semantic cues.\n \n> **2. W2: The comparison with ULTRA is potentially unfair. ULTRA is trained solely on KGs and not designed for general graph tasks. In contrast, the proposed method is designed a broader range, giving it a task diversity advantage.**\n \n\nWe appreciate the reviewer’s valid concern regarding comparison fairness. We clarify that **SCR and ULTRA use the same pretraining knowledge graphs** (FB15k-237, WN18RR, CoDExMedium). ULTRA *can* handle general graphs by utilizing the proposed Unified Reasoning Format, that is why we obtain its performance on general graph tasks. \n \n\nThe core difference lies in SCR’s complementary use of semantic features (e.g., text descriptions, node features) beyond raw graph structure. The advantages of SCR stem from the semantic-augmented graph encoding in SCMP and pretraining with multi-source features.\n \n> **3. W3: The model performs better on homophilic graphs than heterophilic ones, suggesting it relies heavily on feature similarity or local neighborhood consistency. This raises concerns about its robustness across structural regimes, which are common in real-world graphs.**\n\n\nWe sincerely appreciate the reviewer’s insightful observation. We agree that SCR currently exhibits a degree of homophily bias, which we believe primarily stems from the CMP-based backbone architecture that emphasizes local relational connectivity. \n\n\nOur main objective in this work is to validate **the semantic and structural transferability of our pre-trained KG reasoning model to general graph tasks**. To this end, we adopt the standard CMP-based backbone, whose generalization ability has been well established in the KG reasoning domain.\n\n\nTo improve robustness on heterophilic graphs, several promising strategies can be explored, such as pre-training or fine-tuning on heterophilic structures, or replacing standard aggregation functions with operators more suitable for heterophilic settings. In our preliminary experiments, we introduced **a fine-tuning stage on heterophilic benchmarks**, and the results demonstrate clear improvements in SCR’s performance:\n\n|           | ULTRA  | SCR    | SCR-Tune |\n|-----------|--------|--------|----------|\n| Wisconsin | 0.4902 | 0.5491 | 0.5882   |\n| Texas     | 0.5676 | 0.6764 | 0.7027   |\n| Actor     | 0.2261 | 0.2326 | 0.2414   |\n\nThese findings suggest that SCR can indeed be enhanced through additional training on heterophilic graphs. We believe that **incorporating a broader set of training KGs**—especially those exhibiting diverse structural properties—will further improve generalization and reasoning capabilities across varying graph regimes.\n\n\nIn summary, our work aims to improve transferability across graph tasks, and the observed performance gains of SCR over ULTRA validate this contribution. We will include a more in-depth discussion on the challenges of heterophily and potential mitigation strategies in the revised manuscript, and we plan to explore this direction further in future work.\n\n> **4. W4: Over-smoothing and over-squashing are known issues in message-passing-based models, especially in deep architectures or long-range dependency tasks. The paper does not provide any discussion or evaluation on these issues. Benchmarks like LRGB or synthetic long-range tasks would help assess whether the model is scalable in such settings.**\n \n\nWe thank the reviewer for highlighting the critical issues of over-smoothing and over-squashing in message-passing models. While these are well-known challenges, our current focus is to investigate the semantic and structural transferability of KG pre-training to diverse graph tasks—a core goal in the emerging Graph Foundation Model (GFM) paradigm.\n\n\nWe agree that a discussion of these challenges is valuable. **Over-smoothing** typically occurs in deep architectures, where repeated message passing leads to uniform node embeddings. In our model, however, message propagation occurs over relatively shallow subgraphs (3-6 layers), which mitigates this risk. Furthermore, our message passing is source-conditioned: only the source node $e_q$ is initialized with a non-zero embedding, and information flows outward. Thus, each node’s embedding is a view from $e_q$, not a globally shared representation, preserving diversity. \n\n\n**Over-squashing**, caused by bottlenecks in aggregating long-range messages into fixed-size vectors, may arise due to dense multi-hop paths. To address this, we employ the expressive PNA aggregator and set the hidden dimension to 64, balancing representational capacity with computational efficiency, while also accommodating both BERT-based textual features and common graph-domain features.\n\n\nIt is worth noting that unlike conventional GNNs, **Graph Foundation Models are still in their early stages, and many associated challenges remain open**. Our work takes a step forward by focusing on cross-task and cross-graph transferability, which we believe is largely orthogonal to the over-smoothing, over-squashing, and long-range issues. Nonetheless, we agree that evaluating performance on deep or extreme-range benchmarks would further validate scalability. We will include a dedicated discussion on these challenges and possible mitigation strategies in the revised manuscript, and we consider this an important direction for future work.\n\n> **5. Q1: Section \"CMP-based Backbone Model\" is crucial in understanding the paper, but it is not carefully written. Could the author elaborate more, such as what is \"conditioned on the query\" or the initialization process of $h_v$?**\n \n\nThank you for pointing this out. We will revise the manuscript accordingly, which first gives the high‑level intuition and then provides the formal update rules.\n\nIn CMP, the learned node embeddings are conditioned on a query $(e_q, r_q)$, where $e_q$ is the source node and $r_q$ is the specific relation embedding. At initialization, only the source node carries information: its hidden state $h_q$ is set to a non‑zero vector determined by $r_q$, while all other nodes are zeroed out. During message passing, this signal propagates outward, and each target node $e_v$ ultimately learns an embedding $h_v$ that reflects how it is viewed from the perspective of $(e_q, r_q)$."}, {"review_id": "xKogWXXJ36", "reviewer": "Reviewer_zZR9", "summary": "This study broadens the scope of knowledge graph foundation models by enabling their application to both node-level and graph-level tasks. To support this expansion, it introduces a unified topological framework that accommodates diverse task formats and develops a semantic-conditional message passing mechanism to address the challenge of semantic isolation. Experimental results across link-level, node-level, and graph-level datasets confirm the model’s strong generalization capabilities.", "questions": "- Can SCR be applied to knowledge graphs (KGs) that lack textual features?\n\n- Does SCR face limitations when scaling to large KGs? Specifically, is it capable of handling large-scale transductive datasets?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n- The primary contribution of this work lies in extending the capabilities of Knowledge Graph Foundation Models (KGFMs) beyond traditional link prediction, enabling their application to both node-level and graph-level tasks.\n\n- The introduced modules effectively mitigate the identified semantic isolation challenge.\n\n- Extensive experimental results validate the model’s effectiveness across diverse datasets and task types.\n\nWeaknesses:\n\n- The link prediction performance on transductive datasets does not demonstrate a significant advantage compared to ULTRA.\n\n- The reliance on Semantic Conditional Message Passing (SCMP) may constrain the model’s reasoning ability on knowledge graphs that lack rich textual features. Besides, in the introduction, a brief explanation of \"semantic features\" should precede the discussion of the \"semantic isolation issue,\" rather than deferring this explanation to the appendix. This would significantly enhance clarity and readability. Notably, in knowledge graph reasoning, semantic features are not strictly essential—as indicated by the relatively modest performance difference between SCR and ULTRA in Table 1. However, these features are often indispensable in certain node-level and graph-level tasks, which likely underpins the emergence of the semantic isolation issue in this work. I encourage the authors to revise this section to reflect this context more clearly.", "was_revised": true, "final_justification": "I keep my positive score.", "rebuttal": "We thank the reviewer zZR9 for the insightful and valuable comments. We sincerely hope that our rebuttal adequately addresses your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know if you have further concerns, and we will continue actively responding to your comments.\n \n> **1. W1. The link prediction performance on transductive datasets does not demonstrate a significant advantage compared to ULTRA.**\n \n\nWe sincerely thank you for this comment. We agree SCR doesn't surpass ULTRA on transductive link prediction, but it is not the primary objective of SCR. \n\nOur key contribution is to validate the semantic and structural transferability of our pre-trained KG reasoning model to general graph tasks. Towards graph foundation models, achieving consistent performance across diverse tasks with zero-shot topological graph and semantic features is challenging and valuable. \n \n\nWe believe incorporating more diverse training KGs could enhance reasoning capabilities, which we plan to rigorously explore to strengthen SCR's applicability in future work.\n\n> **2. W2. Besides, in the introduction, a brief explanation of \"semantic features\" should precede the discussion of the \"semantic isolation issue\", ... I encourage the authors to revise this section to reflect this context more clearly.**\n \n\nThank you for this essential feedback. We will restructure the related paragraphs in the introduction section to:\n \n1. First define semantic features and their role in KG reasoning/general tasks;\n \n2. Then introduce the semantic isolation issue as a fundamental barrier to cross-task generalization;\n \n3. Explicitly connect both concepts to motivate SCR’s design.\n \nThis logical progression will clarify why resolving semantic isolation is critical for graph foundation models.\n\n> **3. W2&Q1. The reliance on Semantic Conditional Message Passing (SCMP) may constrain the model’s reasoning ability on knowledge graphs that lack rich textual features. Can SCR be applied to knowledge graphs (KGs) that lack textual features?**\n\n\nThank you for your insightful comment. We clarify that SCR is not restricted to graphs with textual features, as shown in the ablation study in Section 5.3. In Table 1, for SCR pretrained on textual features, replacing semantics with all one features (SCORE-One) only marginally degrades performance while still outperforming existing methods, indicating that semantic features do not significantly affect generalizability. \n\n\nBesides, when evaluating on transductive KG datasets, SCR did not employ textual features (unavailable for some KGs) but instead ontology features derived from the KG’s inherent structure. SCR also achieved great performance. \n \n\nThe key lies in SCR’s pre-training design: it systematically trains the model to handle diverse scenarios—from KGs with rich semantics (text/ontology) to those with no input features. SCR learns to reason over KGs with diverse semantics rather than depending on auxiliary textual data. \n \n> **4. Q2. Does SCR face limitations when scaling to large KGs? Specifically, is it capable of handling large-scale transductive datasets?**\n \n\nWe sincerely appreciate this comment. Regarding scalability, we analyzed the computational complexity of SCR in Appendix H, which **exhibits comparable scalability and running time to ULTRA**. We acknowledge that both methods face practical limitations when applied to KGs with millions or billions of triples. Specifically, the time cost of subgraph extraction and message passing becomes non-trivial compared to traditional embedding-based models. This limitation is inherent to subgraph-based inductive frameworks but does not preclude SCR’s applicability to typical large-scale KGs.\n \n\nWe will prioritize this in future work. For large-scale KGs, **recent acceleration techniques** like TIGER [1] (enabling efficient subgraph extraction for inductive reasoning on Freebase) are critical. While SCR’s current implementation does not yet integrate these optimizations, its framework is compatible with such methods. We have discussed this point in Appendix J: Limitations.\n \n\nTo further ease the concern, we recall the results on several large-scale transductive datasets in Table 7. The results demonstrate that SCR outperforms ULTRA, confirming its scalability and effective generalization.\n \n| Datasets                 | KG Scale |  | ULTRA(3g) |        | SCR(3g) |        |\n|--------------------------|:--------:|:-----:|:---------:|:------:|:-------:|:------:|\n|                          |    Entities       |    Rels  |    MRR    |  H@10  |   MRR   |  H@10  |\n| AristoV4                 |   44949  |  1605 |   0.183   | 0.262  |  0.227  | 0.349  |\n| CoDEx-Large               |   77951  |   69  |   0.333   | 0.461  |  0.329  | 0.458  |\n| ConceptNet100k           |   78334  |   34  |   0.061   | 0.117  |  0.115  | 0.218  |\n| DBpedia100k              |   99604  |  470  |   0.397   | 0.565  |  0.401  | 0.573  |\n| YAGO310                  |  123182  |   37  |   0.480   | 0.658  |  0.488  | 0.666  |\n \n\n[1] TIGER: Training Inductive Graph Neural Network for Large-Scale Knowledge Graph Reasoning, Proceedings of the VLDB Endowment, 2024."}, {"review_id": "J0wbJhBidB", "reviewer": "Reviewer_Z3ck", "summary": "This paper proposes a novel graph foundation model (GFM) framework called SCR, which aims to enhance the transferability of knowledge graph (KG) reasoning to general graph learning tasks. The authors introduce a semantic-conditioned message passing mechanism to address the semantic isolation issue in traditional KG reasoning. Extensive experiments across diverse graph datasets demonstrate the effectiveness and adaptability of the proposed approach.", "questions": "1. Can you compare the performance of the proposed SCR with other methods that also incorporate semantic features into the conditioned message passing framework to show the necessity of the proposed late-fusion method? Especially, when setting the dimension of the node features closer to the dimension of the semantic features and using Init^3 fusion, would the trend in Figure 2 still hold?\n\n2. In the homogeneous graphs node classification, are there only two types of edges (i.e., original edges and label edges)? How does the proposed method generate meaningful relation representations from the relation graph for reasoning? \n\n3. Why does the performance of the model drop after a few-shot fine-tuning? Is the model trained from scratch, or is it fine-tuned from a pre-trained model? Would fine-tuning from a pre-trained model improve the performance of the model?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Paper Strength\n1. The paper introduces a novel graph reasoning framework, SCR, which adapts the principles of knowledge graph reasoning to general graphs learning tasks like node classification, link prediction, and graph classification.\n2. The proposed semantic-conditioned message passing mechanism effectively considers the node semantics, addressing the semantic isolation issue in previous KG foundation models.\n3. The paper conducts extensive experiments on diverse graph datasets, covering node-level, link-level, and graph-level tasks across multiple domains, showcasing the effectiveness and generalizability of the proposed approach.\n\n### Paper Weakness\n1.  The paper argues that existing attempts to apply node semantic features into the $Init()$ function would lead to the violation of target node distinguishability following previous research [1]. Motivated by this, SCR proposes a novel Semantic-injected INIT Function, and incorporates semantic features in a late-fusion manner (Eq.7). However, the paper does not provide sufficient comparison with other attempts that incorporate semantic features and also hold the target node distinguishability. Meanwhile, the semantic isolation issue should be further analyzed to enhance the motivation of the proposed method. \n\nFor example, in the Section 4.1 and Appendix C.3 of [1], the authors discuss that the $Init^3()= \\mathcal{1}_{u=v} * (z_q + \\epsilon_u )$ can be used to incorporate node semantic feature $\\epsilon_u$ while maintaining the target node distinguishability by adding query-dependent vector $z_q$. This can be considered as an early-fusion method and is easier to implement than the proposed SCR. The paper should provide more details on why the proposed late-fusion method is necessary and how it outperforms other methods that also incorporate semantic features [2,3]. \n\nBesides, the original embedding dimension of the semantic features is 768, which is much larger than the dimension of the node features (64). Such a large dimension gap may lead to a significant loss of semantic features during the feature fusion process and impair the performance as shown in Figure 2. Can the authors further conduct an analysis on the impact of the dimension gap between the semantic features and node features on the performance of the model to justify the necessity of the proposed method?\n\n2. The proposed SCMP only considers the semantics of the node. How does the proposed method handle the semantics of the edges [4]? This can be quite important for tasks like link prediction, where the edge semantics can provide additional information for reasoning. Moreover, for node classification on homogeneous graphs, there is only one type of edge, which makes the relation graph a fully-connected graph and provides no meaningful information for learning the relation representation.\n\n3. The proposed method shows a great zero-shot performance on node classification and graph classification tasks. However, the performance of the model decreases after a few-shot fine-tuning. The paper does not provide sufficient analysis on why the performance drops after a few-shot fine-tuning. Is the model trained from scratch, or is it fine-tuned from a pre-trained model? If it is fine-tuned from a pre-trained model, how does the pre-training and fine-tuning affect the performance of the model? \n\n\n[1] Huang, Xingyue, et al. \"A theory of link prediction via relational weisfeiler-leman on knowledge graphs.\" Advances in Neural Information Processing Systems 36 (2023): 19714-19748.   \n[2] Combining Structure and Text: Learning Representations for Reasoning on Graphs, https://openreview.net/forum?id=hJ8OQAiTrl   \n[3] Hua, Yin, et al. \"Beyond Completion: A Foundation Model for General Knowledge Graph Reasoning.\" arXiv preprint arXiv:2505.21926 (2025).   \n[4] Arun, Arvindh, et al. \"SEMMA: A Semantic Aware Knowledge Graph Foundation Model.\" arXiv preprint arXiv:2505.20422 (2025).", "was_revised": true, "final_justification": "This paper explores an important and promising direction. While many areas remain unexplored, its contribution still sets a strong precedent for future work.", "rebuttal": "We thank the reviewer Z3ck for the insightful and valuable comments. We sincerely hope that our rebuttal adequately addresses your concerns. If so, we would deeply appreciate it if you could raise your score. If not, please let us know if you have further concerns, and we will continue actively responding to your comments.\n \n> **1. W1&Q1. Can you compare the performance of the proposed SCR with other methods that also incorporate semantic features into the conditioned message passing framework to show the necessity of the proposed late-fusion method?**\n \n\nWe sincerely thank you for this comment! We first discuss the three methods [1,2,3] mentioned by the reviewer:\n \n\n1. The initializer $INIT^3()$ in Huang et. al. [1] incorporates the semantic feature of the query node $u$, but ignores the semantics of other nodes in the neighborhood. As a result, using $INIT^3()$ would not significantly drop the performance of ULTRA in Figure 2, because it still cannot exploit the full range of node semantics. This is also one of the motivations that we propose the semantic isolation issue. \n \n\n2. The second work [2] is not related to graph foundation models and does not utilize CMP-based encoding. It employs PLM-based textual embeddings as the input node feature of GNN, and alternates the training of GNN and PLM within a single dataset. This method cannot handle our zero-shot GFM settings, especially for non-textual semantic features in general graphs. Additionally, the performance drop reported in their Table 2 when directly using pre-trained PLM embeddings indicates the necessity of re-training a PLM for enhanced text representation. It is consistent with our findings in Table 2.\n \n\n3. The third work [3] is a contemporaneous work (published in May 2025) for KG foundational reasoning. While [3] achieves semantic injection, it focuses solely on text embeddings derived from a single semantic space (i.e., an LLM). Consequently, their pretraining approach cannot process zero-shot features originating from different semantic spaces. We note that their late fusion between query‑conditioned structural encoding and global structural semantic encoding is similar to our proposed strategy, indirectly confirming the feasibility and rationale of our design choice.\n\nIn summary, the first method cannot utilize complete node semantics, while the latter two methods, reliant on either an LLM's semantic space or graph-specific training, cannot effectively integrate multi-source zero-shot features. Consequently, none of these approaches provides a viable alternative to our method within Graph Foundation Model. We will incorporate the above discussion and analysis into the revised manuscript to strengthen our method.\n \n> **2. W1&Q1. When setting the dimension of the node features closer to the dimension of the semantic features and using $INIT^3$ fusion, would the trend in Figure 2 still hold?**\n\n\nIn terms of the impact of the dimension gap between semantic features and node features, we conduct additional experiments with 50d Glove Features (with zero-padding), Clipped 64d Bert features, random features, and all-ones features. The results below indicate that using node features with closer dimensions still invokes the performance drop. Additionally, we test the variant using the semantic features of the query node in $INIT^3()$. There still exists a performance drop compared with the original ULTRA on most datasets.\n \n|              |  FB_v1 |  WN_v1 |  NE_v1 |\n|--------------|:------:|:------:|:------:|\n| ULTRA        | 0.486  | 0.593  | 0.716  |\n| +Bert         | 0.163  | 0.014  | 0.580  |\n| +All One(64d)      | 0.227  | 0.024  | 0.684  |\n| +Random(64d)       | 0.218  | 0.015  | 0.658  |\n| +Bert(Clip64) | 0.200  | 0.013  | 0.593  |\n| +Glove(50d)   | 0.160  | 0.007  | 0.609  |\n| +Bert+INIT3   | 0.483  | 0.549  | 0.648  |\n| +Glove+INIT3  | 0.483  | 0.524  | 0.720  |\n\nBecause Bert-based embeddings have 768 dimensions, it is much larger than the dimension of the node features (64). Sorry that we cannot pretrain such a 768-d ULTRA due to limited computational resources in the rebuttal phase. \n \n> **3. W2&Q2.  How does the proposed method handle the semantics of the edges? In the homogeneous graphs node classification, are there only two types of edges (i.e., original edges and label edges)? How does the proposed method generate meaningful relation representations from the relation graph for reasoning?**\n \n\nWe sincerely appreciate these comments and questions. \n \n\nWe focus on node semantic features in this work and acknowledge the value of handling explicit edge features. It is straightforward to extend SCR to incorporate edge semantics by replacing the first CMP module with our proposed SCMP. Similar to our work, the contemporaneous work, SEMMA [4], employs an additional CMP-based semantic relation encoding process and the late-fusion strategy to handle edge features. \n \n\nWe clarify that, in homogeneous node classification, besides original edges and label edges, there are semantically-similar edges involved in the relation graph and CMP-based encoding.  Although there are a few relation types in the relation graph, it still follows strict topological rules. For example, label edges only link from nodes to their labels, while original edges connect among nodes. This creates meaningful asymmetric constraints, i.e. there are no “t-h” and “t-t” interactions from the label edge type to the original edge type. By learning how different relation interactions interact topologically across the graph, our model derives transferable reasoning capabilities that generalize beyond explicit relation semantics.\n \n\nIn Section 5.5 (3), we conducted ablation studies to verify the necessity of the relation representations from the relation graph. As shown in the right panel of Figure 3, despite the presence of only a few relation types in node/graph-level graph structures, the observed performance decline highlights the essential role of relational information.\n \n \n> **4. W3&Q3. Why does the performance of the model drop after a few-shot fine-tuning? Is the model trained from scratch, or is it fine-tuned from a pre-trained model? Would fine-tuning from a pre-trained model improve the performance of the model?**\n \n\nThank you for your comment. We guess the mentioned drop performance is from SCR-5 and SCR-20%. We clarify that these two variants are not few-shot fine-tuning, but few-shot labeling. \nAs explained in the caption of Table 2, SCR-20% uses 20% of the “node-label” edges from the training set, while SCR-5 includes five edges per class. Both variants have no fine-tuning process, but utilize different scopes of “label information” when inference on the pre-trained model.\n \n\nAdditionally, we observed that fine-tuning would enhance the model performance on target tasks. For example, we have conducted additional experiments, which fine-tune on heterophilic graph-derived KGs. We discovered that SCR’s performance is improved on heterophilic node classification benchmarks, as shown in the table below.\n\n|           | ULTRA  | SCR    | SCR-Tune |\n|-----------|--------|--------|----------|\n| Wisconsin | 0.4902 | 0.5491 | 0.5882   |\n| Texas     | 0.5676 | 0.6764 | 0.7027   |\n| Actor     | 0.2261 | 0.2326 | 0.2414   |\n\n[1] Huang, Xingyue, et al. \"A theory of link prediction via relational weisfeiler-leman on knowledge graphs.\" Advances in Neural Information Processing Systems 36 (2023): 19714-19748.\n\n[2] Combining Structure and Text: Learning Representations for Reasoning on Graphs, https://openreview.net/forum?id=hJ8OQAiTrl\n\n[3] Hua, Yin, et al. \"Beyond Completion: A Foundation Model for General Knowledge Graph Reasoning.\" arXiv preprint arXiv:2505.21926 (2025).\n\n[4] Arun, Arvindh, et al. \"SEMMA: A Semantic Aware Knowledge Graph Foundation Model.\" arXiv preprint arXiv:2505.20422 (2025)."}]

Author rebuttal:

Meta-review: The authors cast node classification, graph classification and link prediction as instances of KG completion through suitable introduction of new nodes and edges and graph transformations.  They adopt recent techniques to inform a GNN with an initial query to compute more capable edge relation representations (and induced contextual node representations).  Together, these steps allow the users to provide a "foundation" model for all these classes of graph inference without additional fine tuning.  Extensive experiments on 38 datasets spanning multiple domains show that SCR achieves strong zero-shot and few-shot performance.

Although the topic is densely populated in recent literature, and the submission does not have an easy time setting off its novelty against all of it, it seems to have enough merit for a poster accept.

There was a fairly active and productive rebuttal session where most concerns were addressed satisfactorily.

The title may be slightly misleading to readers who are interested in graph foundation models that solve more discrete or combinatorial problems around graphs.  It would be nice to reword the title to make this clear.

The exposition can be greatly improved.  At least the abstract and intro should set up terminology that is standard in the community and not coined in just one or two papers cited here.  E.g., "the semantic isolation issue", "semantic-conditioned message passing" (in general avoid "semantic" anywhere), etc.  Take the reviewers' comments about improving writeup seriously.

L28 "KG reasoning, also known as KG completion" ― many would disagree with this conflation.  Instead say "KG completion, a popular KG reasoning task".

L51 "initiation" of what? Make this clear at this point, without expecting the reader to read ahead a couple sections.

L155 this limitation holds for only the Init you proposed.  There can be other more natural Init functions without this limitation.

In eq (4), $\tilde{\mathcal{X}}$ is computed, but not used in the second SVD computation.
Why are there two $\bm{U}$ matrices returned by SVD if $\mathcal{X}$ is not psd?

It is not clear why SVD works in this setting.  It is possible for singular values close to each other two swing around singular vectors by 90 degrees, leading to falsely low similarity between training and test situations.

Intuition behind $\bm{v}_a$ is not presented properly.

You want a single is_attributed_with, or two such relations (one for nodes, one for whole graphs)?
Decision: Accept (poster)