One for All: Universal Topological Primitive Transfer for Graph Structure Learning
Authors: Yide Qiu
Tong Zhang
Xing Cai
Hui Yan
Zhen Cui
Venue: NeurIPS 2025 poster ()
Keywords: Graph Structure Learning
Transfer Learning.
Primary area: deep_learning

Abstract: The non-Euclidean geometry inherent in graph structures fundamentally impedes cross-graph knowledge transfer. Drawing inspiration from texture transfer in computer vision, we pioneer topological primitives as transferable semantic units for graph structural knowledge. To address three critical barriers - the absence of specialized benchmarks, aligned semantic representations, and systematic transfer methodologies - we present G²SN-Transfer, a unified framework comprising: (i) TopoGraph-Mapping that transforms non-Euclidean graphs into transferable sequences via topological primitive distribution dictionaries; (ii) G²SN, a dual-stream architecture learning text-topology aligned representations through contrastive alignment; and (iii) AdaCross-Transfer, a data-adaptive knowledge transfer mechanism leveraging cross-attention for both full-parameter and parameter-frozen scenarios. Particularly, G²SN is a dual-stream sequence network driven by ordinary differential equations, and our theoretical analysis establishes the convergence guarantee of G²SN. We construct STA-18, the first large-scale benchmark with aligned topological primitive-text pairs across 18 diverse graph datasets. Comprehensive evaluations demonstrate that G²SN achieves state-of-the-art performance on four structural learning tasks (average 3.2\% F1-score improvement), while our transfer method yields consistent enhancements across 13 downstream tasks (5.2\% average gains) including 10 large-scale graph datasets. The datasets and code are available at https://anonymous.4open.science/r/UGSKT-C10E/.

One for All: Universal Topological Primitive Transfer for Graph Structure Learning
Yide Qiu!-t, Tong Zhang 1. Xing Cai', Hui Yan', Zhen Cui
School of Computer Science and Engineering, Nanjing University of Science and Technology School of Artificial Intelligence, Beijing Normal University {ql 15025886, tong.zhang] @ @njust.edu.en; caixing I @ 163.com; yanhui @ njust.edu.cn, zhen.cuiz bnu.edu.cn
Abstract
The oun-Euclidean geometry inherent in graph structures fundamentally impedes cross-graphe knowledge transfer. Drawing inspiration from texture transfer in com- puter vision, we pioneer topological primitives as transferable semantic units for graph structural knowledge. To address three critical barriers the absence of specialized benchmarks, aligned semantic representations, and systematic transfer methodologies we present
unified framework comprising: (i) aapoGraph-Mappinn that transforms non-Euclidean graphs into transferable se- quences via topological primitive distribution dictionaries; (ii) G?SN, dual-stream architecture learning text-topology aligned representations through contrastive alignment; and (iii) AdaCross-Tramen
data-adaptive knowledge transfer mech- anism leveraging cross-attention for both full full-parameter and parameter-froe frozen scenarios. Particularly, G2SN is dual-stream sequence network driven by ordinary differential equations, and our theoretical analysis establishes the convergence guar- antee of G2SN. We construct STA-18, the first large-scale benchmark with aligned topological primitive-text pairs across 18 diverse graph datasets. Comprehensive evaluations demonstrate that GPSN achieves state-of-the-art performance on four structural learning tasks (average 3.2% Fl Fl-score improvement), while our transfer method yields consistent enhancements across 13 downstream tasks (5.2% average gains) including 10 large-scale graph datasets. The datasets and code are available at tiggth........ cww/ com/Yide--e. comm/YideeQQu/UGSKY
Introduction
The inherent Eun-Euuiidean geometry of graph structures presents fundamental challenges in preserv- ing hierarchical relational semantics. Topological information encoding, which captures multi-order node relationships through connectivity patterns, has emerged as critical component in graph representation learning. This capability has driven significant advances across diverse domains: social network analysis through dynamic interaction modeling Zhao al. (2023), biological system under- standing via molecular interaction patterns Muzio er al. (2021): Li et al. (202T), and recommendation systems leveraging user-item relation graphs Wei al. (2022): Sang al. (2024).
Recent research explores graphlets and motifs as structural building blocks for graph representation. While gl2vec Chen and Koga (209)) employs Subgraph Ratio Profiles (SRP) to encode graphlet distri- butions for classification tasks, and HONE Grover and others (2019) models higher-order interactions through motif- based embeddings, these approaches face three key limitations: (i) handcrafted pattern selection limits semantic generalization; (ii) isolated subgraph analysis disregards global structural contexts; (iii) absence of explicit alignment between structural patterns and transferable semantics.
@
*Corresponiing author: Zhen Cui (zhen.cui bnu.edu.cn). ('hese authors contributed equally to this work.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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TopoGraph-Mapping
Graph Dual-Stream Neural Network
AdaCross-Transfer
Degize WA
1 O
Recunstruct Gruph Siructure
Parameter
Frozen and Tuningg
Thinpics A
Fine- Tuming
Persggess
Topolopical Primitive
Decoder
Decoder
Motils
Distribation Dictionary
G:SN Model
Pre-truined GPNN Model
Mudff
Encoderl
Encoder2
ADC
UnikG
UTiKG-STA
DownStream Graph
Primitive Distributions
DownStream
Graph-STA
Soquence
Text
URIKG-STA
Sequence
Primitive
Sequence
Text
STA-18
Sequence
Primitive
Figure 1: Overall pipeline of G'SN-Transfer Transfer framework. With topological primitive distribu- tion dictionary-driven, it converts non-Euclidean graph structure into sequential representations. thereby establishing the STA-18 benchmark dataset. Subsequently, the proposed G2SN method undergoes large-scale pre-training on the UniKG-STA capture transferable structural invariants. The framework culminates in dual-transe paradigm encompassing parameter fine-tuning and frozen strategies, enabling adaptive transfer of cross-domain structural graph knowledge.
The MPool framework Islam al. (223) partially addresses these issues by preserving
topology in graph pooling, yet fails to establish cross-domain transfer mechanisms. We posit that analogous transferable texture units in visual neural style transfer, graphs inherently contain topo- logical primitives statistically recurrent connectivity patterns that encode domain-agnostic structural semantics. Our key insight establishes that the distribution of these primitives forms transferable structural "textures" across graphs, enabling knowledge transfer from structure-rich source graphs to diverse target domains.
While existing methods have advanced graph representation learning, three fundamental limitations persist in structural knowledge transfer: (i) absence of benchmarks for cross-domait structural semantics alignment; (ii) inherent negative transfer risks in aggregation- bbased approaches due to geometric heterogeneity Pan and Yang (200)): (iii) computational overhead from multi-task auxiliary objectives in current transfer paradigms Xiao et al. 2024): Verma and Zhang (219)). These limitations
collectively hinder the development of "one-for-al structural knowledge transfer frameworks Wu et
al. (2020); Gritsenko et al. (202);; Gu et al. (2023ab) b). Our GPSN Transfer framework addresses
these challenges through three innovations: (i) Topological Primitive Dictionary: We establish
a bijective mapping between recurrent connectivity patterns (motifs) and LLM-ggnerated textual descriptors, creating transferable sructural-semantee units I.LM-Topomotif. (ii) Dual-Modality
Sequence Learning: Overcoming the cross pross-graph semantic gap via contrastive text-topology sequence alignment and structural attention branch for negative transfer mitigation. (iii) Adaptive Knowledge Injection: A parameter-efficient cross cooss-attetion mechanism dynamically aligns source-target structural distributions during transfer.
Pre- Pre-trained on the largest heterogeneous graph dataset UniKG-STA (UniKG from Nom[Qiu et al. (2023a) in the STA-18 benchmark, CPSN-Transfr achieves cross- tross-task structural knowledge transfer across 13 downstream applications through its innovative parameter-efficien cross-attention adapter. This adapter dynamically calibrates structural distribution characteristies between source and target domains, effectively bridging semantic gaps across domains while maintaining base model parameter scale (with fewer than 9% additional parameters). Experimental results demonstrate consistent performance enhancement in diverse scenarios (average improvement of 5.2% across 13 datasets), with particular excellence in ogbl-ppa where it achieves peak improvement of 14.0% accuracy, significantly outperforming conventional transfer methods Li et al. (2023).
Our main contributions be summarized as follows:
i) We establish the first transfer framework defining topological primitives as transferable structural units, formalizing their bijective correspondence with textual semantics through L.LM-annttated distribution dictionaries. This framework underpins our STA-18 benchmark the largest aligned topological-textie -exttull graph dataset.

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Annolation Dictionary
Input Graph
Count Motifs
Motif Distributions
Structural Annotations
1-hop structural Annotations relatively sporse Low average degree Limited edge variety Very quadriLaterols
Degree
GPT-400
Triongle
Liaited number triongles
by Sumple Subgraphs
2-hop structural Annotations High overage degree Very few pentogons Few quadrta noderate number of edges
Lhop
Trianale
Qandrilateral
2-hop
Generate
Neighbor Subgraphs
Statistic All Nodes
Annotations
Figure 2: Annotation generation algorithm. For any given input graph, the annotation generation algorithm counts the occurrences of various motifs within the one-hop and two-hop subgraphs of each node. Then the motif distribution the entire graph will be modelled. Based on this quantified distribution, ChatGPT-4400 translates each component into corresponding structured annotations, producing additional node-level textual annotations.
ii) GPSN the dual-stream sequence network with contrastive text-topology alignment, is developed to overcome non- non-Euclides Euclidean structural barriers through learnable topological primitives. Our AdaCross- Transfer mechanism enables cross-graph structural knowledge flow via adaptive attention.
iii) We build comprehensive transfer dataset STA-18, the most diverse graph-text benchmark spanning 18 graphs. Systematic evaluations verify our framework's 's superiority: state-of-the-r performance on structural tasks (3.2% FI average gain) and consistent improvements across 13 downstream applications (5.2% average gain).
Overview. In the remainder of this paper, we first provide the preliminary of State Space Models (SSMs) in Section _ Then we introduce the graph serialization paradigm Topoprapp--Mppiing in Section 3 Subsequently, we present our dual-stream neural network G2SN in Section 4 and transfer method AdaCross-Transfer in Section 5 Finally, conduct extensive experiments in Section and conclude our work in Section Notably, we provide related work and preliminaries in the Appendix A and B
Transfer
2 Preliminaries
SSMs capture the dynamics of systems through hidden state variables, H(t) E IN,, which evolve according to input sequence z=() E IR. The system dynamics are described by the following linear ordinary differential equations (ODEs):
dH(()
AH() Bx((),
dt
Y(t) CH(t).
(2)
where Yt)) is the output, and A N B Nx1, and C E C I represent system parameters for state evolution and output projection. To convert the continuous-time model discrete form, the Zero-Order Hold (ZOH) method is employed, introducing a timescale A. The discrete-time equivalent of the system is given by:
A = exp (AA),
(3)
B = (Ā I)A - 'BA,
(4)
leading to the recurrence relations:
H(t) = ÁH - 1) + Bx((),
(5)
Y(t) CH(t).
(6)
3

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Algorithm/ Structure-Controolled Selection Mechanism
Input: Sequence u E RVxLxD; Motif score m E RD
Output: Sequence Y
R RxxxD
I: B: L,
Linearg u, m)
2: C: : (V, N.) + Linearc u, m)
3: (V, L, D) log(1 + exp(Linear A (u, m) + Parametera))
4: A, (V, N) + discretize( A, Parametera B)
5: + R-SSM((A B, (u, m)
6: return Y
3 TopGrapph-Mapping Topological Primitive Mapping
We present a graph-to-text framework, shown in Figure 2 grounded in topological primitive distribution-to--exx mapping dictionaries, generating both topological primitive distributions, LLM- Topomotif, and Structural Textual Annotation (STA) for universal graph representation of any given graph data(base). The framework integrates i) an LLLM-drived semantic mapping system and ii) parallel topological primitive quantification module.
Central to our design are fundamental topological primitives characterizing node-centric subgraphs within two hops:
Average node degree, edge count, edge-type diversity, trianglelquatiiaaeraalpprtgggggo frequencies, and homogeneous triangle edge probability.
For computational efficiency, we focus on cyclic structures with less than five hops (triangles, quadri- laterals, pentagons) inspired by clique-based graph theory Zhang al. (2024), )) while incorporating edge heterogeneity and homogeneous cycle likelihoods [Banché er al. (2020). Each topological primitive distribution component is bijectively mapped to textual semantics via dictionary D, with annotations ordered by primitive significance. For instance, nodes the top 1% for average degree receive LLM- -LM--eeerrtted descriptions like "This node exhibits exceptionally dense local connectivity", validated by human experts to ensure linguistic diversity and statistical fidelity. This dual-channel design enables topological distributions to enhance textual semantics through structural grounding, while textual annotations disambiguate primitive patterns, forming mutually reinforcing system. The parallel quantification module Wang al. 2016) computes topological primitive distributions across STA-18 our benchmark encompassing 18 graph datasets of varied scales. By efficiently extracting and encoding primitive occurrences, it constructs discrete topological distribution profiles, which are subsequently translated into STA codebooks via dictionary D for cross-graph transfer.
4 G Graph Dual-Stream Neural Network
In Algorithm T G2SN has three key parameters (B, C, and A) and takes the textual sequence Topomotif sequence m inputs. We first provide a theoretical guarantee for the convergence of GPSN and present formal derivation of its closed-form solution. Then the- oretically demonstrate that GPSN ef- fectively captures the sequential de- pendencies for the input sequences u and m.
and LLM-
Linear
Livear
Norm
Bidirectonal
MLL
Linear
SSM
Linvar
Norm
G Block
Figure 3: G2SN framework. Injecting structural contexts via topological primitive sequence branch.
The discrete zero-order hold (ZOH)
method for linear ordinary differen- tial equations (ODEs) provides re- cursive formulation, as shown in Eqs. (5) and (6). Leveraging the linear Aime-invrriant (LTI) property,

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Pre-trained G'SN Model
Ha e m)
Weight Vector
Skm
Graph
Frozen
max(S,.)
EI
Fine
Frenzen
Q
Y ((H)))
Motif Parallel
E2
Fine-tuned
Z
Statisties Module
Fine-taned
CrossAttention
Hm Cross-
Attention(HH, Hyp Decoder
tratied
G(Aa.Xa)
Adjacency Matrix Node Feature Matrix
DownStream
truined
Ha ((Aa.Xa)
Task Graph
DownStream GNN Model
AdaCross-Trame
Figure 4: The overall framework of AdaCross- Transfer. The Fine-tuned represents the "Full
AdaCross-Transfer Parameter Fine-ture tune- scenario, while the Frozen indicates the "Frozen and fine-tuned" scenario.
the recursive expressions for A, B, C, and A can be parallelized. Furthermore, global convolu- tional approach is adopted to compute the output sequence = x K, where the convolution kernel K IR defined as:
K = [CB, CÁB. CÀ
where L represents the length of the input sequence. Under the ZOH assumption, the closed-form solution for G2SN time is given by:
H (t)(A))((())) /' exp(A(t- (op(A(t=s))Ba(sddl
(8)
By introducing time-invariant constant y, the flosed-form solution for GPSN at time / + 1 can be expressed as:
H(t + cxp(A))(()) + (L' exp(Assdss Br(t),
(9)
which provides a theoretical guarantee for the convergence of G?SN, as stated in Theorem 4.1
Theorem 4.1. For given input æ(t) from the joint distribution Q(u(t), m(t)), the G2SN with generalized form of the time-invariant zero-order hold has a closed- soreedffffmm--oo solution in each discrete sequence step t to t+1 and can be computed as H(t+ exp H) (t) + (oo exp(As) ds Ba(()).
We propose structural control mechanism that enables the selection process depend on both textual sequences and motif quantized distributions. The data-adaptive selection mechanism treats the parameters A. B, C, and A as functions of the input (t). This enables the model to dynamically adjust its behavior based on the input data, allowing G2SN to selectively process and retain relevant context, thereby enhancing its capability to handle complex sequential data. To handle additional motif score inputs, the model incorporates the quantized distribution of structural motifs to recall previously encountered textual sequences, improving its ability reconstruct local structural semantics. In GRSN, the annotation sequence u and topic score sequence v jointly serve as inputs.
Theorem 4.2. Under the discrete ZO11 assumption, this mechanism enables context-aware infor- mation flow through: Y()) = E' ((= ((l-))ACC()B())))) (()))()))(g) in GPSN, which is jointly governed by topological primitive distributions and textual semantics.
The model output depends on both the textual annotations and motif sequences, from the Theorem 4.2 with the two jointly controlling the flow of information during propagation. The 8(u, m)c(u, m measure similarity between the current input and prior ones, demonstrating G2SN's ability to capture long-term dependencies. By modifying the forward and backward gradient functions, G2SN, the text encoder E,, and the motif encoder F. can be jointly trained in an end-to-end manner during pre-training. Please refer to C.l for theoretical derivation of Theorem 4.2
5

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Sa-Crros-TTanssee Graph Structure Knowledge Transfer
Theorem 5.1. GASN's compositional output (f), jointly governed by topological primitive distri- gradient flow, theoretically enabling
butions and textual semantics, satisfies Lipschitz-continn cross-dataset knowledge transfer through attention reweighting.
To enable the "one for all" transferring of graph structure knowledge, we design the knowledge scenarios, as shown in Figure T and Figure 4 This method embeds universal and special graph structure semantics node-level latent features, merging these semantics into the shared representation space, controlled by a structure- aware weight vector w. Please refer to C.3 for the proof of Theorem [.77
transfer method under the "Full Parameter Fine- "ininnT and Brrozen-and-Fine--ee
Given downstream task graph dataset G(V,E), the transfer process first applies the motif parallel statistics module to produce corresponding structural annotation dataset for each graph dataset. Here, V and E represent the set of nodes and edges in G, respectively. Notably, the vocabularies of all dataset are shared, which facilitates the alignment of the generated textual sequence embeddings. The node feature matrix Xa xx and adjacency matrix Aa E R=x" of G are encoded by the downstream task GNN Ç into the latent variable Ha = <(Aa. Xa). We then introduce a transfer encoder O for each downstream task graph, where the first n-1 layers are shared from the pre-trained GPSN, and the final layer corresponds to the first layer of the downstream task's s GNN Ç. This design ensures that: i) the structural textual latent variable H E Rxxd and the node feature latent variable Ha E In share the same representation space and dimension d: and ii) no additional training parameters are introduced, or only fine-tuned parameters are involved.
Considering the uniqueness of each dataset and facilitating the interaction between structural and node features, we compute a data-aware motif attention weight vector w R based the motif quantization distribution. This vector is then integrated into the -ttss-Attention module between structural and node features, formalized by:
M S.m
1 M
W;
(10)
(S..)
m==1
where M represents the number of types of motifs, and S E RR is the motif distribution matrix and S.m. denotes the m-th motif score of node i. We then interact the two streams at the semantic level through a linear rross-attention layer, which can be formulated as:
H WHs:
H (1, - W
(11)
I Linear Attention Q2 K, V) ((Q.) E
(12)
(Q2)) Σj ((₁))
Q₂, K. V. HH q: H.W Ki H,W,,
(13)
O. = Linear Attention Q., K., V.),
(14)
H. LayerNorm(Linearf (O. +..++.. Q.)).
(15)
where 1, is an all-ones vector, * E {d, st), and 6(x) = relu(z) is an activation function. The co-attention operation allows the encoder emphasize relevant shared semantics while suppressing irrelevant ones. The semantic feature can be concatenated by an MLP, formulated as:
Hm RELL(LLnear(HH (H,),
(16)
finally, we use a task decoder to return the predicted probability Y.. { as output.
In the "Full Parameter Fine-Tuning" scenario, the networks E,, Ez, and e are fine-tuned according to the downstream task. In the "Frozen and Fine-Tuning" scenario, these networks are frozen, and no gradients are computed. Each downstream task adopts single learning objective, with knowledge transfer targets for node-level, edge-level, and graph-level representation learning tasks, formulated as:
min Lrade Y nodee Y mode); O.c.E
node-level task,
min Lusk Ø,5i5
min Ledge (Y edges y Yddge), 0.C.8
edge-level task,
(17)
min Cgraph (Y graphh L graph), O.C.C
graph-level task,

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where Luode, Ledge, and Lgraph represent the loss functions for node-level, edge-level, and graph-level tasks, respectively, and Y mode. Y edges and Y graph denote the corresponding task labels.
6 Experiments
Overview. We conduct extensive experiments to evaluate G2SN's efficacy and universal structural knowledge transfer potential through five key research questions: Q1: How does G2SN perform in learning transferable structural representations? Q2: Can structural knowledge transfer enhance downstream task performance? Q3: How does the cross- coss-attention mechanism facilitate structural knowledge transfer? Q4: Is transfer effectiveness correlated with downstream dataset characteris- ties? Q5: What are the computational costs of constructing dual-stream topological primitive-text annotations? Implementation details and hyperparameter configurations are provided in Appendix H
Datasets Overall, we utilize 36 datasets, including 18 graph datasets and the corresponding 18 STA datasets. For graph datasets, we select 15 large-scale datasets, including ogbn-arxiv, ogbn-products, ogbn-proteins, ogbn-mag, ogbl-ppa. ogbl-ddi, ogbl-citation2, ogbg-molhiv, ogbg-molpcha, and ogbg-code2 from Hu et al. (2020), Peptides, PascalVOC-SP. COCO-SP and MALNET-TINY from Behrouz and Hashemi (2024). and UniKG from Qiu et al. (2023a): as well as 3 ssall-scclle graph datasets: Cora, Pubmed, and Citeseer from [Sen er al. (2008). Statistics (e.g., graph scale, graph homogeneity, graph density, and token length) of the datasets are summarized Table and T The dataset protocols are aligned with those of the OGB benchmark Huu et al. (202I) and the original paper Qiu el al. (2023a b); Beehrouz and Hashemi (022)).
Baselines We use nine baselines in total. For comparison experiments on LRGB (Long Range Graph Benchmark) Dwivedi et al. (2022), we utilize GCN Kipf and Welling 2017). GIN Xu et al. (2019). GatedGCN et al. (2020). Exphormer (hhrzad et al. (2023). Performer Choromanski et al. (2020). and BigBird Zaheer et al. (2020) as bascline models. For graph structure transfer. employ GCN Kipf and Welling (2017), 7), GIN Xu et al. (2019), GraphSAGE Hamilton et al. (211)) GraphSAINT Zeng et al. (2020) and RosNi et al. (2020) as baseline models. GCN and GIN are traditional graph convolutional algorithms. We adopt the same sampling techniques as OGB Hu et al. (2020) to extend them to large-scall scale graphs. GraphSAGE and GraphSA aggregate information from neighborhood samples, making them applicable to large-scale graphs. SIGN learns the decoupled propagation feature to reduce computational overhead. Note that not every baseline was used on every dataset, as detailed in Table and Table 2
Metries We utilize eight evaluation metrics in total: Acc (Accuracy), Rocauc (Receiver Operating Characteristic Area Under the Curve), Hits 100, Hits@ 30, Mrr (Mean Reciprocal Rank), F1 score, Ap (Average Precision) and MAE (Mean Absolute Error). These metries provide a comprehensive evaluation of each baseline model's 's performance on the test set. Specifically, Ace is used for node classification tasks to measure the proportion of correctly predicted samples. Rocauc evaluates binary classification models' ability to distinguish between classes. Hits@ 100 is used to assess the model's ability to rank the correct target within the top 100 candidates. Similar to Hits 100, Hits @ 30 evaluates the top 30 candidates. Mrr is used to measure the model's performance ranking tasks by calculating the mean of the reciprocal ranks of the correct answers. Fl score provides harmonic mean of precision and recall in classification tasks. Ap used to assess the model's accuracy in multi-label classification tasks, reflecting the precision across multiple labels. And MAE is used to evaluate graph regression tasks.
6.1 Graph Structure Learning Experiments on LRGB-STA
Experimental Setup To address Q1, we conducted comprehensive graph structure learning com- parisons on five tasks from LRGB (Long-Range Graph Benchmark) Dwivedi er al. (2022). ensuring evaluation fairness through identical input features and training protocols. Specifically, we focus on comparing several state- state-of-the of-the-art art graph models capable of capturing graph long-rang dependencies, including traditional models such as GCN, GIN, and GatedGCN, as well as various variants within the GraphGPS framework, particularly with respect to the selection of their attention modules. We further isolate krructure-controlled selection mechanisms' advantages in structural representation learning by comparing G2SN against dense and sparse variants of Transformers Rampášck al. (2022): Exphormer (hiizad et al. (2023) (expander-graph sparsity). Performer Chhromaaski et al. (220 (kernelized attention), and BigBird Zaheer al. (2020) (block-sparse patterns).
7

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Table 1: Performance comparison of graph structure learning. Metries: AP1 (higher is better), MABI (lower is better), F1 Scoref (higher is better), Accuracyt (higher is better).
Model
Peptides-Func APt
Peptides-Struct MAR
PascalVOC-SP Fl Scoref
COCO-SP FI Scoref
MALNET-TINY
Accuracyt
GCN
0.5930.10.00 0.03
0.349611..0013
0.126810.0000
0.004110.0010
0.8100110.0022
GIN
0.5498++0.0079
0.8547=0.0045
0.1265+0.0076
0.1339=+0.0044
0.8005
GatedGCN
0.5864+0000077
0.5420+0.0013
0.2873+0.0219
0.2641+0.0045
0.9223+000066
Transsffoerrm
0.6575:10.000 0.0499
0.2510=00.015
0.3689::00031
0.3774=0.0150
0OM (bs=8)
GPS+Performer
0.6475.10.000 0.065
0.255811..001
0.372411.0131
0..01110.0101
0,926410.0078
GPS+BigBird
0.5854++0.0077 0079
0.2842+0.01.00
0.2762++0.006
0.2622 0000
0.9234+0.0034
Exphormer
0.6258++0.0092
0.2512+0.0025
0.34466+0.004
0.3430+0.0108
0.9422+0.0024
GPSN (ours)
0.68241000066
0.2462=0.0013
0.4199:10.009
0,4022=000149
0.9391=0.0007
Table 2: Experimental results of structural knowledge transfer. We use an upward arrow "I"
indicates improved performance. The best and suboptimal performances are highlighted in red and blue, respectively. We report both absolute and relative improvements (Ratio).
Dataset
Task
Method
Metric
Base
Frozen
Fine-tuned
Ratio (%)
oghn arxiv
Node Classification
GCN
Accuracy
015238
0,5633 (0.03955)
0,5886 (0.06488))
12.37
ogbn-products
Node Classification
SIGN
Accuracy
0.7423
0.7456 (0.00331)
0.7477 (0.00541)
0.73
ogbn-mug
Node Classification
SAGE
Accuracy
0.3498
0.3673 (0.01751)
0.3544 (0.00461)
5.01
Cora
Node Classification
GCN
Accuracy
018110
0.8167 (0.00571)
0.8117 (0.00071)
0.70
Pubmed
Node Classification
GCN
Accuracy
0.7880
0.8071 (0.01911)
0.8173 (0.02931)
3.72
Citeseer
Node Classification
GCN
Accuracy
0.6820
0.6873 (0.00531)
0.6981 (0:01611)
2.38
Node Classification
SAGE
ROCAUC
0,7614
0.8175 (0.05611)
0.8076 (0.04621)
7.37
ogbl-molhiv
Link Prediction
GIN
ROCAUC
0,7761
0.7922 (0.01611)
0,7950 (0.01891)
2.44
oghl-ppu
Link Prediction
SAGE
Hits@ 100
0.1519
0.1604 (0.00851)
0.1732 (0.02131)
14.02
oghl-ddi
Link Prediction
SAGE
Hits
0.5271
0.5549 (0.02781)
0.5601 (0:03301)
6.26
ogbg-citation2
Graph Classification
SAINT
MRR
0,8001
0.8092 (0.00911)
0,8154 (0.01531)
1.91
ogbg-code2
Graph Classification
GCN
FI Score
0,1515
0.1554 (0.00391)
0,1601 (0.00861)
5.68
oghg-molppho
Graph Classification
GIN
AP
0.2744
0,2809 (0.00651)
0,2892 (0.01481)
5.39
Experimental Analysis Table I systematically compares GPSN's long-range dependency modeling capabilities across five prrpuuncce-itensin tasks. Our framework achieves state-of the-art performance on four tasks with 2.5% metrics (AP and F1-Score) improvements over sparse attention baselines, demonstrating the critical role of topological primitive distribution-aware structural control. The pre-training robustness on UniKG-STA (Appendix T further verifies G2SN's dual-stream contrastive alignment effectiveness under distribution shifts. These results confirm that G'SN's s structure selected mechanism simultaneously enhances context retention through text-topology interaction modeling while maintaining generalizability across diverse graph prediction scenarios.
6.2 Comprehensive Structural Knowledge Transfer Experiments on STA-18
Experimental Setup To address Q2, we systematically evaluate structural knowledge transfer under both frozen fine-tuning and full-parameter adaptation scenarios. For Q5, Tablee]qqantinn the computational costs of constructing dual-stream topological primitive-text annotations across STA-18 benchmark datasets. Our transfer framework operates through three coordinated phases: i) Universal Annotation Generation: Each graph dataset is encoded into topology-tes -txt pairs using our mapping dictionary. These sequences are vectorized via a shared bag-of lag-oof-wod words model to align representation space. ii) Adaptive Encoder Bridging: As illustrated in Fig. 4 the transfer encoder combines the first n-1 layers of pre-trained G?SN with the initial layer of downstream GNNs. This hybrid architecture processes both textual sequences and topological primitive distributions from target domains. iii) Cross-Grap Graph Feature Fusion: Encoder outputs are injected into node-level hidden features through data-adaptive cross-attention modules, which reweight feature importance using structural alignment scores. The fused representations are then processed by task-specific decoders for final predictions. We benchmark transfer effectiveness across both parameter configurations, with implementation details and hyperparameter sensitivity analysis provided in Appendix H
Experimental Analysis From Table 2 we derive three critical insights: i) Universal Performance Enhancement: Structural knowledge transfer delivers consistent gains across all downstream tasks (average +5.2%), confirming its effectiveness in enhancing representation learning for diverse graph data types through topological semantic enrichment. ii) Parameter-Frozer Transfer Superiority: The frozen transfer mode achieves competitive performance with zero training overhead, demonstrating
8

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Table 3: Ablation studies of transfer methods six datasets. Bold represents best performance.
Tranfer Method
Pubmed
ogba-proteins
ogbl-molhiv
oghi-ppa
ogbg-citation2
ogbg-molpcha
Feature Meun
1.21::0.14
2.39::0.12
1.1840.25
0.974:0223
0.47:10.28
0.22::024
Feature Concal
2.18+0.19
2,91+0.17
1.37+0026
1.04+-021
1.22++.24
0.76+0.27
Cross-Atrention
2.93:10.11
5.61=0009
1.89:0.20
2.13:10.14
1.53:20.2
1,48=0.19
that static topological primitive integration alone can provide sufficient inductive bias for improved downstream inference. iii) Fine- Fine-Tuning Tradcoff:: While full-parameter fine-tuning outperforms frozen transfer in 10 in 13 of tasks via structural encoder optimization, its occasional inferiority (e.g.. in ogbn-mag) suggests domain-specific overfitting risks. This highlights the need for future work on balanced optimization strategies that preserve universal topological semantics while adapting to task-specific objectives.
6.3 Ablation Study on Transfer Methods
To address Q3, we conduct ablation studies on three feature fusion strategies to validate AdaCross- Transfer's adaptive feature routing mechanism. Our experiments across six benchmark datasets (PubMed, oghn-proteins, ogbl-molhiv, ogbl-ppa, ogbg-citation2, ogbg-molpcha) compare: i) Feature Mean Pooling, ii) Feature Concatenation, and iii) Our Cross-Attention Fusion. As quantified in Table (absolute performance gains) versus Table (relative ratios), the proposed cross-attention method demonstrates universal applicability. improvement over enhancement ratio of conventional fusion methods. These results confirm that cross-altention enables adaptive and thorough interaction between topological primitives and textual semantics dynamically reweighting feature importance through structural-textual alignment scores. The mechanism particularly excels resolving semantic ambiguity in molecular graphs (ogbl- molpeba: +94.7%) and protein networks (ogbn-proteins: +92.8% ogbl-ppa: +104.8%), where conventional methods suffer from feature collision.
achieves 65.1% average relative
6.4 What affects the effect of graph structure transfer?
To address Q4 and establish generalizable principles for effective structural knowledge transfer, derive three empirical conclusions from the above experiments: i) Density Correlation: Trans- fer efficacy exhibits statistically significant correlations with average degree distributions (pearson correlation coefficient p=0.82, significance p<0.01, the derivations refer to Appendix [F). Node classi- fication tasks reveal substantial gains in high-degree graphs: ogbn-arxiv (legree=13.77, +12.37%) and ogbn-proteins (597.00, +7.3 77,77%) contrasting with minimal improvement in low-degree Cora (4.01, +0.70%). This demonstrates dense topological primitives in high-degree graphs better preserve transferable structural semantics. ii) Homogeneity Superiority: Heterogeneous graphs show reduced transfer efficiency despite comparable degree metrics ogbn-mag (degree=21.76. +5.01 %) under- performs homogeneous counterparts by 2.3-4.8% suggesting structural heterogeneity introduces semantic frugmentation that impedes grass- alignment. iii) Task-Specific Sensitivity: Structural transfer achieves superior gains in link prediction (avg. +7.57% and graph classification (+4.33%) versus node classification (+3.23%), due to their inherent dependency on structural topology rather than feature-driven decisions vulnerable to attribute noise. These findings collectively establish two guidelines: i) Prioritize structural knowledge transfer for aypology-intensin tasks (link prediction/- graph classification) degree-dense homogeneous graphs. ii) Develop heterogeneity-awar transfer methods to address structural fragmentation complex graphs, which implying the interplay between graph heterogeneity and transfer efficiency promising direction for subsequent research.
Conclusion
We present GrSN-Transfer, universal graph structure learning framework that enables cross-domain knowledge transfer through topological primitive-text dual-stream sequence alignment. The frame- work introduces: (i TopoGraph-Mappinn for serializing non-Euclidean graphs into transferable sequences via topological primitive distribution dictionaries, thereby establishing the STA-18 18 bench- mark; (ii) G?SN, dual-stream sequence network achieving text-topology contrastive aligmment through adaptive attention routing, with convergence guarantees under discrete zero-order hold assumptions; (iii) AdaCross-Transfer data-adaptive cross-attention mechanism. Comprehensive evaluations demonstrate wfte-of-thhearr performance on 4 structural learning tasks (3.2% average F1 score gain) and consistent improvements across 13 downstream applications (5.2% average lift), validating the effectiveness of topological primitives as universal structural semantic units.

---

Acknowledgement
This work was supported by the National Natural Science Foundation of China (Grants No. 62476133) and the Fundamental Research Funds for the Central Universities (Grant No. 11300-3122005025077)
References
Ali Behrouz and Farnoosh Hashemi. Graph mamba: Towards learning on graphs with state space models. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 19-133,, 2024.
Alexandre Blanché, Konrad K Dabrowski, Matthew Johnson, Vadim V Lozin, Daniël Paulusma, and Viktor Zamaraev. Clique-widte for graph classes closed under complementation. SIAM Journal on Discrete Mathematics, 100--1177 2020.
Hong Chen and Hisashi Koga. G12vec: Graph embedding enriched by line graphs with edge features. In Neural Information Processing: 26th International Conference, ICONIP 2019, Sydney, NSW; Australia, December 12-15, 2019, Proceedings, Part III 26, pages 3-14. Springer, 2019.
Krzysztof Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreca Gane, Tamas Sarlos, Peter Hawkins, Jared Davis, Afroz Mohiuddin, Lukasz Kaiser, et al. Rethinking attention with performers. arXiv preprint arXiv:2009. 14794, 2020.
Vijay Prakash Dwivedi, Ladislav Rampášek, Michael Galkin, Ali Parviz, Guy Wolf, Anh Tuan Luu, and Dominique Beaini. Long range graph benchmark. Advances in Neural Information Processing Systems, 35:22326-223444 22340, 2022.
Andrey Gritsenko, Kimia Shayestehfard, Yuan Guo, Armin Moharrer, Jennifer Dy, and Stratis Ioannidis. Graph transfer learning. Knowledge and Information Systems, 65(4):1627-1656, 2023,
Aditya Grover et al. Hone: Higher-order network embeddings. Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining, pages 235-243, 2019.
Ziqi Gu, Chunyan Xu, and Zhen Cui. Grassmann graph embedding for few-shot class incremental learning. In Proceedings of the Chinese Conference on Pattern Recognition and Computer Vision, pages 179-191. Springer, 2023.
Ziqi Gu, Chunyan Xu, Jian Yang, and Zhen Cui. Few-shot continual infomax learning. In Proceedings of the International Conference on Computer Vision, pages 19224-19233, 2023.
Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs In Advances in Neural Information Processing Systems (NeurIPS), pages 1024-1034, 2017.
Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong. Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. Advances in Neural Information Processing Systems, 2020.
Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Ogb-Isc: A large-scale challenge for machine learning on graphs. arXiv preprint 1rXiv:2203.0944 2021.
Muhammad Ifte Khairul Islam, Max Khanov, and Esra Akbas. Mpool: motif-based graph pooling. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, pages 105-117. Springer, 2023.
Thomas N Kipf and Max Welling. Semi- classification with graph convolutional networks. In International Conference on Learning Representations (ICIR), 2017.
Rui Li, Xin Yuan, Mohsen Radfar, Peter Marendy, Wei Ni, Terrence J O' OrBreen, and Pablo M Casillas- Espinosa. Graph signal processing, graph neural network and graph learning on biological data: systematic review. IEEE Reviews in Biomedical Engineering, 16:109-135, 2021.
10

---

Xin Li. Dongze Lian, Zhihe Lu, Jiawang Bai, Zhibo Chen, and Xinchao Wang. Graphadapter: Tuning vision-language models with dual knowledge graph. Advances in Neural Information Processing Systems, 36:13448- 18444-11466,, 2023.
Bin Lu, Xiaoying Gan, Haiming Jin, Luoyi Fu, and Haisong Zhang. Spatiotemporal adaptive gated graph convolution network for urban traffic flow forecasting. In Proceedings of the 29th ACM International conference information & knowledge management, pages 1025-1034, 2020.
Giulia Muzio, Leslie O' O'Bray, and Karsten Borgwardt. Biological network analysis with deep learning. 2021.
Briefings in bioinformatics,
Sinno Jialin Pan and Qiang Yang. A survey on transfer learning, IEEE Transactions on knowledge and data engineering, 22(10):1345 1359, 2009.
Yide Qiu, Shaoxiang Ling, Tong Zhang, Bo Huang, and Zhen Cui. Unikg: A benchmark and universal embedding for large-scale knowledge graphs. arXiv preprint 23t.::2300000269, 2023.
Yide Qiu, Tong Zhang, Bo Huang, and Zhen Cui. Global variational convolution network for semi- supervised node classification on large-scale graphs. In Chinese Conference on Pattern Recognition and Computer Vision (PRCV), pages 192-204. Springer, 2023.
Ladislav Rampášek, Michael Galkin, Vijay Prakash Dwivedi, Anh Tuan Luu, Guy Wolf, and Do- minique Beaini. Recipe for general, powerful, scalable graph transformer. Advances in Neural Information Processing Systems, 15:14501- 2022.
Emanuele Rossi, Fabrizio Frasca, Benjamin Paul Chamberlain, Davide Eynard, Federico Monti, and Michael M Bronstein. Sign: Scalable inception graph neural networks. In International Conference on Machine Learning (ICML), pages 8883-8893, 2020.
Lei Sang. Hang Yuan, Yuee Huang, and Yiwen Zhang. Graph structure learning for robust recom- mendation. Tsinghua Science and Technology, 2024.
Prithviraj Sen, Galen Namata, Mustafa Bilgic, Lise Getoor, Brian Galligher, and Tina Eliassi-Rad. Collective classification in network data. Al magazine, 29(3):93-93, 2008.
Hamed Shirzad, Ameya Velingker, Balaji Venkatachalam, Danica J Sutherland, and Ali Kemal Sinop. Exphormer: Sparse transformers for graphs. In International Conference on Machine Learning. pages 31613-31632. PMLR, 2023.
Saurabh Verma and Zhi-Li Zhang. Learning universal graph neural network embeddings with aid of transfer learning. arXiv preprint arXiv: 10086, 2019.
Pinghui Wang, John CS Lui, Don Towsley, and Junzhou Zhao. Minfer: A method of inferring motif statistics from sampled edges. In 2016 IEEE 32nd international conference on data engineering (ICDE), pages 1050-1061. IEEE, 2016.
Chunyu Wei, Bing Bai, Kun Bai, and Fei Wang. Gsl4rec: dession-based recommendations with collective graph structure learning and next interaction prediction. In Proceedings of the ACM Web Conference 2022, pages 2120-2132 2022.
Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and S Yu Philip. A comprehensive survey on graph neural networks. IEEE transactions on neural networks and learning systems, 32(1):4-24, 2020.
Zijun Xiao, Minghua Zhu, Jingwen Chen, and Zecang You. Integrated transfer learning and multitask learning strategies to construct graph neural network models for predicting bioaccumulation parameters of chemicals. Environmental Science & Technology, 15655)15500-115660 2024.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In International Conference on Learning Representations (ICLR), 2019.
Manzil Zaheer, Guru Guruganesh, Kumar Avinava Dubey, Joshua Ainslie, Chris Alberti, Santiago Ontanon, Philip Pham, Anirudh Ravula, Qifan Wang, Yang, et al. Big bird: Transformers for longer sequences, Advances in neural information processing systems, 33:17283-17299 2020.

---

Hanqing Zeng, Hongkuan Zhou, Ajitesh Srivastava, Ravi Kannan, and Viktor Prasanna. Graphsaint: Graph sampling based inductive learning method. In International Conference on Learning Representations (ICIR), 2020.
Beichen Zhang, Liang Li, Shohui Wang, Shaofei Cai, Zheng-Jun Zha, Qi Tian, and Qingming Huang. Inductive state-relabeling adversarial active learning with heuristic clique rescaling. IEEE Transactions Pattern Analysis and Machine Intelligence, 2024.
Wentao Zhao, Qitian Wu, Chenxiao Yang, and Junchi Yan. Graphglow: Universal and generalizable structure learning for graph neural networks. In Proceedings of the 29th ACM SIGKDD Conference Knowledge Discovery and Data Mining, pages 3525-3536, 2023.
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A Related Work
Table 4: Statisties for the graph datasets. Where 'N.C.' denotes 'Node Classification task', 'L.P.' represents 'Link Prediction task', 'G.C.' 'Graph Classification task' and 'G.R.' denotes 'Graph Regression task'.
Dataset
#Nodes
#bddees
Degree
WHeterogeneity
#Task
#Metric
#Domain
Cora
2,708
5.429
4.01
No
N.C.
Acc
Citation
Citeseer
3,327
4.732
2.84
No
N.C.
Ace
Citation
Pubmed
19,717
44,338
N.C.
Ace
Citation
ogoneisootein
132.534
39.56112522
597.00
No
N.C.
ROCAUC
Biology
ogba-arxiv
169,343
1,166,243
13.77
No
N.C.
Ace
Citation
ogbn-mag
1.939,733
21,111,007
21.76
N.C.
Ace
Citation
cebn-produucts
2,449,129
61,859,140
50.52
No
N.C.
Acc
Product
ogbl-ddi
4.267
1,334,889
625.68
No
L.P.
Hits @ 30
Biology
ogbl-ppa
576,289
30.326,273
105.24
L.P.
Hits 100
Biology
ogbl-citttion2
2,927,963
30,561,187
20.74
L.P.
MIT
Citation
ogbg molhii
1,048,738
1,130,992
2.15
No
G.C.
ROCAUC AP
Biology
ogbg-molpeba
15,386.154
12.305,804
2.16
G.C.
Biology
ogbg-code2
56,683,173
56,230,432
1.98
No
G.C.
FI score
Code
Peptides
2.344,231
4.773.905
2.04
No
G.C. & G.R.
AP & MAE
Biology
PascalVOC-SP
5,443,587
30,777,727
N.C.
Fl score
COCO-SP
58,795.093
332.095,498
5.64
No
N.C.
FI
CV
MalNet-Tiuy -uny
7,051,500
14,299.500
2.03
No
G.C.
Aoe
Cybersecurity
UniKG
77,312,474
641,738,096
16.60
N.C.
Acc
Universal
Table 5: Statistics for STA-18 benchmark.
Dataset
#Nodes
PTokens
#Lengths
ASpaces
iGenerationn Time
#Tsk
#Mettrcc
#Domain
Cora-STA
342.249
Citeseer-SS STA
3.327
420.580
126.4
0.13 MB
4.65
N.C.
Acc
Citation
Pubmed-STA
19.717
2,195,065
126.5
0.75 MB
108.94s
N.C.
Acc
Citation
oghn proteins
132,534
17,028,774
127.7
MB
6.83
N.C.
ROCAUC
Biology
ogbn-arxiv-S1X
169.343
21,338,811
126.0
616.12
N.C.
Ace
Citation
oghn-mag-STD STA
1,939,743
242.542,736
125.0
74.00MB
4,56
N.C.
Ace
Citation
Sgbn-productt-STA
2,449,029
312,639,453
127.7
93,42MB
113,14
N.C.
Ace
Product
oghl-ddi ddi-STA
Hiss 30
Biology
ogbl-ppa-STD
576.289
73,507.315
1274
21.98 MB
3.01 h
L.P.
Hitx 100
Biology
oghl colaiiiition2-S STA
2,927.963
36,996,424
126.4
11 69 MB
12.81 h
L.P.
Mrr
Citation
oghg-molliv--See
M52
MB
ROCALI
Biology
oghg- Sohg-molpcho-STA.
11,386.154
1,528,3355622
Binlogy
ogbg-code2-STA 56,683.173
7,528.675, 744
132.8
2.11 GB
2,84
G.C.
FI score
Code
PepiidesSTA.
2,3442331
299,346.341
127.7
89.45 MB
930.91
G.C. & G.R.
AP MAE
Biology
PasealOC--SP
COCO-SP-STA
58.795,093
7,619.844,052
129.6
2.22
6.58
N.C.
Fl score
MalNat-Tiny-STa TTA
7,051,500
897.665, 950
127.3
268.23 MB
0.77
G.C.
Ace
Cyhersecurity
UniKG-STA
77.312,474
10,274.87.794
132.9
214.22h
N.C.
Universal
Graph Structure Learning have gained significant traction for their ability to learn complex graph representations, particularly through the use structural subcomponents like Graphlets and Motif'. These subcomponents are small non-isomorphic induced subgraphs, serve fundamental building blocks for capturing local structural information in graphs. They have been employed various network embedding techniques to improve the expressiveness of GNNs.
Several studies have explored the utilization graphlets in structural representation learning. For instance, the gl2vec model generates embeddings by computing the Subgraph Ratio Profile (SRP) of graphlets, which encodes distribution of different types of graphlets has demonstrated improvements in classification tasks, particularly when combined with other feature extraction methods. Similarly, the work by Rossi et al. proposed the Higher-Orde Network Embedding (HONE) framework, which uses subgraph patterns, including motifs and graphlet orbits, to capture higher-order network structures. Other notable approaches include leveraging graph convolutional networks (GCNs) with motif-based attention mechanisms. For example, MPool, motif-based graph pooling method, has shown that incorporating motif structures can improve graph classification performance by preserving essential topological information during pooling.
network. This approach
Our work differentiates itself from existing methods by focusing on the distribution of motifs and constructing these distributions as text sequences, akin to a growth series of motifs. This novel approach allows for the capture of both the frequency and evolution of motifs within a graph, which can be beneficial for tasks requiring more nuanced understanding of network dynamics. Unlike the
13

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gl2vec approach, which relies on random models to generate SRPs, our method does not depend on such models, thereby offering potentially more robust and consistent embeddings across different datasets. By integrating this with existing language model frameworks, our approach not only captures the local structure but also the evolution of these structures, offering a comprehensive view of the graph's 's topology.
More Preliminaries
B.1 Notation
A graph be defined as G = (V, in which V and & represent the sets of nodes and edges, respectively. For homogeneous graph, the number of types of nodes and edges is strictly equal to one. For heterogeneous graphs, the of the types of nodes and edges is strictly greater than two. Formally, a heterogeneous graph can be defined as follows:
g EV,E,C C,E, Ro, 1b),
where:
V {u1, 001,022-0 , uN denotes the set of nodes, and N is the total number of nodes.
E {ey) denotes the of directed edges between nodes.
C = (21,02...... Cr.} is the set of node types, and is the total number of node types.
R = (r,, .MM)
(M) is the set of edge types, and M is the total number of edge types.
dv + {ci, (21.02,......................... ,,,..,,, CL} represents the node type function that maps nodes to their
corresponding types.
de 3 fri, ................................ PM represents the edge type function that maps edges to their corresponding types.
B.2 Graph Neural Network Paradigm
The fundamental idea behind GNNs to iteratively update the representation of each node by aggregating information from its neighbors. This process can be generally formulated
h (
(GGREGATE(#) (LNS+
(18)
(OMBINE
(19)
where h denotes the representation of node the k-th layer, (N() represents the set of neighbors of U. and AGGREGATE() and COMBINE()) are functions that aggregate information from the neighbors and combine it with the node's previous representation, respectively.
B.3 Frozen/Fine-tuned Knowledge Transfer
Frozen knowledge transfer aims inject prior semantic knowledge, acquired through pre-training, into downstream tasks without additional training cost. The large-scale training set that provides prior knowledge is referred the target set. This transfer is achieved by pre-training shared semantic space. Unlike zero-shot learning, frozen knowledge transfer does impose strict constraints on class labels. In TA-LSSR framework, we use UniKG-STA, a dataset with rich structural information, as the support set, and various downstream graph datasets as the target sets ensure alignment with the shared semantic space hypothesis. Fine-tuned knowledge transfer aims to optimize both the pre-traines model and the downstream task model through end-to-end training. The objective to adapt existing knowledge to the downstream task with minimal training data and parameters, while aligning with the task-specific optimization goals. In our fine-tuning scenario, we first pre-train the GPSN model on UniKG-STA dataset, and fine-tune it on various downstream graph datasets.
the support set, while the dataset for downstream tasks is termed
14

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C Proofs for Theorems
C.1 Proofs of Theorem
In this section, we prove that the closed-formed solution of GPSN can be calculated as:
H(t 1) exp(A)H((t) + (% exp(As)ds) (Xxs)((s))
Br(().
(20)
From Eq. [ the linear time-invariant ODE function of the state space models can be described:
dH(() (t) + Bx(t),
(21)
dt
where x(() is the input function discrete sequences and (()) denotes the hidden state variables. First and foremost, we derive the H(k) in G2SN. Multiply both sides of the ODE function by exp(-At).
exp(-AN At) dH(() exp( (s)(-))))HH() + exp((AttBx(())
(22)
dt
according to the partial integration, the above formula can be derived follows:
= (t))a))))
(23)
dt integrating both sides with respect to t:
exp( exp(-A()H(() H() I/" exp(-As)BB after a merging, we can prove that:
(24)
f exp(A(t- s)))))
H(t) (x)(At)
(25)
Under the assumption of zero-order hold (ZOH), xt)) is constant during each time interval At, which means xt + 7) = xz(() if < At. Let us) = + 1 the H(1 + 1) can be further derived as:
H(t + = exp( + 1) H() / exp(A(t + B.)s)Bsrssss
(26)
ex () + cxp(() ( exp(A(( Ba) + / exp(A(t-s)) - Br)
(27)
=cxp(A) ()) S exp(A(t- 5) Bx) + +/, //' exp(A(t+11 B))Bss)
(28)
= =exp(A)H(1) (Preett exp(Au)du Br(()
(29)
=exp(A)H(() + (f. exp(As)ds) BI(().
(30)
C.2 Proofs of Theorem
In this section, we prove that the context dependencies of GPSN are controlled by the structural semantics u and m. According to Algorithm [1 GSSN has two essential parameters B and C, which are functions text annotation u and motif sequence m. Thus, they can represented as 8(u, m) and (u,, m), respectively. Under the assumption of ZOH, discrete-time equivalent of ODE can be represented as:
H(t) = A(t) - 1) B(t)x(t),
(31)
15

---

Y(t) - (t).
(32)
Eq. 31 is an iterative equation. The (1) can decomposed as follows:
t-2
t-g
H(t) II
A(t ())
II
A(t i) 1) 1) B(t)a(t). (33)
1=0
2=
From the Eq.
have A exp(AA), thus the (t)) can be represented as:
9-1
(t) C(t)
II
II
exp (A -1 ())) B(g)=(() +...+ (ool(()))...BB(BBt)))) +B())((t)
(34)
1-2
4-4-1
= C(t)
exp(
L i=0
A(t - ()==))))((I((((+++.....))))))))) +. exp(
... A(t - ((t=))))((()(()))) .... B(t)x(t)
(35)
t-q-1
= expl
A(t (lf-i)4m (()) + exp(
A - A(t=))A)(((BB(x(()) +.. C(t)B(()x((),
1=0
(36)
where the (t) are time-invariant parameter matrices, thus we have:
(() elt ( (() + (e a)Ab (ale=))AA(()B(((())))) C(1)B(g)=())+ C(1)B())x(( (37)
elt (l--)AACHBB))
(38)
The x(() is t-th imput of Mu i(t) = M(t). and B(g) is the parameter matrix Linear (onearg(((((()) (8(u(q), m(4))) and C(t) the parameter matrix Linearc(c(u(t). m(t))) Thus 5(u(t), m()) can be considered as one query of ærft, and c(u(g), m()) can be considered as one key of =Q)). Then, 5(u, m)((u, m) can measure the similarity between current input to the previ- ous ones and selectively copy the previous input, which demonstrates G2SN's s long-term dependencies for text annotations and motif sequences.
C.3 Proofs Theorem
Proof. Let Y(t) E elt- (i--jjAACCAA (()((())(())(()))))) We prove its gradient flow satisfies Lipschitz continuity as follows:
The gradient w.n.t parameters contains:
VY(I) Σ A& AAA (AA
AA Vo CB
(39)
Time evolution term
Parameter dynamics
where 9 denotes model parameters. For matrix exponential operators:
le AAr e A 1| S |AA| 2e | ||A|| max( 121-
(40)
yielding Lipschitz constant L1 |A / AAAI for maximum timestep Z'.
The parameter matrices C(t) = Linear (c(uu, m)) and B(q) = Linear (6(u, m)) are constrained
by:
Spectral Normalization:
max W B)) max Wc) 1
(41)
16

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where WB. We are weight matrices in Linearg, Linearg. ii) K-I.ipschizz Similarity Functions:
[ mi) - m2)ll S K(Ilu) uall ||m: m2)))
(42)
with analogous bound for e(:,-). Combining these yields:
Vo CB
& L2(
n'll
||m -m'll)
(43)
where L2 2K /d with d as hidden dimension. The total Lipschitz constant becomes:
L= Li L2 max [C()) 6g
(44)
Spectral normalization ensures |CB||2 S 1, thus L is finite and data- cata-independent.
Pross-Dataset Transfer Mechanism. The Lipschitz continuity guarantees that attention reweighting through (-) maintains bounded feature distortion when transferring between domains Ds (source) and Dr (target):
Y DD Yo, (I)l L. MMD(Ds, Dr),
(45)
where MMD denotes Maximum Mean Discrepancy. This theoretically enables stable knowledge transfer through attention adjustment.
D Details of Datasets
D.1 Graph Datasets Statistics
Table presents statistics for the utilized pre-training graph dataset UniKG and downstream graph datasets. The table compares characteristies such the number of nodes and edges, graph density, heterogeneity, task type, evaluation metric, and application domain for each dataset. Specially, "#Nodes" shows the number of nodes for each dataset. Datasets vary significantly in size, from small networks like Cora (2,708 nodes) to much larger networks like ogbn-products (2,449,029 nodes) and UniKG (77,312,474 nodes). "#Edges" reports the number of edges in the graph. For instance, Pubmed contains 44,338 edges, while the largest dataset, UniKG, has 6,1,738,000 736 edges, illustrating the scale variation across datasets. Graph "#Density" is the ratio of actual edges to possible edges in the graph. For instance, Cora and Citeseer have densities of 2.00 and 1.42. respectively, indicating sparse graphs, while ogbl-ddi has very high density of 312.84, suggesting a more densely connected network. "#Heterogeneity" indicates whether the graph is heterogeneous (i.e., contains multiple types of nodes and edges). Some datasets, such ogbn-mag and UniKG-STA, are marked as "Yes., indicating heterogeneity, while others, such as Cora, Citeseer, and Pubmed, are homogeneous ('No'). '#Task' describes the type learning task associated with each dataset. The tasks include Node Classification (N.C.), I Link Prediction (L.P.). and Graph Classification (G.C.). For instance, Cora and Pubmed are used for node classification, while ogbl-ddi used for link prediction. "#Metric" outlines the evaluation metries used for performance comparison. Common metrics include Accuracy (Acc) for classification tasks, rocauc (receiver operating characteristic area under the curve) for link prediction tasks, Hits @ 30, and the F1 score for graph classification. "#Domain" " provides the domain or application area the dataset, such as Citation for academic citation networks, Biology for biological networks, Product for recommendation systems, and Code for programming-rehee related graphs.
presents
D.2 Structural Textual Annotation Codebooks Datasets Statistics
describes the data statistics of STA-18 benchmark. Specifically, we further provide total number of tokens (including semantic tokens and format tokens) of these text sequence datasets, the average lengths of the tokens each node, the disk space required to store the dataset, and the time required to generate the dataset using our proposed method.
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E Self-Supervised Pre-Training Experiments
E.1
Experimental Setup
To answer the Q1. we apply the G2SN model to a self-supervised feature reconstruction task on the UniKG-STA dataset. 'hee experimental procedure is as follows: We propose the structural annotation generation algorithm to convert motif quantification distribution scores into text sequences, which were then vectorized into word frequency matrices by bag-of-words algorithm. The gen- erated sequences and distribution scores were prepared as training datasets. ii) The architecture of G2SN consists of multiple stacked G2SN blocks. The model's input includes mini-batches of text sequences and distribution scores, which undergo several transformations to reconstruct the original text sequences features. iii) G2SN is trained using a Mean Squared Error (MSE) loss function to minimize the difference between the reconstructed and original sequences, iv) To evaluate the effectiveness of feature reconstruction, we visualize node embeddings before and after training using t-SNE dimensionality reduction. Additionally, we plot the loss progression, as shown in Figure [
E.2 Experimental Analysis
Based on the results shown in Figure we make the following observations: Figure 5 (left) shows that the model's reconstruction loss decreases rapidly and steadily, indicating efficient and stable training convergence. This suggests that the model can effectively reconstruct unbiased local structural semantics based on the input quantification distribution. ii) Pre-training GPSN on the large-scale UniKG-ST dataset takes only 5.06 hours using single RTX 4090 GPU. This efficiency is attributed to Mamba's 's linear complexity when handling long sequence inputs. This highlights G2SN's capability to efficiently process both long sequence input text sequences and quantification distribution scores simultaneously. iii) Figure (right) reveals that the input text sequence embeddings exhibit relatively dispersed distribution in the 2D space of iSNE, indicating the annotation generation algorithm can produce diverse text descriptions, offering broad search space. The reconstructed output embeddings, while maintaining the original distribution, show partial clustering in the 2D space of iSNE, suggesting that the model captures quantification distribution similarities inherent in high- order structural semantics, thereby enhancing its ability to learn generalized structural knowledge. These observations consistently demonstrate the effectiveness of G2SN in pre- pre-training structural representation learning on UniKG-STA.
F Statistical Validation of Graph Structure Transfer Correlation
Data Preparation: Let D ( } represent paired observations where x; denotes average degree and y the transfer performance gain for dataset i.
Pearson Correlation Coefficient:
ELn(s (z. x) (1
(46)
3)2 (y: 7)
where z = 128.52 and ÿ 6.28 are sample means. Our calculation yields p 0.82.
Significance Testing: The t-statistic is computed as:
n = 0.82 1= PV 1 0
12 12-2
Rs 4.93,
(47)
0.822
with degrees of freedom df n 10. The critical L-value for a = 0.01 (000 3.169,
leading to p < 0.01.
Table 6: Sensitivity Analysis of Correlation Results
Method
P
p-value
Original Calculation
0.82
<0,01
Rullier-Remveed (Cora excluded)
0.85
<0.005
Nonparametric Bootstrap (10,000 samples)
0.81 = 0.04
<0.01
Normality Validation: Shapiro Wilk tests confirm normality assumptions:
18

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Figure 5: The visualization of self-supervised pre-training results. The left figure illustrates the con- vergence of structural semantic reconstruction loss. The right figure visualizes the I-SNE embeddings of node representations before and after pre-training.
Table Hyper- plapeeeparameter of the knowledge transfer tasks.
Datasets
Methods
num, hops
layers
hiddlen hidden_channels
epochs
a
seed
Cora
GCN
3
256
400
Citeseer
GCN
3
256
0.01
400
2025
Puhmed
GCN
3
256
0.01
400
2025
ogbn-proteins
GraphSAGE
3
256
400
2025
ogbn-arxiv
GCN
2
512
0.01
400
2025
ogbn-man
GraphSAGE
2
256
1000
2025
ogbn-products
SIGN
3
256
0.01
200
0.5
2025
ogbl-ddi
GraphSAGE
2
0.005
ughl ppa
GraphSAGE
3
256
0.01
100
2025
ogbl-citation2
GraphSAINT
ogbg-molhiv
GIN
5
300
0.001
100
2025
ogbg-molpeha
5
300
0.001
100
2025
ogbg
codgecode2 code2
GCN
5
300
0.001
25
2025
Average degree: W 0.96, 0.85
Transfer gain: W = 0.94, = 0.89
G Complexity Analysis
G.1 Pre-training Experiments Overhead
Pre-training G2SN on the large-scale UniKG-STA dataset takes only 5.06 hours using single RTX 4090 GPU. This efficiency attributed Mamba's linear complexity when handling long sequence inputs. This highlights G?SN's capability to efficiently process both long sequence input text sequences and guantification distribution scores simultaneously.
H Hyperparameters and Environments
To maintain fairness, the hyperparameter settings are kept consistent for all experiments on each dataset. In the self-supervised pre-training experiment, we set the bag-of-words length to 66 for each text sequence and 10 for the motif score sequence. For the bidirectional Mamba model, configure dstate as 16, deone as 4, and expand as 2. During training, we use the Adam optimizer with learning rate of 0.001, training for 10 epochs. Each batch consists of 50,000 pairs of text and motif score sequences. The overall dropout rate is set to 0, and the hidden dimension fixed at 256. The G2SN model contains 3 blocks, each comprising convolutional layers from the Mamba architecture. The random seed is fixed at 2024. Among the 13 downstream graph datasets, only the eebn-produce dataset uses the SIGN method, a decoupled graph neural network that requires precomputed 5-hop feature propagation matrix. The depth of these methods varies between 2, 3, and
Table 8: Hyper-parameters for self-supervised pre-training experiment.
Methods lon,
len.
expend
batch
epochs
dropout
hidden
layers
blocks
seed
19

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5 layers, with hidden feature dimensions 256, 512, or 300. The learning rates are set to 0.01, 0.005, or 0.001, and the number of training epochs is 400, 1000. 200, 100, or 25. All experiments use a fixed random seed of 2024 to ensure reproducibilityy All experiments were conducted using single 24GB GeForee RTX 4090 GPU. The hyperparameters of the pre-train experiments and knowledge transfer experiments can be found in Table 8 and 7
I Limitation
Considering the balance between mapping overhead, current hardware limitations and model perfor- mance, topological primitives mainly design substructures within two neighborhoods. Extending to three-hop or higher neighborhoods may be able to improve the effect structural knowledge transfer.
20

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27


Reviews:
[{"review_id": "1QyGjy6v1T", "reviewer": "Reviewer_qrzB", "summary": "The paper \"One for All: Universal Topological Primitive Transfer for Graph Structure Learning\" introduces a novel framework, GSN-Transfer, for transferring structural knowledge across diverse graph datasets by leveraging topological primitives as transferable semantic units. It addresses challenges in cross-graph knowledge transfer due to the non-Euclidean nature of graphs through three main contributions:\n\n1. **TopoGraph Mapping**: This component converts non-Euclidean graph structures into sequential representations using topological primitive distribution dictionaries, enabling the creation of the STA-18 benchmark dataset, a diverse graph-text dataset spanning 18 graphs.\n\n2. **GSN (Graph Structure Network)**: A dual-stream neural network architecture that learns aligned text-topology representations through contrastive alignment and large-scale pre-training on the UniKG-STA dataset. It captures transferable structural invariants, supporting both full-parameter fine-tuning and frozen parameter strategies.\n\n3. **AutoCross-Transfer**: A data-adaptive knowledge transfer mechanism that uses cross-attention to merge universal and dataset-specific graph structure semantics, facilitating effective transfer across domains under full-parameter and frozen-and-fine-tuned scenarios.\n\nThe framework achieves state-of-the-art performance, demonstrating a 3.2% average F1 score gain across 16 structural tasks and a 5.2% average gain in 13 downstream applications. Extensive experiments on 36 datasets validate GSN-Transfer’s efficacy in learning transferable structural representations, enhancing downstream task performance, and handling computational efficiency. The paper also provides comprehensive documentation, including dataset details, hyperparameters, and reproducibility instructions, alongside a new dataset release.", "questions": "Below are 3–5 actionable questions and suggestions for the authors of \"One for All: Universal Topological Primitive Transfer for Graph Structure Learning,\" focusing on critical areas to address limitations and clarify key points. Each includes clear guidance and criteria for how responses could influence the evaluation score, facilitating a productive rebuttal phase.\n\n1. **Expand Baseline Comparisons**\n   - **Question/Suggestion**: The evaluation in Table 1 (Page 8) compares GSN-Transfer only to GCN and GIN. Could the authors include comparisons with recent GNN architectures (e.g., GraphSAGE, GAT) and graph transfer learning methods (e.g., GraphCL, DANN) across key datasets? Please provide updated performance metrics or justify the omission.\n   - **Guidance**: Conduct experiments on at least 2–3 additional baselines, reporting metrics like F1 Score and Accuracy on datasets like Cora and ogbn-protein. Alternatively, explain why these baselines are less relevant, citing specific architectural or methodological differences.\n   - **Criteria for Score Change**: Including robust comparisons demonstrating GSN-Transfer’s superiority (e.g., >2% F1 improvement) would strengthen the quality and significance, potentially raising the score from “Accept with Minor Revisions” to “Strong Accept.” Omitting this or providing weak justifications could lower the score to “Weak Accept” due to insufficient benchmarking.\n\n2. **Deepen Ablation Studies**\n   - **Question/Suggestion**: The ablation studies (Table 3, Page 9) cover only six datasets and focus on transfer methods. Could the authors expand these to evaluate the contributions of TopoGraph Mapping, dual-stream GSN, and AutoCross-Transfer individually, across a broader dataset range? Please report quantitative impacts (e.g., F1 Score changes).\n   - **Guidance**: Perform ablations by disabling/removing each component (e.g., replacing TopoGraph Mapping with a simpler embedding) on at least 10 datasets, including STA-18. Provide a table summarizing performance drops or gains.\n   - **Criteria for Score Change**: Comprehensive ablations showing significant performance degradation without each component (e.g., >5% F1 drop) would bolster the quality and originality, reinforcing the necessity of the proposed design and potentially elevating the score. Superficial or inconclusive ablations could maintain or lower the score, signaling design weaknesses.\n\n3. **Clarify Terminology and Enhance Accessibility**\n   - **Question/Suggestion**: Terms like “topological primitives” and “structural textures” (Pages 1–2) are introduced without intuitive explanations. Could the authors provide clearer definitions or examples in the introduction or Section 2, targeting readers unfamiliar with graph learning? Please revise the text to include these clarifications.\n   - **Guidance**: Add 1–2 sentences or a brief example (e.g., comparing topological primitives to visual texture patches) in the introduction. Ensure definitions are self-contained in the main text, reducing reliance on external references.\n   - **Criteria for Score Change**: Clear, accessible explanations improving readability for a broader audience would enhance clarity, supporting a higher score (e.g., “Strong Accept”). Persistent jargon without clarification could maintain or lower the score to “Weak Accept” due to reduced accessibility.\n\n4. **Address Computational Complexity**\n   - **Question/Suggestion**: The complexity analysis (Page 18) lacks quantitative details. Could the authors provide time complexity (e.g., O-notation) and empirical runtime metrics for pre-training and inference on a representative dataset (e.g., Cora)? Please include these in Section 6 or an appendix.\n   - **Guidance**: Compute theoretical complexity for key operations (e.g., motif statistics, cross-attention) and report runtimes (e.g., hours/epoch) on a standard GPU. Compare with GCN/GIN to contextualize efficiency.\n   - **Criteria for Score Change**: Detailed complexity metrics showing competitive efficiency (e.g., comparable or faster than GIN) would strengthen quality and practical relevance, potentially raising the score. Lack of specifics or evidence of high complexity could lower the score, raising scalability concerns.\n\n**Overall Impact on Evaluation**: Addressing these points with rigorous experiments, clear revisions, and quantitative evidence would solidify the manuscript’s claims, potentially elevating the evaluation to “Strong Accept” by demonstrating superior performance, robust design, and accessibility. Incomplete or unconvincing responses could lower the score to “Weak Accept” or “Reject” if critical gaps (e.g., weak baselines, unclear methodology) persist. The authors are encouraged to prioritize baseline comparisons and ablations, as these directly impact the perceived quality and originality.", "limitations": "In the \"Limitations\" section, explicitly address 1–2 technical limitations (e.g., scalability or sensitivity to graph heterogeneity) with brief explanations of their implications.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Quality\n**Strengths**:\n- **Robust Experimental Design**: The manuscript demonstrates comprehensive empirical validation, evaluating the GSN-Transfer framework across 36 datasets (18 graph datasets and 18 corresponding STA datasets) spanning domains such as citation networks (e.g., Cora, Pubmed) and biological networks (e.g., ogbn-protein) (Page 12). Quantitative results indicate a 3.2% mean F1 score improvement across 16 structural tasks and a 5.2% mean improvement across 13 downstream applications (Page 3), supported by performance metrics (AP, MAEL, F1 Score, Accuracy) in Table 1 (Page 8). These results are benchmarked against established baselines (GCN, GIN), affirming the framework’s efficacy.\n- **Theoretical Rigor**: The inclusion of Theorem 5.1 (Page 6), which establishes Lipschitz-continuous gradient flow for GSN’s compositional output, provides a formal foundation for cross-dataset knowledge transfer. The proof, detailed in Appendix C (Page 14), leverages state space models (SSMs) and is mathematically sound, enhancing the work’s credibility. Spectral normalization and K-Lipschitz similarity functions (Page 16) further ensure stable gradient dynamics.\n- **Reproducibility**: The manuscript adheres to reproducibility standards, providing an anonymized link to datasets and code (Page 21), hyperparameter details in Appendix H and Table 7 (Page 18), and computational resource specifications (e.g., single 24GB GeForce RTX 4090 GPU, Page 19). These elements align with NeurIPS guidelines, facilitating independent verification.\n\n**Weaknesses**:\n- **Limited Baseline Comparisons**: The evaluation includes only GCN and GIN as baselines (Table 1, Page 8), omitting comparisons with contemporary graph neural network (GNN) architectures (e.g., GraphSAGE, GAT) or transfer learning methods (e.g., GraphCL, DANN). This restricts the ability to position GSN-Transfer’s performance relative to the state-of-the-art, potentially undermining claims of superiority (Page 3).\n- **Insufficient Ablation Analysis**: Ablation studies (Table 3, Page 9) are conducted on only six datasets and focus solely on transfer methods, neglecting to dissect contributions of key components (e.g., TopoGraph Mapping, dual-stream architecture, motif selection). This limits the evidence for the necessity and optimality of each module.\n- **Incomplete Complexity Analysis**: While computational complexity is briefly addressed (Page 18), the manuscript lacks quantitative metrics (e.g., time complexity for pre-training or inference). Given the framework’s reliance on large-scale pre-training and cross-attention, this omission raises concerns about scalability and practical deployment.\n\n**Accept/Reject Rationale**: The extensive empirical validation and theoretical grounding strongly support acceptance, reflecting high scientific quality. However, the limited baseline comparisons and shallow ablation studies warrant minor revisions to substantiate claims of state-of-the-art performance and component efficacy.\n\n Clarity\n**Strengths**:\n- **Structured Exposition**: The manuscript is organized logically, progressing from preliminaries (Section 2, Page 3) to methodology (Sections 3–5, Pages 3–6) and experiments (Section 6, Page 7). Visual aids, including Figure 1 (GSN-Transfer pipeline, Page 2) and Figure 4 (AdaCross-Transfer, Page 5), effectively illustrate complex mechanisms, enhancing comprehension.\n- **Detailed Technical Descriptions**: Key components are articulated with precision. TopoGraph Mapping is defined as transforming non-Euclidean graphs into sequential representations via topological primitive distribution dictionaries (Page 1). The GSN dual-stream architecture, incorporating contrastive alignment, is similarly well-specified (Page 1). Algorithm 1 (Page 4) and the annotation generation algorithm (Figure 2, Page 3) provide clear procedural details.\n- **Transparent Reporting**: The NeurIPS checklist (Pages 20–26) is thoroughly completed, addressing reproducibility, experimental settings, and compute resources (Pages 21–23). This transparency ensures that methodological and empirical claims are accessible to reviewers.\n\n**Weaknesses**:\n- **Specialized Terminology**: Terms such as “topological primitives,” “structural textures,” and “motif parallel statistics” are introduced without sufficient introductory explanation (Pages 1–2). This may hinder accessibility for readers unfamiliar with graph structure learning, necessitating clearer definitions or examples.\n- **Content Truncation**: The OCR output indicates significant truncation (e.g., 7187 characters on Page 1, 10173 on Page 4), potentially omitting critical methodological or experimental details. While core concepts are conveyed, these gaps could obscure full understanding of proofs (Page 14) or pre-training protocols (Page 17).\n- **Over-Reliance on Appendices**: Critical details, such as GSN block implementation (Page 17) and hyperparameter configurations (Appendix H, Page 23), are deferred to appendices. This disrupts the main text’s self-containment, potentially challenging readers seeking a cohesive narrative.\n\n**Accept/Reject Rationale**: The structured exposition and detailed figures support acceptance by ensuring methodological clarity. However, dense terminology and appendix reliance suggest minor revisions to enhance accessibility and narrative flow. Truncation, if present in the original submission, could justify a conditional acceptance pending clarification.\n\nSignificance\n**Strengths**:\n- **Addressing a Critical Challenge**: The manuscript tackles a pressing issue in graph structure learning: the difficulty of cross-graph knowledge transfer due to non-Euclidean geometries (Page 1). By proposing topological primitives as transferable semantic units, it offers a generalizable solution applicable to diverse domains, from citation to biological networks.\n- **Broad Impact Potential**: The STA-18 dataset (Page 3), spanning 18 graph-text pairs, is a significant contribution, providing a novel benchmark for graph transfer learning. Its diversity and public release (Page 25) enhance its utility for the research community. The 5.2% downstream task improvement (Page 3) underscores practical relevance for applications like node classification and link prediction (Page 12).\n- **Scalable Framework**: The GSN-Transfer framework’s ability to operate under both full-parameter fine-tuning and frozen-and-fine-tuned scenarios (Page 6) ensures flexibility for resource-constrained settings, increasing its applicability in real-world scenarios.\n\n**Weaknesses**:\n- **Narrow Task Focus**: The evaluation primarily focuses on structural tasks (e.g., motif prediction) and standard graph tasks (node classification, link prediction) (Page 7). The manuscript does not explore more complex applications, such as graph generation or temporal graph analysis, limiting the perceived breadth of impact.\n- **Dataset Scale Concerns**: While STA-18 is diverse, the manuscript does not discuss the scale of individual datasets (e.g., node/edge counts beyond Table 4, Page 12) or their representativeness of large-scale real-world graphs. This raises questions about generalizability to massive graphs encountered in industry settings.\n- **Limited Discussion of Societal Impact**: The NeurIPS checklist (Page 25) claims no societal risks, but the manuscript does not explore potential implications (e.g., biases in graph-based recommendation systems). A brief discussion could strengthen its relevance to responsible AI research.\n\n**Accept/Reject Rationale**: The novel dataset and broad applicability strongly support acceptance, addressing a significant gap in graph learning. However, the narrow task focus and lack of societal impact discussion suggest minor revisions to clarify the framework’s scope and ethical considerations.\n Originality\n**Strengths**:\n- **Novel Conceptual Framework**: The use of topological primitives as transferable semantic units, analogous to texture units in visual transfer (Page 2), is a highly original contribution. This abstraction, combined with the distribution of primitives as “structural textures,” introduces a new paradigm for graph knowledge transfer.\n- **Innovative Architecture**: The GSN dual-stream architecture, integrating text-topology alignment via contrastive learning (Page 1), is a distinctive approach. The AutoCross-Transfer mechanism, leveraging cross-attention for adaptive knowledge transfer (Page 5), further differentiates the work from existing GNN-based transfer methods.\n- **New Benchmark**: The creation of STA-18, a graph-text benchmark with 18 diverse datasets (Page 3), is a novel contribution. Its integration of motif-based annotations generated via ChatGPT-4.0 (Page 3) is an innovative application of large language models to graph learning.\n\n**Weaknesses**:\n- **Incremental Relation to Prior Work**: While the topological primitive concept is novel, the manuscript builds on existing ideas like state space models (SSMs) (Page 3) and graph motif analysis (Page 10, references to Choromanski et al., 2020). The distinction from prior motif-based methods (e.g., Graph2Vec, Chen & Koga, 2019) is not fully clarified, raising questions about incremental novelty.\n- **Limited Engagement with Transfer Learning Literature**: The manuscript cites transfer learning broadly (e.g., Pan & Yang, 2019, Page 10) but does not deeply engage with graph-specific transfer learning works (e.g., GraphAdapter, Li et al., 2023). A clearer differentiation from these methods would strengthen the originality claim.\n- **Dependence on Existing Tools**: The use of ChatGPT-4.0 for annotation generation (Page 3) relies on an external tool, which, while innovative, reduces the methodological novelty of the annotation process itself.\n\n**Accept/Reject Rationale**: The novel conceptual framework and STA-18 dataset strongly support acceptance, marking a significant departure from existing methods. However, the incremental relation to prior motif-based work and limited engagement with graph transfer learning literature suggest minor revisions to better articulate the work’s unique contributions.", "was_revised": true, "final_justification": "I think the paper has a strong experimentation section that justifies the claims in the paper. I think the paper can benefit from more clarity. I changed my score to borderline accept as the authors addressed most of my comments.", "rebuttal": "Thanks for your positive comments on our theoretical rigor, detailed technical descriptions, broad impact potential, and innovative architecture. For your concerns, below we make the responses.\n\n### **Q1**: Limited Baseline Comparisons: The evaluation includes only GCN and GIN as baselines (Table 1, Page 8), omitting comparisons with contemporary graph neural network (GNN) architectures (e.g., GraphSAGE, GAT) or transfer learning methods (e.g., GraphCL, DANN). This restricts the ability to position GSN-Transfer’s performance relative to the state-of-the-art, potentially undermining claims of superiority (Page 3).\n\n**A1**: Thanks for your comment. The compared baselines include **seven** graph learning methods, including three popular ones named GCN, GIN, GatedGCN, and four recent SOTA models GPS+Transformer, GPS+Performer, GPS+BigBird, and Exphormer, rather than **only GCN and GIN**. Our G²SN outperforms all these seven baselines, please refer to Table 1 (Page 8). In addition, GraphSAGE was reported in Table 2. Following your suggestion, we also used GAT, GraphCL, and DANN to handle structure migration tasks, but encountered out-of-memory issues.\n\n\n### **Q2**: Insufficient Ablation Analysis: Ablation studies (Table 3, Page 9) are conducted on only six datasets and focus solely on transfer methods, neglecting to dissect contributions of key components (e.g., TopoGraph Mapping, dual-stream architecture, motif selection). This limits the evidence for the necessity and optimality of each module.\n﻿\n**A2**: Thanks for your comment. These six datasets used in ablation studies include five large-scale datasets, and cover three fields, including citation classification (node classification), molecular property prediction (link prediction), and protein property prediction (graph classification). This should be sufficient to evaluate the contributions of our designed modules in ablation study.\n \nFollowing your suggestions, we have added ablation studies on **motif selection** and **dual-stream architecture**. Due to the rebuttal period limitation, these ablation studies are conducted on two datasets. The experiment results are as below:\n\ni) **Motif (Topological Primitive) Selection**: We conduct the motif selection ablation experiments on the ogbn-arxiv and Pubmed datasets. Specifically, We compared the original performance against performances selecting 8, 10, and 12 motifs. The experimental results are as follows:\n\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|14 motifs Frozen|3.95↑|1.91↑|\n|12 motifs Frozen|2.61↑|1.20↑|\n|10 motifs Frozen|1.99↑|0.57↑|\n|8 motifs Frozen|1.04↑|0.29↓|\n\nExperimental results show that increasing motif types improves model performance but introduces additional computational overhead. To balance performance and complexity, we selected 14 motifs in our manuscript.\n\n\nii) **Dual-Stream Architecture**: We independently ablated both topological primitive sequence branch and text sequence branch in the dual-stream architecture. The ablation experiment results are as follows:\n\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|The original dual-stream|3.95↑|1.91↑|\n|Without the text sequence branch|0.88↑|0.72↑|\n|Without the primitive sequence branch|1.46↑|1.09↑|\n\nThe experimental results show that each branch contributes to model performance.\n\n\n### **Q3**: Incomplete Complexity Analysis: While computational complexity is briefly addressed (Page 18), the manuscript lacks quantitative metrics (e.g., time complexity for pre-training or inference). Given the framework’s reliance on large-scale pre-training and cross-attention, this omission raises concerns about scalability and practical deployment.\n\n**A3**: Thanks for your comments. Following your suggestion, we provide the time complexity analysis of the pre-training. The time complexity of G²SN is mainly determined by the SSM backbone, which has $O(Ld^2)$ complexity ($L$=seq len, $d$=hidden dim). And it is lower than transformer’s $O(L^2)$. On UniKG-STA (77M nodes), pre-training takes **5.06 hours** (using single RTX 4090, please refer to Appendix G).  \n\n\n### **Q4**: Over-Reliance on Appendices: Critical details, such as G²SN block implementation (Page 17) and hyperparameter configurations (Appendix H, Page 23), are deferred to appendices. This disrupts the main text’s self-containment, potentially challenging readers seeking a cohesive narrative.\n\n**A4**: Thanks for your comments. We will migrate critical details to the main text: G²SN implementation (Appendix C.1) and Hyperparameters (Appendix H) in the next version.\n\n### **Q5**: Narrow Task Focus: The evaluation primarily focuses on structural tasks (e.g., motif prediction) and standard graph tasks (node classification, link prediction) (Page 7). The manuscript does not explore more complex applications, such as graph generation or temporal graph analysis, limiting the perceived breadth of impact.\n\n**A5**: Thanks for your comments. It should be emphasized that the proposed knowledge transfer framework has already modeled **13 downstream tasks**, which exceeds other similar works [GraphControl WWW’24, G-Adapter AAAI’24].\n\nWhile the temporal graph learning and graph generation you mentioned are promising research fields, they are not suitable in this work. Specifically, our data lacks temporal information, leading to a fundamental mismatch to temporal graph learning. Moreover, achieving graph generation requires redesigning the model architecture. \n\n\n### **Q6**: Incremental Relation to Prior Work: While the topological primitive concept is novel, the manuscript builds on existing ideas like state space models (SSMs) (Page 3) and graph motif analysis (Page 10, references to Choromanski et al., 2020). The distinction from prior motif-based methods (e.g., Graph2Vec, Chen & Koga, 2019) is not fully clarified, raising questions about incremental novelty.\n\n**A6**: Thanks for acknowledging the novelty of our topological primitive. Regarding relation to prior works, we would like to clarify your concerns as follows:\n\n- Firstly, a fundamental contribution of our work is construction and release of the 18 graph datasets (please refer to lines 72-75) to promote the graph structure transfer task, which differs from the previous tasks you mentioned.\n﻿\n- Secondly, we summarize the differences between our method and the two ones you mentioned as follows:\n\ni)Our G²SN vs. SSMs: We proposed the structural control mechanism to inject the graph structure knowledge through a dual-stream framework. In this framework, topological primitives can act as structural control flow, guiding attention to topology-critical regions (please refer to Theorem 4.2). In contrast, SSMs cannot explicitly and adequately model graph structure.\n\nii)Our G²SN vs. Graph2Vec [Chen & Koga, 2019]: Our G²SN algorithm incorporates sequence learning derived from ordinary differential equations (ODEs), providing theoretical guarantees for capturing contextual graph structures (see Appendix C.2, lines 496-510). In contrast, Graph2Vec's approach relies on dynamic neighborhood sampling during training rather than employing predefined motifs, which differs from our method in terms of mechanism.\n \n\n### **Q7**: Terms like “topological primitives” and “structural textures” (Pages 1–2) are introduced without intuitive explanations. Could the authors provide clearer definitions or examples in the introduction or Section 2, targeting readers unfamiliar with graph learning? Please revise the text to include these clarifications.\n\n**A7**: Thank you for your suggestion. We will add intuitive definitions of these terms in the revised version. Specifically:\n\n- Topological Primitives: representative local connectivity patterns (e.g., triangles, stars) and their distribution.\n\n- Structural Textures: Transferable semantic units (analogous to CV textures) formed by primitive distributions.\n\nWe will provide a clear explanation of these terms in the next version."}, {"review_id": "xpEGIRQZP8", "reviewer": "Reviewer_xpqy", "summary": "The manuscript introduces **G²SN-Transfer**, a three-stage framework that serialises graph substructures into textual “topological primitives,” injects the learned knowledge into downstream GNNs through a lightweight cross-attention adapter. \n\nOn the new STA-18 benchmark, the method achieves an average 3.2% F1 improvement over strong long-range baselines.", "questions": "1. How sensitive are the results to the chosen set of seven primitives? Would including non-cyclic motifs such as stars or cliques improve transfer?\n\n2. LLM-generated descriptors can vary stylistically; what mechanisms ensure annotation consistency?\n\n3. Have you observed negative transfer on heterogeneous datasets ?", "limitations": "Please refer to the questions.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\n* **Technical soundness**: Provides closed-form solutions and convergence guarantees for the state-space backbone.\n\n* **Empirical rigor**: Demonstrates consistent performance boosts on 18 datasets and releases code and data for reproduction.\n\n### Weaknesses\n\n* The fixed dictionary of seven primitives may underspecify higher-order motifs, limiting generality.\n\n* Theoretical analysis assumes linear time-invariant dynamics; applicability to dynamic or weighted graphs remains unverified.\n\n* The writing requires non-trivial improvement. There are too many rare words/complex sentences used in the paper, which does not align with the goal of academic writing. \n\n* Representative GFM + LLM studies (related works) not discussed sufficiently.", "was_revised": true, "final_justification": "Please refer to the discussions.", "rebuttal": "Thanks for your positive comments on technical soundness, empirical rigor, consistent performance boosts, releases code and data. For your concerns, below we make the responses.\n\n### **Q1** [Weaknesses1 & Questions1]: The fixed dictionary of seven primitives may underspecify higher-order motifs, limiting generality. How sensitive are the results to the chosen set of seven primitives? Would including non-cyclic motifs such as stars or cliques improve transfer?\n\n**A1**: Thanks for your comments. Regarding your concerns about i) fixed length, ii) sensitivity, and iii) more topological primitives including non-cyclic motifs, we provide the following response:\n\n\n- **Fixed Length**: Although the topological primitives vector has a fixed length after setting, the GSN framework ensures effective learning of high-order graph information—both theoretically and empirically—without relying on excessive high-order motifs. The reason is three-folds: a) Based on first- and second-order motifs, we performed multi-layer SSM learning, which implemented weighted union driven by graph structure sequences. This process actually corresponds to the neighborhood-selective aggregation mechanism of GAT, thus achieving high-order topological pattern learning through low-order motifs. b) Excessive high-order motifs can lead to high computational complexity, and we need to balance the relationship between performance and complexity. c) The excellent performance on the LRGB benchmark also evaluate that the proposed method can effectively learn high-order graph topology (please refer to Table 1).\n\n- **Sensitivity of Topological Primitives Vector Length**：We select topological primitive vectors of different lengths to test sensitivity. Specifically, We compared the original performance against performances selecting 8, 10, and 12 length. The experimental results are as follows:\n\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|14 motifs Frozen|3.95↑|1.91↑|\n|12 motifs Frozen|2.61↑|1.20↑|\n|10 motifs Frozen|1.99↑|0.57↑|\n|8 motifs Frozen|1.04↑|0.29↓|\n\nExperimental results show that increasing motif vector length improves model performance but introduces additional computational overhead. To balance performance and complexity, we selected 14 in our manuscript.\n\n- **More Topological Primitives**: Following your suggestions, we conducted additional experiments incorporating 3-star, 4-star, and 4-clique structures as new topological primitives. The experimental results are as follows:\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|Original Frozen|3.95↑|1.91↑|\n|+3-star Frozen|4.11↑|2.30↑|\n|+4-star Frozen|3.92↑|2.16↑|\n|+4-clique Frozen|3.41↑|1.78↑|\n\nThe experimental results demonstrate that incorporating additional motifs does not consistently enhance performance. The 4-star and 4-clique structures may introduce redundant information.\n\n### **Q2**: Theoretical analysis assumes linear time-invariant dynamics; applicability to dynamic or weighted graphs remains unverified.\n\n**A2**: Thanks for this insightful comment. While our current experiments focus on static graphs (the primary domain of STA-18), our framework does support dynamic or weighted graphs through the following mechanisms:  \n\n- **Weighted Graphs**: Our topological primitives explicitly encode **edge-type diversity** (Section 3), which can naturally treate edge weight as extra motif. Specifically, edge weights are used as new motifs to expand the text sequence $\\mathbf{u}$ to $\\mathbf{u}\\_{ew}$ and the topological primitive sequence $\\mathbf{m}$ to $\\mathbf{m}\\_{ew}$. Thereby obtain the similar conclusion through theoretical deduction (please refer to the pages 14 lines 496-510). \n\n- **Dynamic Graphs**: Dynamic graph data can be naturelly handled through G²SN's SSM backbone. Specifically, Input the temporal motif sequence $\\mathbf{m}\\_t$and the temporal text sequence $\\mathbf {u}\\_t$. The G²SN learns dynamic node embeddings through SSM and selects important temporal topological relationships through a structure selection mechanism. Thereby obtain the similar conclusion through theoretical deduction (please refer to the pages 14 lines 496-510).\n\nThe above specific derivation will be included in the appendix of the next version. \n\n### **Q3**: The writing requires non-trivial improvement. There are too many rare words/complex sentences used in the paper, which does not align with the goal of academic writing.\n\n**A3**: Thanks for your comments. In next version, we will simplify complex sentences and replace rare words to improve readability.\n\n\n### **Q4**: Representative GFM + LLM studies (related works) not discussed sufficiently.\n\n**A4**: Thanks for your comments. Following your suggestions, we here discuss more GFM + LLM studies, including LangGFM, GFM-RAG and PromptGFM:\n\n- LangGFM: Integrates formal grammars (e.g., Context-Free Grammars) with LLMs to enforce syntactic validity in generated text. Unlike standard LLMs that rely solely on statistical patterns, LangGFM uses grammar parsers as decoders to constrain outputs to linguistically valid structures. \n﻿\n- GFM-RAG: Augments Retrieval-Augmented Generation (RAG) with grammatical knowledge graphs. By structuring retrieved content using grammar frameworks before feeding it to the LLM, GFM-RAG improves factual coherence and reduces hallucination. \n﻿\n- PromptGFM: Embeds grammatical rules directly into LLM prompts via constrained decoding templates. This lightweight approach steers generation toward grammatically valid outputs without modifying the model architecture. In multilingual applications, PromptGFM dynamically switches grammar templates based on input language, significantly reducing structural errors in low-resource languages where LLMs typically struggle.\n\nWe will add the above discussion to related work in the next version.\n\n\n### **Q5**: LLM-generated descriptors can vary stylistically; what mechanisms ensure annotation consistency?\n\n**A5**: We sincerely thank you for this suggestion. As the universal SOTA model, GPT-4 have been extensively validated for robustness and applied on various benchmark tasks. Further, we have taken specific mechanisms to enhance annotation consistency:\n\ni) **Prompt engineering**: Prompt templates could enforce structured outputs (e.g., \"Node degree: [value]; Triangles: [count]\") , enhancing noise resilience.  \n\nii) **Manual Checking**: The Topograph mapping dictionary generated by pretrained models were further verified manually, specifically, per mapping (from motifs to text) was checked by at least 3 annotators. This human verification process can further ensure annotation consistency.\n\nBy incorporating prompt design and manual verification, we can reduce the risk of vary stylistically from foundation models. Following your suggestions, we make sure to add the above discussion in the next version.\n\n### **Q6**: Have you observed negative transfer on heterogeneous datasets ?\n\n**A6**: Thanks for your question. We have discussed the negative transfer of heterogeneous graph data (please refer to the **Homogeneity Superiority** section in Section 6.4, pages 9, lines 302-319). According to the experimental results, the heterogeneous graph ogbn-mag underperforms homogeneous graphs with similar scale by 2.3–4.8%, indicating that the heterogeneous structure introduces semantic fragmentation and hinders cross graph alignment. To mitigate negative transfer, careful parameter tuning and extended iteration steps are necessary when working with heterogeneous graphs."}, {"review_id": "HKZWtU2jJC", "reviewer": "Reviewer_6Ykv", "summary": "The paper introduces G²SN-Transfer, a “one-for-all” framework that treats recurring topological primitives (small, statistically frequent sub-structures) as transferable units of graph knowledge. It first serializes any graph into a dual sequence of (i) motif-distribution codes and (ii) LLM-generated textual descriptors via TopoGraph-Mapping, creating the 18-dataset STA-18 benchmark. A dual-stream state-space model (G²SN) is then pre-trained to align topology and text with a provably convergent formulation. Finally, AdaCross-Transfer injects these representations into downstream GNNs through parameter-efficient cross-attention, yielding significant gains on long-range structure tasks and transfer benchmarks.", "questions": "- In Figure 3, which is the textual sequence $u$ and LLM-Topomotif sequence $m$?\n- How might the learned topological-textual latent space enable inverse problems—for example, generating synthetic graphs that satisfy a natural-language specification of desired structural properties?\n- What theoretical or empirical considerations led to a state-space model over other more common graph-aware transformers or message-passing models? Have you evaluated G²SN against a parameter-matched Transformer encoder that is fed the same motif distribution and text embeddings? \n- Motif distributions are treated as fixed-length vectors of size $M$. Did you test the sensitivity of the whole pipeline to $M$ (e.g., 16 vs. 64 primitives)?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n- The concept of topological primitives as graph textures is interesting and novel, bridging the gap between non-Euclidean data and textual information.\n- STA-18 is the first (to my knowledge) graph-text benchmark, which should benefit the future researcher.\n- The proposed State space model is backed by closed-form solutions and guaranteed convergence.\n- Results show promising and consistent improvement over previous baselines. \n\n## Weaknesses\n- Automatically generated textual descriptors may embed bias or noise, yet no human evaluation or further verification confirms their fidelity or usefulness for transfer.\n- It is unclear how the theoretical time/space complexity and the empirical runtime of G²SN-Transfer compare with standard GNN baselines such as GCN and GraphSAGE, especially when all components (motif extraction, dual-stream encoder, AdaCross) are included.\n- It is unclear how the number of primitives is selected, what exact algorithm is used to compute each graph’s motif-frequency vector, and how the computation scales (e.g., to k-node motifs) on large graphs.", "was_revised": true, "final_justification": "All issues have been addressed, and I maintain my recommendation.", "rebuttal": "Thanks for your positive comments on our framework's innovative concept, the first graph-text benchmark, theoretical convergence guarantees, and consistent performance improvements. For your concerns, below we make the responses.\n\n### **Q1**: Automatically generated textual descriptors may embed bias or noise, yet no human evaluation or further verification confirms their fidelity or usefulness for transfer.\n\n**A1**: We sincerely thank you for this suggestion. As the universal SOTA model, GPT-4 have been extensively validated for robustness and applied on various benchmark tasks. Further, we have taken specific mechanisms to reduce bias or noise:\n\ni) **Prompt engineering**: Prompt templates could enforce structured outputs (e.g., \"Node degree: [value]; Triangles: [count]\") , enhancing noise resilience.  \n\nii) **Manual Checking**: The Topograph mapping dictionary generated by pretrained models were further verified manually, specifically, per mapping (from motifs to text) was checked by at least 3 annotators. This human verification process can further reduce bias or noise.\n\nBy incorporating prompt design and manual verification, we can reduce bias/noise from large foundation models. Following your suggestions, we make sure to add the above discussion in the next version.\n\n\n### **Q2**: It is unclear how the theoretical time/space complexity and the empirical runtime of G²SN-Transfer compare with standard GNN baselines such as GCN and GraphSAGE, especially when all components (motif extraction, dual-stream encoder, AdaCross) are included.\n\n**A2**: Thanks for your comments. We hope to address your concerns through the following three points:\n\ni) **Empirical Runtime of Motif Extraction**: The complexity of motif extraction is $O(|V| \\cdot d\\^k)$ ($d$=avg. degree, $k$=2-hops). For Cora (2,708 nodes) and UniHG-STA (77.3M nodes), this takes **7.07s** and **214.22h** (please refer to Table 5, Pages 12).  \n\nii) **AdaCross Overhead**: The parameter count of AdaCross is 9% lower than the average downstream baseline models used (please refer to pages 2, lines 55-63). \n\niii) **G²SN Inference**: For an input sequence of length $L$, G²SN processes sequences in $O(Ld\\^2)$ time, while GraphSAGE and GCN in $O(L\\^2d$) time ($d$ represents the hidden layer dimension). Empirical runtime of pretraining is 5.06 hours on single 4090 (please refer to Appendix G.1).\n\nIn next version, we will emphasize above theoretical time/space complexity and the empirical runtime.\n\n\n### **Q3**: It is unclear how the number of primitives is selected, what exact algorithm is used to compute each graph’s motif-frequency vector, and how the computation scales (e.g., to k-node motifs) on large graphs.\n\n**A3**: Thanks for your comments. \n\n- Firstly, this choice is the result of balancing performance and complexity. Considering the balance between expressive ability and computational complexity, we determine the motif as within a 2-hop neighborhood. The spatiotemporal cost of motif statistics in the three hop neighborhood is too high.\n﻿\n- Additionally, capturing long-range information does not require excessive higher-order motif design. The reason is three-folds: a) Based on first- and second-order motifs, we performed multi-layer SSM learning, which implemented weighted union driven by graph structure sequences. This process actually corresponds to the neighborhood-selective aggregation mechanism of GAT, thus achieving high-order topological pattern learning through low-order motifs. b) Excessive high-order motifs can lead to high computational complexity, and we need to balance the relationship between performance and complexity. c) The excellent performance on the LRGB benchmark also evaluate that the proposed method can effectively learn high-order graph topology (please refer to Table 1).\n\n- Further, for the motif-frequency vector calculation problem that you concerned, primitives were selected via **statistical recurrence analysis** (Blanche et al., 2020) for each node's 1-hop and 2-hop subgraphs. To ensure numerical accuracy, we traverse all nodes on the large-scale graph. Complexity is $O(|V| \\cdot \\Delta\\^2)$ for 2-hop primitives ($\\Delta$=max degree), thus it can be directly used for large-scale graphs.\n\n\n### **Q4**: In Figure 3, which is the textual sequence $u$ and LLM-Topomotif sequence $m$?\n\n**A4**: Thanks for your questions. The upper input is textual sequence $u$, and the lower input is LLM-Topomotif sequence $m$. We will clarify captions in the next version. \n\n\n### **Q5**: How might the learned topological-textual latent space enable inverse problems—for example, generating synthetic graphs that satisfy a natural-language specification of desired structural properties?\n\n**A5**: Thanks for your insightful comments. This is a very interesting question but not the focus of this research. Based on the experience of text-graph generation, it may be feasible to solve related problems by establishing a generation algorithm and alignment benchmarks between graph motifs and text pairs. We will defer this design to the future work.\n\n### **Q6**: What theoretical or empirical considerations led to a state-space model over other more common graph-aware transformers or message-passing models? Have you evaluated G²SN against a parameter-matched Transformer encoder that is fed the same motif distribution and text embeddings?\n\n**A6**: Thanks for your insightful comments. We choose SSMs due to considerations of performance and efficiency.\n\n- Compared with graph-aware transformer or message-passing models, firstly, SSM has lower time complexity while possessing equivalent long-range learning capabilities, which is beneficial for large-scale tasks during pre training. Specifically, for input sequences of length $L$, G²SN processes sequences in $O(Ld\\^2)$ time, while transformers and GNNs in $O(L^2d)$ time ($d$ represents the hidden layer dimension).\n﻿\n- Furthermore, our G²SN has a more flexible adaptive topology selection mechanism. We performed multi-layer SSM learning, which implemented weighted union driven by graph structure sequences. This process actually corresponds to the neighborhood-selective aggregation mechanism of GNN, thus achieving high-order topological pattern learning through low-order motifs. This promotes the mining and transfer of universa structure knowledge.\n﻿\n- Following your suggestion, we conducted a further experiment to validate the advantages of our G²SN model. We used transformer as the representation learning model and applied it to the frozen transfer scenarios on the ogbn-arxiv and Pubmed datasets. The topological primitive sequence and text sequence are concatenated together as transformer inputs. The experimental results are as follows:\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|G²SN Frozen|3.95↑|1.91↑|\n|Transformer Frozen|2.86↑|0.72↑|\n\nThe experimental results show that the transformer underperforms G²SN.\n\n\n### **Q7**: Motif distributions are treated as fixed-length vectors of size $M$. Did you test the sensitivity of the whole pipeline to $M$ (e.g., 16 vs. 64 primitives)?\n\n**A7**: Thanks for your insightful comments. We have added a sensitivity experiment, considering the high time overhead of statistically analyzing more motifs on the pre training dataset UniKG (currently requiring 214.22 hours), we have used motif vectors of different lengths (10, 12, 14, 16), and we also attempted to add some new motif (17=16+1(a 3-star/4-star/4-clique motif)). The results of the sensitivity experiment are as follows:\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|Length 16 Frozen|3.95↑|1.91↑|\n|Length 16 Fine-tuned|6.48↑|2.93↑|\n|Length 14 Frozen|2.61↑|1.20↑|\n|Length 12 Frozen|1.99↑|0.57↑|\n|Length 10 Frozen|1.04↑|0.29↓|\n|Length 17 (+3-star) Frozen|4.11↑|2.30↑|\n|Length 17 (+4-star) Frozen|3.92↑|2.16↑|\n|Length 17 (+4-clique) Frozen|3.41↑|1.78↑|\n\nThe experimental results show that the model is robust to the length of motif vectors, and introducing new motif (e.g. 3-star) can improve performance."}, {"review_id": "lGUdv9V1KV", "reviewer": "Reviewer_eAfk", "summary": "The paper proposes a method for universal topological primitive transfer in graph structure learning, introducing an approach based on State Space Models (SSM) for addressing domain generalization in graph-based tasks. The model aims to pre-train on large-scale graphs and transfer learned structures to smaller graphs with domain shifts. The paper includes theoretical analysis based on SSM and evaluates the model on several standard datasets.", "questions": "See Weaknesses.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. Interesting Problem Domain: The idea of domain generalization in graph learning is an interesting area of exploration. The attempt to leverage pre-trained topological features across different domains is valuable for advancing the field.\n\n2. Model Novelty: The proposed method introduces a unique combination of SSM-based modeling with graph structure transfer, which has the potential to lead to advancements in graph learning.\n\nWeaknesses:\n\n1. Lack of Strong Motivation for Using SSM\n\nThe paper introduces State Space Models (SSM) without sufficiently explaining why SSM is necessary for graph structure learning. Traditional GNN models or Graph Transformers could potentially handle the graph structure transfer task without the complexity introduced by SSM. The lack of motivation for choosing SSM over more standard models makes the innovation feel less compelling.\n\n2. No Domain Generalization Theory or Analysis\n\nDespite the paper's claim of addressing domain generalization, it lacks any formal theory or analysis regarding generalization bounds or invariant representation in the context of graph learning. There is no mention of foundational work such as IRM (Invariant Risk Minimization), domain adaptation theory, or generalization bounds. This gap makes it difficult to assess the actual effectiveness of the proposed approach in handling domain shifts.\n\n3. Missing Comparison to Existing Domain Generalization Works\n\nThe paper does not cite or compare the proposed method to any established domain generalization approaches in the context of graph learning, such as the Multi-Domain Graph Foundation Model. Without this context, it is unclear how this method advances or improves upon the current state-of-the-art in domain generalization for graph data [1][2].\n\n[1] Yu X, Gong Z, Zhou C, et al. Samgpt: Text-free graph foundation model for multi-domain pre-training and cross-domain adaptation. Proceedings of the ACM on Web Conference 2025.\n\n[2] Wang S, Wang B, Shen Z, et al. Multi-domain graph foundation models: Robust knowledge transfer via topology alignment. ICML 2025.", "was_revised": true, "final_justification": "Thank you for the response, and I will keep my score.", "rebuttal": "Thanks for your positive comments on interesting problem domain and model novelty. For your concerns, below we make the responses.\n\n\n### **Q1**: The paper introduces State Space Models (SSM) without sufficiently explaining why SSM is necessary for graph structure learning. Traditional GNN models or Graph Transformers could potentially handle the graph structure transfer task without the complexity introduced by SSM. The lack of motivation for choosing SSM over more standard models makes the innovation feel less compelling.\n\n**A1**: Thanks for your insightful comments. We choose SSMs due to considerations of performance and efficiency.\n\n- Compared with Traditional GNN models or Graph Transformers, firstly, SSM has lower time complexity while possessing equivalent long-range learning capabilities, which is beneficial for large-scale tasks during pre training. Specifically, for input sequences of length $L$, G²SN processes sequences in $O(Ld\\^2)$ time, while transformers and GNNs in $O(L^2d)$ time ($d$ represents the hidden layer dimension).\n\n- Furthermore, our G²SN has a more flexible adaptive topology selection mechanism. We performed multi-layer SSM learning, which implemented weighted union driven by graph structure sequences. This process actually corresponds to the neighborhood-selective aggregation mechanism of GNN, thus achieving high-order topological pattern learning through low-order motifs. This promotes the mining and transfer of universa structure knowledge.\n\n- Following your suggestion, we conducted a further experiment to validate the advantages of our G²SN model. We used transformer as the representation learning model and applied it to the frozen transfer scenarios on the ogbn-arxiv and Pubmed datasets. The topological primitive sequence and text sequence are concatenated together as transformer inputs. The experimental results are as follows:\n|Methods|ogbn-arxiv|Pubmed|\n|---|---|---|\n|G²SN Frozen|3.95↑|1.91↑|\n|Transformer Frozen|2.86↑|0.72↑|\n\nThe experimental results show that the transformer underperforms G²SN.\n\n\n\n### **Q2**: Despite the paper's claim of addressing domain generalization, it lacks any formal theory or analysis regarding generalization bounds or invariant representation in the context of graph learning. There is no mention of foundational work such as IRM (Invariant Risk Minimization), domain adaptation theory, or generalization bounds. This gap makes it difficult to assess the actual effectiveness of the proposed approach in handling domain shifts.\n\n\n**A2**: Thanks for your comments. We acknowledge that our initial submission emphasized empirical validation, and we agree that incorporating foundations like IRM and generalization bounds would strengthen the work. Following your suggestions, we have derived the theoretical connection to domain adaptation/generalization:\n\nOur AdaCross-Transfer mechanism implicitly aligns with IRM’s core principle of learning *invariant representations* across domains. Specifically:  \n\n-  **Invariant Representation Learning**: The cross-attention module (Eqs. 10–15) dynamically aligns structural-textual features using a data-adaptive weight vector $\\hat{\\mathbf{w}}$, which reweights features based on topological primitive distributions. This forces the model to prioritize *domain-agnostic structural semantics* (motif distributions) over spurious domain-specific correlations, analogous to IRM’s invariance objective.  \n\n- **Generalization Bounds**: Theorem 5.1 (and Appendix C.3) proves that G²SN’s output $\\mathbf{Y}(t)$ exhibits **Lipschitz-continuous gradient flow** under cross-domain shifts. This provides a theoretical foundation for stability during transfer, as bounded gradient sensitivity implies robustness to input perturbations (e.g., structural distribution shifts). Formally, the Lipschitz constant $L$ (Eq. 44) upper-bounds the feature distortion $\\|\\mathbf{Y}\\_{\\mathcal{D}\\_S}(t) - \\mathbf{Y}\\_{\\mathcal{D}\\_T}(t)\\|$ by the MMD distance between source ($\\mathcal{D}\\_S$) and target ($\\mathcal{D}\\_T$) domains (Eq. 45). This aligns with classical domain adaptation theory [Ben-David et al., 2010], where generalization error depends on domain discrepancy and feature stability.  \n\n\n### **Q3**: The paper does not cite or compare the proposed method to any established domain generalization approaches in the context of graph learning, such as the Multi-Domain Graph Foundation Model. Without this context, it is unclear how this method advances or improves upon the current state-of-the-art in domain generalization for graph data [1][2].\n\n\n**A3**: Thanks for your insightful comments. Following your suggestions, we have carefully investigated these works of your concern. We have found that although the two methods you mentioned have significant effects, they are **inherently different** from our transfer settings and application scenarios. Specifically:\n\n- **Different Transfer Settings**: These two methods emphasize cross-domain transfer tasks under **few-shot settings**, which is different from our **supervised** transfer tasks. Therefore, directly comparing performance is unfair.\n\n- **Fusion of Node Features**: From the methodological perspective, these two methods emphasize the deep fusion of structural information and **node features**, which is fundamentally different from our **pure structure driven knowledge transfer**. Our method can be applied to graph data without node features. Therefore, it should not be compared with these two methods together.\n\n**In summary**, due to the inherently different transfer settings and application scenarios, these methods are not suitable as baselines for comparison."}, {"review_id": "3L1RjoxJYA", "reviewer": "Reviewer_e58L", "summary": "This paper presents G²SN-Transfer, a framework for universal graph structure learning. It transforms non-Euclidean graphs into transferable sequences using topological primitive distribution dictionaries, learns aligned representations via a dual-stream G²SN architecture, and enables adaptive knowledge transfer through AdaCross-Transfer. The framework is validated on the STA-18 benchmark, showing state-of-the-art performance on structural learning tasks and consistent improvements across downstream applications.", "questions": "- How does the framework perform on graphs with dynamic topological changes over time?  \n- Can the transfer mechanism be extended to heterogeneous graphs with diverse node/edge types?", "limitations": "The computational overhead of constructing topological-text annotations increases with graph size, affecting scalability to extremely large datasets. The reliance on LLM annotations may introduce bias if textual descriptions do not fully capture structural nuances.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- Proposes topological primitives as transferable units, bridging non-Euclidean graph geometry for cross-domain knowledge transfer.  \n- Develops G²SN, a dual-stream network with ODE-driven dynamics, theoretically guaranteed to converge and capture structural-textual dependencies.  \n- Creates STA-18, the first large-scale benchmark with aligned topological-text pairs, enabling rigorous evaluation of graph transfer methods.  \n\nWeaknesses:\n- Topological primitives are limited to two-hop neighborhoods, potentially missing higher-order structural patterns.  \n- LLM-generated annotations require manual validation, introducing human oversight in dictionary construction.", "was_revised": true, "final_justification": "The discussions with the authors have addressed my concerns regarding this paper, and therefore I have decided to raise my score.", "rebuttal": "Thanks for your positive comments on theoretically guarantee, and our first large-scale benchmark. For your concerns, below we make the responses.\n\n\n### **Q1**: Topological primitives are limited to two-hop neighborhoods, potentially missing higher-order structural patterns.\n\n**A1**: Thanks for your comments. Although the topological primitives focus on two-hop neighborhoods, the GSN framework ensures effective learning of high-order graph information—both theoretically and empirically—without relying on excessive high-order motifs. The reason is three-folds: \n- Based on first- and second-order motifs, we performed multi-layer SSM learning, which implemented weighted union driven by graph structure sequences. This process actually corresponds to the neighborhood-selective aggregation mechanism of GAT, thus achieving high-order topological pattern learning through low-order motifs.\n- Excessive high-order motifs can lead to high computational complexity, and we need to balance the relationship between performance and complexity. \n- The excellent performance on the LRGB benchmark also evaluate that the proposed method can effectively learn high-order graph topology (please refer to Table 1).\n\n\n### **Q2**: LLM-generated annotations require manual validation, introducing human oversight in dictionary construction.\n\n**A2**: Thanks for your comments. We acknowledge the LLM-generated annotations require manual validation. Our design alleviates human oversight by efforts of these two aspects:\n﻿\n- **Manual Checking**: The Topograph mapping dictionary generated by pretrained models were verified manually, specifically, per mapping (from motifs to text) was checked by at least 3 annotators. The mutual check between multiple annotators ensures consistency, thereby reducing the possibility of human oversight.\n﻿\n- **Efficient Workflow**: Each annotator does not check the annotation information of all nodes, but only checks the annotations of the mapping dictionary, which includes 14 primitives * 10 descriptive variants. Thus, less verification content also reduces the possibility of human oversight.\n\n\n### **Q3**: How does the framework perform on graphs with dynamic topological changes over time?\n\n**A3**: Thanks for your question. According to your concerned dynamic graph tasks, we would will to make classifications as follows:\n\n- Firstly, our work mainly focuses on universal knowledge transfer tasks for public knowledge graphs (mostly static). while the temporal graph learning you mentioned are promising research fields, dynamic graph tasks are not the research focus.\n\n- Especially, following your suggestion, it may be feasible to handle dynamic graph topology inputs by modifying the SSM backbone network of G²SN. Specifically, SSM requires merging a new temporal branch and an existing topological sequence branch, so that G²SN can capture the dynamic patterns of the topological structure. In this way, for the temporal motif sequence $\\mathbf{m}\\_t$and the temporal text sequence $\\mathbf {u}\\_t$, the G²SN learns dynamic node embeddings through SSM and selects important temporal topological relationships through a structure selection mechanism. Thereby obtain the similar conclusion through theoretical deduction in Appendix C.2 (please refer to the pages 14 lines 496-510).\n\nThanks for your question again. We will defer this design to the future work.\n\n\n\n### **Q4**: Can the transfer mechanism be extended to heterogeneous graphs with diverse node/edge types?\n\n**A4**: Thank you for your question. We have successfully applied it to HGs. Specifically, knowledge transfer experiment on heterogeneous graph dataset **ogbn-mag** achieves **+5.01%** accuracy gain (please refer to Table 2, pages 8).\n\n### **Q5**: The computational overhead of constructing topological-text annotations increases with graph size, affecting scalability to extremely large datasets. The reliance on LLM annotations may introduce bias if textual descriptions do not fully capture structural nuances.\n\n**A5**: Thanks for your comment. We will address your concerns from the following two aspects:\n\ni) **Scalability**: The complexity of topological mapping is $\\mathcal{O}(N\\cdot d\\^2)$ ($d$: average degree), which can extend to large-scale graph. And the dataset we are currently using has reached a scale of billion-edges (please refer to Table 4, Pages 12).\n\nii) **Deviation mitigation**: As the universal SOTA model, GPT-4 have been extensively validated for robustness and applied on various benchmark tasks. Further, we have taken specific mechanisms to reduce bias:\n\n- **Prompt engineering**: Prompt templates could enforce structured outputs (e.g., \"Node degree: [value]; Triangles: [count]\") , enhancing noise resilience.  \n﻿\n- **Manual Checking**: The Topograph mapping dictionary generated by pretrained models were further verified manually, specifically, per mapping (from motifs to text) was checked by at least 3 annotators. This human verification process can further reduce bias or noise.\n﻿\nBy incorporating prompt design and manual verification, we can reduce bias from large foundation models. Following your suggestions, we make sure to add the above discussion in the next version."}]

Author rebuttal:

Meta-review: This paper presents G2SN-Transfer, a novel framework using topological primitives, the STA-18 benchmark, a dual-stream SSM encoder, and AdaCross-Transfer for efficient cross-graph transfer. It is well motivated, theoretically grounded, and shows consistent gains across tasks with public code and data. Rebuttal additions on baselines, ablations, complexity, and annotation validation addressed reviewer concerns, leading to raised scores. I recommend acceptance, with suggestion for clarity improvements for the camera-ready version.
Decision: Accept (poster)