A Closer Look at the Application of Causal Inference in Graph Representation Learning

Hang Gao; Kunyu Li; Huang Hong; Baoquan Cui; Fengge Wu

cs.LGApr 10, 2026

A Closer Look at the Application of Causal Inference in Graph Representation Learning

Authors: Hang Gao, Kunyu Li, Huang Hong, Baoquan Cui, Fengge Wu

Organizations: Institute of Software Chinese Academy of Science

Abstract

Modeling causal relationships in graph representation learning remains a fundamental challenge. Existing approaches often draw on theories and methods from causal inference to identify causal subgraphs or mitigate confounders. However, due to the inherent complexity of graph-structured data, these approaches frequently aggregate diverse graph elements into single causal variables, an operation that risks violating the core assumptions of causal inference. In this work, we prove that such aggregation compromises causal validity. Building on this conclusion, we propose a theoretical model grounded in the smallest indivisible units of graph data to ensure that the causal validity is guaranteed. With this model, we further analyze the costs of achieving precise causal modeling in graph representation learning and identify the conditions under which the problem can be simplified. To empirically support our theory, we construct a controllable synthetic dataset that reflects realworld causal structures and conduct extensive experiments for validation. Finally, we develop a causal modeling enhancement module that can be seamlessly integrated into existing graph learning pipelines, and we demonstrate its effectiveness through comprehensive comparative experiments.

Figures & tables

Figure 1: An example of the ideal case and the actual case in causal model building. In the actual case, the causal model cannot be constructed as in the ideal case due to the complex reciprocal causal relationships between the merged variables.

Figure 2: Graphical illustration of the proposed SCM of the graph representation learning scenario.

Dataset	Adjustable	Known	Adjustable	Adjustable	Adjustable	Adjustable	Real-world
Dataset	Elements ( $\uparrow$ )	Causality	Motif	Node Feature	Edge Connection	Assemble Mode	Grounded Data
Citeseer ( Giles et al., 1998 )	Fixed	$\times$	$\times$	$\times$	$\times$	$\times$	✓
PROTEINS ( Morris et al., 2020 )	Fixed	$\times$	$\times$	$\times$	$\times$	$\times$	✓
Synthetic Graph ( Ying et al., 2019 )	5	✓	✓	$\times$	$\times$	$\times$	$\times$
Spurious-Motif ( Wu et al., 2022b )	6	✓	✓	$\times$	$\times$	$\times$	$\times$
CRCG ( Gao et al., 2024 )	54	✓	✓	✓	✓	$\times$	$\times$

Table 1: Comparison between our proposed RWG dataset and existing benchmark datasets.

Panel of Figure 3 — Figure 3: Test accuracy comparison across three different scenarios.

Panel of Figure 4 — Figure 4: Performance of the methods when Theorem 4 is violated to varying degrees. The horizontal axis represents the percentage of data in $X^{\text{cfd}}$ that is erroneously merged into $X^{\text{caus}}$ .

Panel of Figure 5 — Figure 5: Performance comparison across different scenarios.

Panel of Figure 6 — Figure 6: Performance of models trained solely with causal data.

Figure 7: The illustration of how REC works.

Method	RWG-Molecular	Spmotif-M	Spmotif-C	RWG–Citation	CRCG	CiteSeer	ENZYMES
CaNet	52.17 ± 2.02	32.40 ± 1.30	45.00 ± 1.32	59.33 ± 1.04	32.77 ± 1.27	83.87 ± 0.67	17.00 ± 6.78
CaNet+REC	56.50 ± 2.65	34.17 ± 1.35	46.83 ± 3.06	61.83 ± 0.76	36.43 ± 1.17	84.90 ± 0.12	18.33 ± 6.94
Improvement	+4.33	+1.77	+1.83	+2.50	+3.66	+1.03	+1.33
CRCG	45.50 ± 3.53	36.80 ± 1.89	44.50 ± 2.91	45.50 ± 6.29	29.70 ± 4.62	42.78 ± 3.76	34.67 ± 7.10
CRCG+REC	45.50 ± 4.39	38.17 ± 3.83	50.50 ± 3.05	47.50 ± 6.26	33.10 ± 5.29	44.07 ± 3.30	40.33 ± 3.24
Improvement	+0.00	+1.37	+6.00	+2.00	+3.40	+1.29	+5.66

Table 2: Performance comparison of different methods with and without REC enhancement on various datasets. The improvement row shows the absolute performance gain achieved by REC.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8: The graphical illustration of the causal relationships between variables

a

b

c

, and

d

Panel of Figure 9 — Figure 9: Results of the PC algorithm for SCM reconstruction.

Molecule	Molecular Formula	Node Count	Edge Count
Acetic Acid	C 2 H 4 O 2	3	2
Adrenaline	C 9 H 13 NO 3	5	6
Ammonia	NH 3	2	3
Anthracene	C 14 H 10	24	12
Benzene Ring	C 6 H 6	6	6
Benzoic Acid	C 7 H 6 O 2	9	8

Appendix

Table 3: Fundamental molecular motifs.

Motif Name	Construction Method	Functionality Description
Star Motif	Central node connected to all others	Generates a star structure with one center node connected to all peripheral nodes.
Path Motif	Nodes connected in sequence	Constructs a linear path where each node connects to the next in sequence.
Fan Motif	Central node with multiple branch nodes	Creates a fan-like shape with a central hub and several outward branches, possibly interconnected.
Cusped Polygon Motif	Polygon with potential branches	Builds a polygon structure with pointed (cusped) corners and optional branching substructures.
Random Bipartite Motif	Bipartite graph with random connections	Generates a bipartite graph where two partitions are randomly interconnected.
Tree Motif	Hierarchical branching structure	Constructs a tree graph where each node may connect to multiple child nodes.

Appendix

Table 4: Connector modules.

Link Rule	Description
Random Citation Generation	Each paper randomly cites a set of papers; the number of citations follows a Poisson distribution.
Citation by High Citation Count	Each paper cites papers with higher citation counts to increase connectivity among highly cited papers.
Co-Author Based Citation	Papers by authors who have collaborated with the current paper’s authors are preferentially cited.
Propagation-Based Citation	Citation links are simulated using an information diffusion model (e.g., Independent Cascade).
Topic Similarity-Based Citation	Papers with high topic similarity (e.g., via cosine similarity on keywords/abstracts) are cited.
Temporal Citation	Older papers are preferentially cited to simulate time-evolving citation behavior.

Appendix

Table 5: Citation Link Rules in Citation Network Construction

Type	Description
Normal Distribution	Generates node features based on a normal distribution with specified mean and standard deviation.
Uniform Distribution	Generates node features based on a uniform distribution over a specified range.
Exponential Distribution	Generates node features based on an exponential distribution.
Lognormal Distribution	Generates node features based on a lognormal distribution.
Gamma Distribution	Generates node features based on a gamma distribution.
Beta Distribution	Generates node features based on a beta distribution.

Appendix

Table 6: Node Feature Generation Methods based on Statistical Distributions and Mathematical Sequences

Panel of Figure 10 — Figure 10: Test Accuracy comparison with different bias.

Panel of Figure 11 — Figure 11: Validation accuracy upon training procedure.

Panel of Figure 12 — Figure 12: Motif Confounders

Panel of Figure 13 — Figure 13: Molecular Structure Confounders

Panel of Figure 14 — Figure 14: Citation Confounders

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Graph data is becoming increasingly prevalent due to the growing demand for relational insights in AI across various domains. Organizations regularly use graph data to solve complex problems involving relationships and connections. Causal learning is especially important in this context, since it helps to understand cause-effect relationships rather than mere associations. Since many real-world systems are inherently causal, graphs can efficiently model these systems. However, traditional graph machine learning methods including graph neural networks (GNNs), rely on correlations and are sensitive to spurious patterns and distribution changes. On the other hand, causal models enable robust predictions by isolating true causal factors, thus making them more stable under such shifts. Causal learning also helps in identifying and adjusting for confounders, ensuring that predictions reflect true causal relationships and remain accurate even under interventions. To address these challenges and build models that are robust and causally informed, we propose CCAGNN, a Confounder-Aware causal GNN framework that incorporates causal reasoning into graph learning, supporting counterfactual reasoning and providing reliable predictions in real-world settings. Comprehensive experiments on six publicly available datasets from diverse domains show that CCAGNN consistently outperforms leading state-of-the-art models.

Abstract

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