HEHRGNN: A Unified Embedding Model for Knowledge Graphs with Hyperedges and Hyper-Relational Edges

Rajesh Rajagopalamenon; Unnikrishnan Cheramangalath

cs.LGFeb 21, 2026

HEHRGNN: A Unified Embedding Model for Knowledge Graphs with Hyperedges and Hyper-Relational Edges

Authors: Rajesh Rajagopalamenon, Unnikrishnan Cheramangalath

Organizations: Department of Computer Science and Engineering, Indian Institute of Technology Palakkad, India

Abstract

Knowledge Graph(KG) has gained traction as a machine-readable organization of real-world knowledge for analytics using artificial intelligence systems. Graph Neural Network(GNN), is proven to be an effective KG embedding technique that enables various downstream tasks like link prediction, node classification, and graph classification. The focus of research in both KG embedding and GNNs has been mostly oriented towards simple graphs with binary relations. However, real-world knowledge bases have a significant share of complex and n-ary facts that cannot be represented by binary edges. More specifically, real-world knowledge bases are often a mix of two types of n-ary facts - (i) that require hyperedges and (ii) that require hyper-relational edges. Though there are research efforts catering to these n-ary fact types, they are pursued independently for each type. We propose $H$ yper $E$ dge $H$ yper- $R$ elational edge $GNN$ (HEHRGNN), a unified embedding model for n-ary relational KGs with both hyperedges and hyper-relational edges. The two main components of the model are i)HEHR unified fact representation format, and ii)HEHRGNN encoder, a GNN-based encoder with a novel message propagation model capable of capturing complex graph structures comprising both hyperedges and hyper-relational edges. The experimental results of HEHRGNN on link prediction tasks show its effectiveness as a unified embedding model, with inductive prediction capability, for link prediction across real-world datasets having different types of n-ary facts. The model also shows improved link prediction performance over baseline models for hyperedge and hyper-relational datasets.

Figures & tables

Model	Whether GNN-based	Types of Graphs supported
		GMR	GHE	GHR
HyPE [ 8 ]	✗	✓	✓	✗
MPNN-R [ 43 ]	✓	✓	✓	✗
HINGE [ 31 ]	✗	✓	✗	✓
STARE [ 11 ]	✓	✓	✗	✓
HGNN [ 10 ]	✓	✗	✓	✗

Table 1: Comparison of our work with related works

Figure 3: Data structures for HEHR unified fact representation

Panel of Figure 4 — Figure 4: HEHRGNN message propagation

Dataset	Type	Train facts	Valid facts	Test facts	$\|Entities\|$	$\|Relations\|$
JF17K [ 41 ]	HE	61911	15822	24915	28,645	322
FB-AUTO [ 8 ]	HE	6778	2255	2180	3410	8
M-FB15K [ 8 ]	HE	415375	39348	38797	10314	71
WD50K [ 11 ]	HR	166,435	23,913	46,159	47,156	532
WikiPeople [ 13 ]	HR	305725	38223	38281	47766	305
Combined-HEHR	HEHR	228346	24913	71074	75801	854

Table 2: Dataset Details (HE: Hyperedge, HR: Hyper-relational)

Model	JF17K				FB-AUTO				M-FB15K
	MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10
r-SimplE	0.102	0.069	0.112	0.168	0.106	0.082	0.115	0.147	0.051	0.042	0.054	0.070
m-DistMult	0.463	0.372	0.510	0.634	0.784	0.745	0.815	0.845	0.705	0.633	0.740	0.844
m-CP	0.391	0.298	0.443	0.563	0.752	0.704	0.785	0.837	0.680	0.605	0.715	0.828
m-TransH	0.444	0.370	0.475	0.581	0.728	0.727	0.728	0.728	0.623	0.531	0.669	0.809
HSimplE	0.472	0.378	0.520	0.645	0.798	0.766	0.821	0.855	0.730	0.664	0.763	0.859

Table 3: Link Prediction Results for Hyperedge Facts. Results of r-SimplE, m-DistMult, m-CP, m-TransH, HSimplE and HyPE are taken from [ 8 ]

Model	WD50K				WikiPeople
	MRR	Hits@1	Hits@3	Hits@10	MRR	Hits@1	Hits@3	Hits@10
m-TransH	-	-	-	-	0.063	0.063	-	0.300
RAE	-	-	-	-	0.059	0.059	-	0.306
NaLP-Fix	0.177	0.131	-	0.264	0.420	0.343	-	0.556
HINGE	0.243	0.176	-	0.377	0.476	0.415	-	0.585
STARE	0.349	0.271	-	0.496	0.491	0.398	0.592

Table 4: Link Prediction Results on Hyper-Relational Facts. Results of m-TransH, RAE, NaLP-Fix, HINGE, STARE are taken from [ 11 ]

Model	Combined-HEHR dataset
	MRR	Hits@1	Hits@3	Hits@10
HEHRGNN	0.612	0.385	0.458	0.562

Table 5: Link Prediction Results on Mix of Hyperedge and Hyper-Relational Facts

Panel of Figure 5 — Figure 5: Link Prediction Performance vs. Embedding Dimension

Panel of Figure 6 — Figure 6: Link Prediction Performance vs. Number of GNN layers

Dataset	Train facts	Valid facts	Test facts	$\|Entities\|$	$\|Relations\|$
Yago-6M	4463123	463781	1448986	5196467	127
Yago-4M	3708488	45678	3708488	4761044	127
Yago-2M	1817158	26523	108335	2502638	125

Table 6: Large datasets

Model	Yago-6M dataset
	MRR	Hits@1	Hits@3	Hits@10
HEHRGNN	0.506	0.315	0.603	0.956

Table 7: Link Prediction results on large dataset with millions of facts

	Dataset
	JF17K	WD50K	Combined-HEHR	Yago-2M	Yago-4M	Yago-6M
Memory(GB)	1.9	3.1	4.2	28	56	89
Compute(% utilization)	30	50	55	85	90	95

Table 8: Memory and Compute usage by HEHRGNN for different datasets(with embedding dimension of 128)

Dataset	WD50K		JF17K		Yago-4M			Yago-6M
Model	HEHRGNN	STARE	HypE	HEHRGNN	HypE	HEHRGNN	STARE	HypE	HEHRGNN	STARE
Memory(GB)	3.1	5.8	1.1	1.9	9	56	80	14	89	-
Compute(% utilization)	50	70	25	30	90	90	100	100	95	-

Table 9: Comparison of Memory and Compute usage by HEHRGNN and the two baselines

Panel of Figure 7 — Figure 7: Training curves of GNN-based encoder and Shallow embedding for WD50K dataset

Panel of Figure 8 — Figure 8: Comparison of MRR growth when WD50K is processed with and without qualifiers

Panel of Figure 9 — Figure 9: Comparison of MRR growth for the two different methods of updating relation embeddings

Dataset	Sample propagations for attaining MRR threshold	Calculation of sample propagations (No of facts in dataset x Epochs for threshold)
WD50K_33	1101090	73406 x 15
WD50K_66	791296	35968 x 22
WD50K_100	318332	22738 x 14

Table 10: Convergence on datasets with different ratios of qualifiers

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