HyperRAG: Reasoning N-ary Facts over Hypergraphs for Retrieval Augmented Generation

Wen-Sheng Lien; Yu-Kai Chan; Hao-Lung Hsiao; Bo-Kai Ruan; Meng-Fen Chiang; Chien-An Chen; Yi-Ren Yeh; Hong-Han Shuai

cs.CLFeb 16, 2026

HyperRAG: Reasoning N-ary Facts over Hypergraphs for Retrieval Augmented Generation

Authors: Wen-Sheng Lien, Yu-Kai Chan, Hao-Lung Hsiao, Bo-Kai Ruan, Meng-Fen Chiang, Chien-An Chen, Yi-Ren Yeh, Hong-Han Shuai

Organizations: National Yang Ming Chiao Tung University, Hsinchu, Taiwan · E.SUN Bank, Taipei, Taiwan · National Kaohsiung Normal University, Kaohsiung, Taiwan

Abstract

Graph-based retrieval-augmented generation (RAG) methods, typically built on knowledge graphs (KGs) with binary relational facts, have shown promise in multi-hop open-domain QA. However, their rigid retrieval schemes and dense similarity search often introduce irrelevant context, increase computational overhead, and limit relational expressiveness. In contrast, n-ary hypergraphs encode higher-order relational facts that capture richer inter-entity dependencies and enable shallower, more efficient reasoning paths. To address this limitation, we propose HyperRAG, a RAG framework tailored for n-ary hypergraphs with two complementary retrieval variants: (i) HyperRetriever learns structural-semantic reasoning over n-ary facts to construct query-conditioned relational chains. It enables accurate factual tracking, adaptive high-order traversal, and interpretable multi-hop reasoning under context constraints. (ii) HyperMemory leverages the LLM's parametric memory to guide beam search, dynamically scoring n-ary facts and entities for query-aware path expansion. Extensive evaluations on WikiTopics (11 closed-domain datasets) and three open-domain QA benchmarks (HotpotQA, MuSiQue, and 2WikiMultiHopQA) validate HyperRAG's effectiveness. HyperRetriever achieves the highest answer accuracy overall, with average gains of 2.95% in MRR and 1.23% in Hits@10 over the strongest baseline. Qualitative analysis further shows that HyperRetriever bridges reasoning gaps through adaptive and interpretable n-ary chain construction, benefiting both open and closed-domain QA.

Figures & tables

Figure 1. Structural Comparison of (a) Knowledge Graphs and (b) Hypergraphs. For a given question $q$ , (a) requires 3-hop reasoning over binary facts, while (b) enables single-hop inference via an $n$ -ary relational fact, yielding a more compact and expressive multi-entity representation.

Figure 2. The overall framework of HyperRAG.

Topic	RAPTOR		HippoRAG		ToG		HyperGraphRAG		HyperRetriever		HyperMemory		Rel. Gain (%)
Topic	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10
art	3.44	4.13	8.42	9.77	2.99	3.20	17.18	21.68	19.31	24.31	15.63	19.17	12.40	12.13
award	20.57	25.13	32.80	38.65	8.70	9.35	51.64	63.43	52.66	65.28	47.34	56.98	1.98	2.93
edu	4.94	5.90	23.82	26.37	9.09	9.49	43.44	50.05	44.79	51.63	41.68	46.95	3.11	3.16
health	18.85	22.04	25.72	29.59	7.14	7.95	31.46	37.94	32.68	39.26	27.48	33.13	3.88	3.48
infra	10.95	12.79	23.88	27.11	9.87	10.67	37.18	44.82	38.92	45.77	35.77	41.69	4.68	2.12

Table 1. Performance comparison of domain generalization across 11 diverse topics. The “Rel. Gain” column highlights the substantial relative improvement of our approach over the best baseline, averaged across all domains (metrics in %).

Model	HotpotQA		MuSiQue		2WikiMultiHopQA
Model	EM(%)	F1(%)	EM(%)	F1(%)	EM(%)	F1(%)
RAPTOR	35.50	41.56	15.00	16.31	22.50	22.95
HippoRAG	49.50	55.87	14.50	17.43	30.00	30.44
ToG	10.08	11.00	0 2.70	0 2.69	0 5.20	0 5.34
HyperGraphRAG	51.00	42.69	22.00	20.02	42.50	30.17
HyperRetriever	42.50	43.65	13.50	14.15	34.00	34.06

Table 2. Performance comparison on HotpotQA, MuSiQue, and 2WikiMultiHopQA. Rel. Gain (%) indicates the relative performance gains achieved by our model compared with the best baselines. The best results are bolded , and the second best are underlined .

Topic	Full		w/o Entities		w/o Hyperedges		w/o Chunks		w/o Adaptive Search		w Binary KG
Topic	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10	MRR	Hits@10
art	26.03	31.00	27.28	31.00	24.03	27.00	24.17	27.00	26.33	31.00	14.00	15.00
award	56.91	70.00	43.22	61.00	55.95	69.00	55.01	66.00	52.98	66.00	48.92	53.00
edu	49.00	56.00	43.24	52.00	47.93	52.00	42.67	47.00	47.53	53.00	38.20	42.00
health	41.25	47.00	37.17	43.00	37.70	40.00	39.33	47.00	39.20	46.00	36.17	39.00
infra	34.85	43.00	35.17	43.00	30.87	39.00	38.75	44.00	35.50	45.00	30.50	32.00

Table 3. Ablation on the Contribution of Context Formation and Adaptive Search. The full model incorporates all components essential for context formation, including entities, hyperedges involved in learnable relational chains, and retrieved chunks. The best results in MRR are bolded , and the best in Hits@10 are underlined .

Dimension	RAPTOR ( Sarthi et al., 2024 )	HippoRAG ( Gutiérrez et al., 2024 )	ToG ( Sun et al., 2024 )	HyperGraphRAG ( Luo et al., 2025a )	OG-RAG ( Sharma et al., 2024 )	HyperRetriever / Memory
Structure type	Doc tree (summ.)	KG (binary)	KG (binary)	Hypergraph ( $n$ -ary)	Object graph (mostly bin.)	Hypergraph ( $n$ -ary)
Unit of fact	Passage / summary	Entity-entity edge	Step / subgoal	Hyperedge ( $n$ -ary fact)	Object-object edge	Hyperedge ( $n$ -ary fact)
Candidate growth	Additive (levels)	Additive on edge	LLM-var.	Additive on hyperedges	Additive on objects	Additive on hyperedges
Per-query overhead	Tokens only	$\mathcal{O}(n{-}k)$	Var.	$\mathcal{O}(1)$ †	$\mathcal{O}(1)$	$\mathcal{O}(1)$ †
Depth for reasoning chain	Deep	Deep (pairwise)	LLM-var.	Shallow ( $n$ -ary edges)	Deep (pairwise)	Shallow ( $n$ -ary edges)
Retrieval strategy	Dense tree search	Graph walk + dense	LLM on graph	Static	Object-centric walk	Adaptive / LLM on graph

Table 4. Method Comparison. HyperRetriever utilizes adaptive search on

n

ary hyperedges, enabling higher-order reasoning with shallow chains and near constant per-query retrieval overhead

\mathcal{O}(1)

. In contrast, static or object-centric walks on binary graphs entail deeper pairwise chains and materialization cost.

\dagger

denotes bounded arity; ✓ indicates an ontology requirement.

Figure 3. The visualization shows the efficiency-effectiveness tradeoff in multi-hop QA: retrieval time (

x

-axis), answer quality (Hits@10,

y

-axis), and context volume (bubble size, log-scaled by retrieved tokens).

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4. Prompt for Entity Salience Scoring (

p_{\text{entity}}

Dataset	Train	Validation	Test	Total
Wikitopics	89815	89726	89749	269290
HotpotQA	640	160	200	1,000
MuSiQue	640	160	200	1,000
2WikiMultiHopQA	640	160	200	1,000

Appendix

Table 5. Statistics of QA benchmarks across domain settings

Panel of Figure 5 — Figure 5. Prompt templates for (a) Open-Domain Question Answering, and (b) Closed-Domain Question Answering.

Figure 6. Comparison of evidential

n

-ary relational chains. We contrast Ground-Truth (GT) answers with reasoning paths derived by ToG and HyperRetriever. While ToG operates on standard knowledge graphs restricted to binary relations, HyperRetriever leverages hypergraphs to preserve the semantic integrity of dense

n

-ary facts.

Panel of Figure 7 — Figure 7. Prompt for (a) Edge Plausibility Scoring, and (b) Context Relevance Evaluation.

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While retrieval-augmented generation (RAG) has proven effective at giving LLMs access to external knowledge, mainstream dense-retrieval implementations remain inherently limited in handling structured constraints and multi-hop reasoning. Graph-based methods address this by constructing knowledge graphs offline, but they often fragment semantics, incur high maintenance, and complicate incremental updates. We propose SAG (SQL-Retrieval Augmented Generation), a structured retrieval architecture that organizes documents into an event-entity index without building a global knowledge graph. SAG represents each chunk as a semantically complete event paired with its entities, forming a latent hyperedge that preserves n-ary relations without decomposing them into triples. At query time, SAG treats shared entities as join keys to connect related chunks. This dynamically yields a query-scoped neighborhood of events, and yet every piece of evidence remains the original chunk throughout. Experiments on HotpotQA, 2WikiMultiHopQA, and MuSiQue show that SAG achieves the best retrieval and end-to-end QA performance on every benchmark, with gains that widen as reasoning-chain complexity increases. On MuSiQue, where multi-hop evidence chaining is most demanding, SAG reaches 80.36% Recall@5, outperforming the strongest baseline by 11.52 points. This work paves the way for knowledge infrastructure that enables LLM agents to retrieve and reason over continually growing organizational knowledge.

Abstract

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