Knowledge Is Not Static: Order-Aware Hypergraph RAG for Language Models
Organizations: Texas A&M University · University of Illinois Urbana-Champaign · The University of Kansas
Abstract
Retrieval-augmented generation (RAG) enhances large language models by grounding outputs in retrieved knowledge. However, existing RAG methods including graph- and hypergraph-based approaches treat retrieved evidence as an unordered set, implicitly assuming permutation invariance. This assumption is misaligned with many real-world reasoning tasks, where outcomes depend not only on which interactions occur, but also on the order in which they unfold. We propose Order-Aware Knowledge Hypergraph RAG (OKH-RAG), which treats order as a first-class structural property. OKH-RAG represents knowledge as higher-order interactions within a hypergraph augmented with precedence structure, and reformulates retrieval as sequence inference over hyperedges. Instead of selecting independent facts, it recovers coherent interaction trajectories that reflect underlying reasoning processes. A learned transition model infers precedence directly from data without requiring explicit temporal supervision. We evaluate OKH-RAG on order-sensitive question answering and explanation tasks, including tropical cyclone and port operation scenarios. OKH-RAG consistently outperforms permutation-invariant baselines, and ablations show that these gains arise specifically from modeling interaction order. These results highlight a key limitation of set-based retrieval: effective reasoning requires not only retrieving relevant evidence, but organizing it into structured sequences.
Figures & tables
| Method | TF | MC | SA | TD | Overall |
|---|---|---|---|---|---|
| Text-RAG | 0.694 | 0.378 | 0.198 | 0.224 | 0.287 |
| GraphRAG | 0.806 | 0.506 | 0.321 | 0.362 | 0.414 |
| HyperGraphRAG | 0.819 | 0.620 | 0.435 | 0.432 | 0.511 |
| OKH-RAG (ours) | 0.833 | 0.652 | 0.452 | 0.441 | 0.534 |
| Group | Variant | TF | MC | SA | TD | Overall | |
| Full Model | OKH-RAG (full) | 0.833 | 0.652 | 0.452 | 0.441 | 0.534 | — |
| Shuffle | OKH-RAG (shuffled) | 0.750 | 0.618 | 0.397 | 0.399 | 0.487 | 0.047 |
| Components | (order coherence) | 0.833 | 0.650 | 0.449 | 0.445 | 0.532 | 0.002 |
| (precedence) | 0.819 | 0.633 | 0.434 | 0.395 | 0.510 | 0.024 | |
| (entity continuity) | 0.819 | 0.646 | 0.440 | 0.407 | 0.519 | 0.015 | |
| (phase coverage) | 0.819 | 0.633 | 0.434 | 0.395 | 0.510 | 0.024 |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| # | Family | Representative relations |
|---|---|---|
| 1 | Cyclone state | has_cyclone_state , has_category_state , has_motion |
| 2 | Track & landfall | forecasts_track , forecasts_landfall |
| 3 | Timing | has_hours_to_landfall , has_forecast_window |
| 4 | Advisory | has_watch_status , has_warning_status |
| 5 | Probability | has_leadtime_probability , has_cumulative_probability |
| 6 | Hazard forecast | forecasts_hazard_at_horizon |