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This paper claims that organizing retrieved evidence into confidence-propagated hypergraph chains, and feeding the LLM explicit supporting and contradictory evidence paths, substantially improves multi-hop question answering over flat or pa

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2026-08-02 11:31 UTC pith:AHOIIE6K

load-bearing objection A plausible post-retrieval hypergraph evidence-chain framework whose math is sound but whose headline gains rest on an under-specified, partly self-referential LLM-judge evaluation; worth refereeing, not accepting as-is. the 3 major comments →

arxiv 2607.22597 v1 pith:AHOIIE6K submitted 2026-06-12 cs.AI

HyCE-RAG: Hypergraph Chain-of-Evidence Retrieval-Augmented Generation for Explainable Multi-hop Question Answering

Hong-Yu An , Yun-Jian Zhang , Chen-Wei Liang , Tian-Yi Zhang , Jian Ding , Yi-Lun Wu , Ao-Bo Li , Wei-Cong Su
show 2 more authors
Saifullah Mujiangshan Wang
This is my paper
classification cs.AI
keywords multi-hop question answeringretrieval-augmented generationhypergraphevidence chainconfidence propagationfaithfulnessexplainabilitystructured context
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

HyCE-RAG tries to establish that the post-retrieval stage of retrieval-augmented generation should be structured reasoning, not just passage concatenation. It builds a query-aware hypergraph over entities, relations, and evidence units, propagates query confidence through that structure, and assembles the highest-confidence paths into labeled evidence chains for the LLM. The paper reports consistent gains across five datasets, including an 11.4-to-29.6 absolute point improvement in answer correctness over the strongest baseline on HotpotQA, 2Wiki, and MuSiQue. A sympathetic reader would care because the approach directly targets a known weakness of RAG—connecting scattered facts and suppressing distractors—and offers a concrete mechanism for more faithful, interpretable answers.

Core claim

HyCE-RAG's central claim is that representing evidence as hyperedges—where one edge can connect multiple entities that jointly support a fact—and then propagating confidence over the entity–hyperedge incidence graph yields better multi-hop QA than standard chunk retrieval or pairwise graph retrieval. After propagation, the system scores and selects evidence units by combining coverage, propagated confidence, extraction confidence, entry-entity presence, and relation reliability, then separates them into supporting and lower-confidence paths. The paper argues this structured context helps the LLM focus on the true reasoning chain while staying aware of conflicting evidence, and reports that t

What carries the argument

The load-bearing object is the query-aware evidence hypergraph, where vertices are entities or evidence units and hyperedges encode higher-order associations among multiple entities within a textual segment. Confidence is propagated over this structure via a two-stage random walk with restart (Eq. 27), which the paper proves converges to a unique fixed point because the transition matrix is column-stochastic; the fixed point assigns each entity a question-conditioned importance. The propagated scores feed a confidence-guided evidence assembly that builds compact hyperedge-centered paths, fuses redundant ones by Jaccard overlap, and separates supporting from lower-confidence paths before gene

Load-bearing premise

The load-bearing premise is that the LLM-as-a-judge evaluation protocol (with the same model family used for construction, generation, and judging) ranks the methods correctly and does not systematically reward HyCE-RAG's confidence-labeled structured context format over the content of other baselines' contexts.

What would settle it

Re-run the comparison on HotpotQA and MuSiQue with a different judge model (e.g., an open-weight model from another family) or with standard Exact Match / F1 on the gold answers, and additionally feed the baselines the same supporting/contradictory labeled context structure with confidence scores. If HyCE-RAG's accuracy gains drop below significance or shrink to a few points, the central claim that hypergraph-structured evidence organization causes the improvement would be falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If HyCE-RAG is correct, post-retrieval evidence organization—not just retrieval quality—is a major lever for multi-hop QA accuracy and faithfulness.
  • Hypergraph construction alone is insufficient: the ablation shows that confidence propagation and hyperedge-based assembly each add substantial accuracy on MuSiQue, so the reasoning thread within the retrieved structure matters.
  • Explicitly labeling supporting versus contradictory evidence paths helps the LLM ground answers and reduce the influence of off-path distractors, as illustrated in the four-hop case study.
  • The framework's gains scale to domain-specific settings (medical, novel narrative), suggesting the mechanism transfers beyond Wikipedia-style benchmarks.
  • Because the hypergraph is built offline and online inference uses sparse matrix operations, structured evidence reasoning can be added without fundamentally changing the online generation pipeline.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reported gains may partly reflect a measurement instrument bias: the same model family (gpt-oss-120b) builds the hypergraph, judges correctness/relevance/faithfulness, and generates answers, and the faithfulness judge sees HyCE-RAG's confidence-labeled context. An independent test with a different judge model or standard EM/F1 metrics would reveal how much of the 11–30 point gains is format pr
  • The evaluation blends LLM judgments with embedding similarity using coefficients α and λ (Eqs. 44–45) that are never reported. Since these weights shape every score, publishing them and varying them would be a simple robustness check.
  • A concrete extension would be to feed baselines the same structured supporting/contradictory context labels (with confidence scores) and see whether the accuracy gap narrows—that would isolate whether the benefit comes from the hypergraph's structural reasoning or merely from the labeled context format.
  • The offline hypergraph construction cost is described as one-time, but the extraction quality still depends on the LLM; on noisy or low-resource domains, extraction errors could propagate through confidence propagation and mislead evidence assembly, an area the paper does not stress-test.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. HyCE-RAG proposes a retrieval-augmented generation framework for multi-hop QA that organizes entities, relations, and evidence units into a hypergraph, propagates query-conditioned confidence over the entity--hyperedge incidence structure, and then assembles supporting/contradictory evidence chains for the generator. The paper's central claim is that this structured post-retrieval organization yields consistent double-digit gains over vector RAG and graph RAG baselines on HotpotQA, 2Wiki, MuSiQue, and two GraphRAG-Bench subsets in answer correctness, context relevance, and faithfulness. The mathematical framework is presented in detail (Sections 3.2--3.3, Appendix B), and the empirical evaluation uses LLM-as-a-judge metrics defined in Eqs. (43)--(46).

Significance. If the empirical claim were established, the paper would make a useful contribution: it gives a principled way to move from flat passage or pairwise-graph context to higher-order, confidence-ranked evidence chains, and the propagation/assembly components are modular and clearly specified. The convergence proof in Appendix B is correct, and the method is a plausible direction for post-retrieval reasoning. However, the empirical support is not currently convincing: the headline gains rest on an unreported-coefficient judge-based metric whose judge is the same model family used to construct HyCE-RAG's contexts, and no standard QA metrics, confidence intervals, or human evaluation are provided. The framework's mathematical heart is sound, but the validation is the load-bearing part of the paper and is not yet established.

major comments (3)
  1. [§4.1.3, Eqs. (43)–(46); §4.1.4; Tables 1–2] The headline claim in §4.2 ('HyCE-RAG consistently achieves the best performance across all datasets and all applicable metrics') rests entirely on the LLM-as-a-judge protocol. Two issues make this unverifiable. First, the blend coefficients α in Eq. (44) and λ in Eq. (45) are never reported, so the Acc and Rel values cannot be recomputed or interpreted; depending on α, 'answer correctness' could be mostly embedding similarity rather than factual content. Second, the judge is gpt-oss-120, the same model family used for hypergraph extraction, evidence-chain assembly, and answer generation. Faithfulness (Eq. 46) asks this judge whether answer statements are supported by the retrieved context, and HyCE-RAG's context explicitly labels paths as supporting/contradictory with evidence scores and extraction confidences, whereas baselines receive flat or graph contexts without such labels. This i
  2. [Tables 1–3] All reported values are single-point estimates with no variance, sample size, or significance testing. Given the stochasticity of both LLM generation and judge scoring, the observed double-digit gaps cannot be distinguished from run-to-run noise without repeated runs or confidence intervals. This is particularly important for the domain-specific GraphRAG-Bench subsets, where the test sets are smaller and the baselines vary widely. The authors should report statistics over multiple independent runs, and ideally include a second independent judge or human evaluation to confirm the ranking.
  3. [Eq. (32) and Appendix C] The method is not fully reproducible as specified. The five evidence-score weights w_cov, w_prop, w_ext, w_entry, w_rel in Eq. (32) are never given, and neither are β (Eq. 16), α (Eq. 22), λ (Eq. 27), θ_v (Eq. 30), θ_s (Eq. 40), or τ (Eq. 39). Appendix C reports only the entry-entity count, expansion hops, propagation steps, selected evidence units, and final context segments. Without these hyperparameters, the exact algorithm cannot be reimplemented, and the claimed robustness across five datasets cannot be checked. This is secondary to the evaluation-metric issue but still blocks verification.
minor comments (4)
  1. [Eq. (1)] The contradiction score δ_q appears in the pipeline definition and in the Generate step, but it is never defined in the text and is absent from the actual generation equation (42). Either define it explicitly or remove it from the formal pipeline.
  2. [Notation] The same symbols are overloaded: α is used for the initial-score blend in Eq. (22) and for the accuracy blend in Eq. (44); λ is used for the restart strength in Eq. (27) and for the relevance blend in Eq. (45). Distinct symbols should be used to avoid confusion.
  3. [§4.1.4] The backbone model is referred to as both 'gpt-oss-120' and 'gpt-oss-120b' (Ref. [21]); please standardize the name consistently.
  4. [Table 4] The case-study table uses long arrow chains that are already difficult to read in the text; use a clearer path notation, such as 'entity --relation--> entity', with scores in a separate column.

Circularity Check

0 steps flagged

No circularity: HyCE-RAG's method construction and benchmark comparisons are anchored in external datasets and an independent convergence proof; the LLM-judge protocol is a validity concern, not a by-construction circular step.

full rationale

The paper's central claims are empirical benchmark results against external datasets (HotpotQA, 2WikiMultihopQA, MuSiQue, GraphRAG-Bench) and a method design whose core formal component—the confidence-propagation fixed point—is proved independently in Appendix B (Eqs. 57–68). The evidence-scoring heuristic of Eq. 32 is a defined combination of retrieval signals, not a quantity fitted to the evaluation outcome. The evaluation metrics in Eqs. 43–46 are LLM-as-a-judge measurements, and there is a legitimate validity threat in that the judge (gpt-oss-120b) is the same model family used to construct HyCE-RAG's contexts and sees HyCE-RAG's supporting/contradictory labels and confidence scores, which could bias Acc/Rel/Faith scores. Also, coefficients α, λ, and the weights in Eq. 32 are unreported, making the numbers hard to reproduce. However, this is a measurement-design and reproducibility concern, not a circular derivation: no equation in the paper defines the judge's verdict as equivalent to HyCE-RAG's own labels or scores, and the comparisons are not predictions derived from the method's equations. The self-citations ([11], [26]–[29], [37]) are contextual related-work references and are not load-bearing for the central claim. Therefore no specific circular step can be exhibited, and the honest finding is no significant circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The framework is transparent about most structural choices, but the central empirical claims rest on several unreported free parameters and on assumptions about extraction quality and judge neutrality. The one standard_math axiom (convergence) is proven in the paper and is not itself a risk; the risks are the domain assumptions (extraction fidelity, entry-entity recall) and, above all, the ad hoc evaluation axiom that an LLM judge from the same family as the generator ranks all methods without bias.

free parameters (4)
  • Evidence-score weights w_cov, w_prop, w_ext, w_entry, w_rel (Eq. 32) = not reported
    These five weights determine which evidence units are selected and therefore directly shape every number in Tables 1–3. The paper calls them 'tunable hyperparameters' but never reports values; Appendix C lists only five unrelated budget parameters.
  • Accuracy blend α (Eq. 44) and relevance blend λ (Eq. 45) = not reported
    These coefficients define the dependent variables Acc and Rel for all methods; without their values the scores are not reproducible, and test-set tuning of them would make the headline gains fitted rather than predicted.
  • Structural/retrieval hyperparameters: β (Eq. 16), α (Eq. 22), λ restart (Eq. 27), θ_v (Eq. 30), θ_s (Eq. 40), τ (Eq. 39) = not reported
    β, α, λ, θ_v, θ_s and the Jaccard threshold τ control retrieval, propagation, and the split into 'supporting' vs 'contradictory' evidence; none of their values is reported.
  • Budgets K_v (5), hops (4), steps (10), evidence units (15), context segments (6); K_h, L, O = 5 / 4 / 10 / 15 / 6; K_h, L, O not reported
    Appendix C reports entry entities, expansion hops, propagation steps, selected evidence units, and final context segments. K_h (Eq. 19), chunk length L and overlap O (Eq. 2) are unreported, and these determine what the LLM ever sees.
axioms (4)
  • standard math The transition matrix S = B D_e^-1 B^T D_v^-1 is column-stochastic with spectral radius ≤ 1, so Eq. (27) converges to the unique fixed point of Eq. (28).
    Proven in Appendix B under the stated removal of isolated vertices and empty hyperedges; the proof is a correct Neumann-series argument and does not by itself threaten the central claim.
  • domain assumption LLM-based extraction of entities, hyperedges, relations, and confidence scores from chunks yields a corpus hypergraph that preserves the true evidence structure.
    Invoked in §3.2 and Appendix A; extraction is performed by gpt-oss-120b with no verification step. The paper itself adds γ(e) as a 'noise-aware safeguard' (§3.3.4), acknowledging extraction errors are expected; if extraction systematically mangles relations, the resulting evidence chains are spurious.
  • domain assumption The entry entity set E_0 (LLM-extracted mentions plus top-5 vector matches) always contains an anchor entity from which gold evidence is reachable within the 4-hop expansion.
    The entire online pipeline (§3.3.1–3.3.2) depends on E_0; no backtracking or alternate-anchor mechanism is described. With K_v = 5 entry entities and 4 expansion hops (Appendix C), a missed anchor entity excludes the correct reasoning path from the query-aware hypergraph.
  • ad hoc to paper The LLM-as-a-judge protocol (Eqs. 43–46) ranks all methods without systematic bias toward HyCE-RAG's structured, confidence-labeled context.
    Evaluator and generator are the same model family (gpt-oss-120b), and HyCE-RAG's context embeds the supporting/contradictory labels and confidence scores the judge is asked to verify; no validation against human judgments or standard metrics is provided.

pith-pipeline@v1.3.0-alltime-deepseek · 20859 in / 33437 out tokens · 330238 ms · 2026-08-02T11:31:54.706929+00:00 · methodology

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read the original abstract

Multi-hop question answering requires systems to retrieve evidence from multiple documents and connect scattered facts into a coherent reasoning process. Standard retrieval-augmented generation (RAG) mainly relies on semantic similarity between a query and text chunks, and therefore often fails to model structural relations among entities, facts, and evidence units. Graph-based RAG improves this by introducing graph-structured knowledge, but pairwise edges are still limited in representing higher-order associations involving multiple entities and contexts. We propose HyCE-RAG, a Hypergraph Chain-of-Evidence Retrieval-Augmented Generation framework for explainable multi-hop question answering. HyCE-RAG organizes entities, relations, and contextual evidence into hyperedges, builds a query-aware evidence hypergraph, and performs confidence propagation over entity--hyperedge incidence structures. It then uses confidence-guided evidence assembly to select, connect, and rank evidence paths before answer generation. The scoring process jointly considers semantic relevance, entity connectivity, evidence coverage, relation reliability, extraction confidence, and propagated confidence. By providing the language model with structured evidence chains rather than flat retrieved passages, HyCE-RAG supports more faithful and interpretable reasoning. Experiments on HotpotQA, 2WikiMultihopQA, MuSiQue, and two GraphRAG-Bench subsets show that HyCE-RAG consistently outperforms standard RAG and graph-based RAG baselines in answer accuracy, context relevance, and faithfulness. These results suggest that hypergraph-based evidence organization is a promising direction for post-retrieval reasoning in complex question answering.

Figures

Figures reproduced from arXiv: 2607.22597 by Ao-Bo Li, Chen-Wei Liang, Hong-Yu An, Jian Ding, Mujiangshan Wang, Saifullah, Tian-Yi Zhang, Wei-Cong Su, Yi-Lun Wu, Yun-Jian Zhang.

Figure 1
Figure 1. Figure 1: Cverview of the proposed HyCE-RAG framework. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Conceptual comparison among Naive RAG, GraphRAG, and HyCE-RAG. HyCE-RAG constructs confidence-guided evidence chains over hypergraph representations for structured post-retrieval reasoning. However, conventional graphs mainly represent pairwise relations between entities, which may be insufficient for complex reasoning scenarios where multiple entities, events, relations, or evidence units jointly support … view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the proposed HyCE-RAG framework. HyCE-RAG first builds an offline hypergraph store from corpus level evidence, and then retrieves a query aware hypergraph for a given question. Confidence propagation estimates the importance of entities and hyperedges through their incidence links. Evidence units with high confidence and potential divergence are organized into a structured context for large lan… view at source ↗

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Reference graph

Works this paper leans on

43 extracted references · 11 linked inside Pith

  1. [1]

    A survey on rag with llms

    Arslan, M., Ghanem, H., Munawar, S., Cruz, C., 2024. A survey on rag with llms. Procedia computer science 246, 3781–3790

    2024

  2. [2]

    Learningtoretrievereasoningpathsoverwikipediagraphforquestion answering

    Asai, A., Hashimoto, K., Hajishirzi, H., Socher, R., Xiong, C., 2019. Learningtoretrievereasoningpathsoverwikipediagraphforquestion answering. arXiv preprint arXiv:1911.10470

    Pith/arXiv arXiv 2019

  3. [3]

    Self-rag: Learningtoretrieve,generate,andcritiquethroughself-reflection,in: Internationalconferenceonlearningrepresentations,pp.9112–9141

    Asai, A., Wu, Z., Wang, Y., Sil, A., Hajishirzi, H., 2024. Self-rag: Learningtoretrieve,generate,andcritiquethroughself-reflection,in: Internationalconferenceonlearningrepresentations,pp.9112–9141

    2024

  4. [4]

    Multi-hop question answering via reasoning chains

    Chen, J., Lin, S.t., Durrett, G., 2019. Multi-hop question answering via reasoning chains. arXiv preprint arXiv:1910.02610

    Pith/arXiv arXiv 2019

  5. [5]

    From local to global:Agraphragapproachtoquery-focusedsummarization

    Edge,D.,Trinh,H.,Cheng,N.,Bradley,J.,Chao,A.,Mody,A.,Truitt, S., Metropolitansky, D., Ness, R.O., Larson, J., 2024. From local to global:Agraphragapproachtoquery-focusedsummarization. arXiv preprint arXiv:2404.16130

    Pith/arXiv arXiv 2024

  6. [6]

    Retrieval- augmented generation for large language models: A survey

    Gao, Y., Xiong, Y., Gao, X., Jia, K., Pan, J., Bi, Y., Dai, Y., Sun, J., Guo, Q., Wang, M., Wang, H., 2023. Retrieval- augmented generation for large language models: A survey. CoRR abs/2312.10997. URL:https://doi.org/10.48550/arXiv.2312.10997, doi:10.48550/ARXIV.2312.10997,arXiv:2312.10997

    Pith/arXiv arXiv doi:10.48550/arxiv.2312.10997 2023

  7. [7]

    Lightrag: Simple and fast retrieval-augmented generation

    Guo, Z., Xia, L., Yu, Y., Ao, T., Huang, C., 2024. Lightrag: Simple and fast retrieval-augmented generation. arXiv preprint arXiv:2410.05779 2

    Pith/arXiv arXiv 2024

  8. [8]

    A comprehensive survey ofretrieval-augmentedgeneration(rag):Evolution,currentlandscape and future directions

    Gupta, S., Ranjan, R., Singh, S.N., 2024. A comprehensive survey ofretrieval-augmentedgeneration(rag):Evolution,currentlandscape and future directions. arXiv preprint arXiv:2410.12837

    Pith/arXiv arXiv 2024

  9. [9]

    REALM: retrieval-augmented language model pre-training

    Guu, K., Lee, K., Tung, Z., Pasupat, P., Chang, M., 2020. REALM: retrieval-augmented language model pre-training. CoRR abs/2002.08909. URL:https://arxiv.org/abs/2002.08909, arXiv:2002.08909

    Pith/arXiv arXiv 2020

  10. [10]

    Con- structing a multi-hop qa dataset for comprehensive evaluation of reasoningsteps,in:Proceedingsofthe28thInternationalConference on Computational Linguistics, pp

    Ho, X., Nguyen, A.K.D., Sugawara, S., Aizawa, A., 2020. Con- structing a multi-hop qa dataset for comprehensive evaluation of reasoningsteps,in:Proceedingsofthe28thInternationalConference on Computational Linguistics, pp. 6609–6625

    2020

  11. [11]

    Jian, Y., Tian, D., Chen, X.J., Wei, Z.Y., Liang, C.W., Wang, M.J.S.,

  12. [12]

    Retrieve, summarize, plan: Advancing multi-hop question answering with an iterative ap- proach, in: Companion Proceedings of the ACM on Web Conference 2025, pp

    Jiang, Z., Sun, M., Liang, L., Zhang, Z., 2025. Retrieve, summarize, plan: Advancing multi-hop question answering with an iterative ap- proach, in: Companion Proceedings of the ACM on Web Conference 2025, pp. 1677–1686

    2025

  13. [13]

    Active retrieval augmented generation, in: Proceedings of the 2023 conference on empirical methods in natural language processing, pp

    Jiang,Z.,Xu,F.F.,Gao,L.,Sun,Z.,Liu,Q.,Dwivedi-Yu,J.,Yang,Y., Callan, J., Neubig, G., 2023. Active retrieval augmented generation, in: Proceedings of the 2023 conference on empirical methods in natural language processing, pp. 7969–7992

    2023

  14. [14]

    Densepassageretrievalforopen-domainquestion answering, in: Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP), pp

    Karpukhin,V.,Oguz,B.,Min,S.,Lewis,P.,Wu,L.,Edunov,S.,Chen, D.,Yih,W.t.,2020. Densepassageretrievalforopen-domainquestion answering, in: Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP), pp. 6769–6781

    2020

  15. [15]

    Efficient memory man- agement for large language model serving with pagedattention, in: Proceedings of the ACM SIGOPS 29th Symposium on Operating Systems Principles

    Kwon, W., Li, Z., Zhuang, S., Sheng, Y., Zheng, L., Yu, C.H., Gonzalez, J.E., Zhang, H., Stoica, I., 2023. Efficient memory man- agement for large language model serving with pagedattention, in: Proceedings of the ACM SIGOPS 29th Symposium on Operating Systems Principles

    2023

  16. [16]

    Retrieval-augmented generation for knowledge-intensive nlp tasks

    Lewis, P., Perez, E., Piktus, A., Petroni, F., Karpukhin, V., Goyal, N., Küttler, H., Lewis, M., Yih, W.t., Rocktäschel, T., et al., 2020. Retrieval-augmented generation for knowledge-intensive nlp tasks. Advances in neural information processing systems 33, 9459–9474

    2020

  17. [17]

    Advances in Neural Information Processing Systems 38, 152206–152234

    Luo, H., Chen, G., Zheng, Y., Wu, X., Guo, Y., Lin, Q., Feng, Y., Kuang,Z.,Song,M.,Zhu,Y.,etal.,2026a.Hypergraphrag:Retrieval- augmented generation via hypergraph-structured knowledge repre- sentation. Advances in Neural Information Processing Systems 38, 152206–152234

  18. [18]

    Gfm-rag:graphfoundationmodelforretrievalaugmentedgeneration

    Luo, L., Zhao, Z., Haffari, R., Phung, D., Gong, C., Pan, S., 2026b. Gfm-rag:graphfoundationmodelforretrievalaugmentedgeneration. Advances in Neural Information Processing Systems 38, 36371– 36405

  19. [19]

    Multi-hopquestionanswering

    Mavi,V.,Jangra,A.,Jatowt,A.,2024. Multi-hopquestionanswering. Foundations and Trends®in Information Retrieval 17, 457–586

    2024

  20. [20]

    Ordered and hamilton digraphs

    Mu-Jiang-shan, W., Jun, Y., Shang-wei, L., et al., 2010. Ordered and hamilton digraphs. Chinese Quarterly Journal of Mathematics 25, 317–326

    2010

  21. [21]

    gpt-oss-120b & gpt-oss-20b model card

    OpenAI, 2025. gpt-oss-120b & gpt-oss-20b model card. URL: https://arxiv.org/abs/2508.10925,arXiv:2508.10925

    Pith/arXiv arXiv 2025

  22. [22]

    IEEE Transactions on Knowledge and Data Engineering 36, 3580–3599

    Pan,S.,Luo,L.,Wang,Y.,Chen,C.,Wang,J.,Wu,X.,2024.Unifying large language models and knowledge graphs: A roadmap. IEEE Transactions on Knowledge and Data Engineering 36, 3580–3599

    2024

  23. [23]

    Howmuchknowledgecan you pack into the parameters of a language model?, in: Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP), pp

    Roberts,A.,Raffel,C.,Shazeer,N.,2020. Howmuchknowledgecan you pack into the parameters of a language model?, in: Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP), pp. 5418–5426

    2020

  24. [24]

    Transactions of the Association for Computational Linguistics 10, 539–554

    Trivedi, H., Balasubramanian, N., Khot, T., Sabharwal, A., 2022.♪ musique: Multihop questions via single-hop question composition. Transactions of the Association for Computational Linguistics 10, 539–554

    2022

  25. [25]

    Trivedi, H., Balasubramanian, N., Khot, T., Sabharwal, A., 2023. Interleavingretrievalwithchain-of-thoughtreasoningforknowledge- intensive multi-step questions, in: Proceedings of the 61st annual meeting of the association for computational linguistics (volume 1: long papers), pp. 10014–10037

    2023

  26. [26]

    Diagnosability of cayley graph networks generated by transposition trees under the comparison diagnosis model

    Wang, M., Wang, S., 2016. Diagnosability of cayley graph networks generated by transposition trees under the comparison diagnosis model. Annals of Applied Mathematics 32, 166–173

    2016

  27. [27]

    The edge connectivity of expanded k-ary n-cubes

    Wang, S., Wang, M., 2018. The edge connectivity of expanded k-ary n-cubes. Discrete Dynamics in Nature and Society 2018, 7867342

    2018

  28. [28]

    Embedding paths into the4-aryn-cubewithfaultynodes,in:2011InternationalConference onConsumerElectronics,CommunicationsandNetworks(CECNet), IEEE

    Wang, S., Wangmu, J., Qi, Z., Ren, Y., 2011. Embedding paths into the4-aryn-cubewithfaultynodes,in:2011InternationalConference onConsumerElectronics,CommunicationsandNetworks(CECNet), IEEE. pp. 4949–4951

    2011

  29. [29]

    Fstgat:Financialspatio-temporalgraphattention network for non-stationary financial systems and its application in stock price prediction

    Wei, Z.L., An, H.Y., Yao, Y., Su, W.C., Li, G., Saifullah, Sun, B.F., Wang,M.J.S.,2025. Fstgat:Financialspatio-temporalgraphattention network for non-stationary financial systems and its application in stock price prediction. Symmetry 17, 1344

    2025

  30. [30]

    Xiang, Z., Wu, C., Zhang, Q., Chen, S., Hong, Z., Huang, X., Su, J.,

  31. [31]

    Graphrag-bench: Challenging domain-specific reasoningforevaluatinggraphretrieval-augmentedgeneration

    Xiao, Y., Dong, J., Zhou, C., Dong, S., Zhang, Q.w., Yin, D., Sun, X., Huang, X., 2025. Graphrag-bench: Challenging domain-specific reasoningforevaluatinggraphretrieval-augmentedgeneration. arXiv preprint arXiv:2506.02404

    Pith/arXiv arXiv 2025

  32. [32]

    Answering complex open-domainquestionswithmulti-hopdenseretrieval

    Xiong, W., Li, X.L., Iyer, S., Du, J., Lewis, P., Wang, W.Y., Mehdad, Y., Yih, W.t., Riedel, S., Kiela, D., et al., 2020. Answering complex open-domainquestionswithmulti-hopdenseretrieval. arXivpreprint arXiv:2009.12756

    Pith/arXiv arXiv 2020

  33. [33]

    Xu, D., Zhang, Z., Lin, Z., Wu, X., Zhu, Z., Xu, T., Zhao, X., Zheng, Y., Chen, E., 2024. Multi-perspective improvement of knowledge graph completion with large language models, in: Proceedings of the 2024jointinternationalconferenceoncomputationallinguistics,lan- guage resources and evaluation (LREC-COLING 2024), pp. 11956– 11968

    2024

  34. [34]

    Hotpotqa: A dataset for diverse, explainable multi-hopquestionanswering,in:Proceedingsofthe2018conference onempiricalmethodsinnaturallanguageprocessing,pp.2369–2380

    Yang,Z.,Qi,P.,Zhang,S.,Bengio,Y.,Cohen,W.,Salakhutdinov,R., Manning, C.D., 2018. Hotpotqa: A dataset for diverse, explainable multi-hopquestionanswering,in:Proceedingsofthe2018conference onempiricalmethodsinnaturallanguageprocessing,pp.2369–2380

    2018

  35. [35]

    Yao,S.,Zhao,J.,Yu,D.,Du,N.,Shafran,I.,Narasimhan,K.,Cao,Y.,

  36. [36]

    Ragpowered llmsforqa:Evolution,challenges,applications,andfuturedirections, in: 2025 International Conference on Communication Technologies (ComTech), IEEE

    Zeeshan,H.M.A.,Faizan,M.,Zia,U.,Gohar,A.,2025. Ragpowered llmsforqa:Evolution,challenges,applications,andfuturedirections, in: 2025 International Conference on Communication Technologies (ComTech), IEEE. pp. 1–6

    2025

  37. [37]

    Zhao, L., Wang, M., Zhang, X., Lin, Y., Wang, S., 2017. An algorithm for the orientation of complete bipartite graphs, in: 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017), Atlantis Press. pp. 361–364

    2017

  38. [38]

    A survey of large language models

    Zhao, W.X., Zhou, K., Li, J., Tang, T., Dong, Z., Hou, Y., Zhang, B., Min, Y., Zhang, J., Liu, P., et al., 2026. A survey of large language models. Frontiers of Computer Science 20, 2012627

    2026

  39. [39]

    Zhu, X., Xie, Y., Liu, Y., Li, Y., Hu, W., 2025. Knowledge graph- guided retrieval augmented generation, in: Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Associa- tion for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), pp. 8912–8924

    2025

  40. [40]

    Linearrag: Linear graph retrieval augmented generationonlarge-scalecorpora

    Zhuang,L.,Chen,S.,Xiao,Y.,Zhou,H.,Zhang,Y.,Chen,H.,Zhang, Q., Huang, X., 2025. Linearrag: Linear graph retrieval augmented generationonlarge-scalecorpora. arXivpreprintarXiv:2510.10114. Hong-Yu An et al.:Preprint submitted to ElsevierPage 16 of 16

    arXiv 2025

  41. [2022]

    arXiv preprint arXiv:2210.03629

    React: Synergizing reasoning and acting in language models. arXiv preprint arXiv:2210.03629

    Pith/arXiv arXiv

  42. [2025]

    arXiv preprint arXiv:2506.05690

    Whentousegraphsinrag:Acomprehensiveanalysisforgraph Hong-Yu An et al.:Preprint submitted to ElsevierPage 15 of 16 retrieval-augmented generation. arXiv preprint arXiv:2506.05690

    arXiv

  43. [2026]

    Symmetry 18, 394

    Pi-vla: Adaptive symmetry-aware decision-making for long- horizon vision–language–action manipulation. Symmetry 18, 394