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SpectRAG: Weighted Chunk Graphs for Token-Budgeted Context Selection in Multi-Hop Retrieval-Augmented Generation

Zafer Sahinoglu, Abdulazeez Mohammed, Buse Yaren Kazangirler, Cahit Berkay Kazangirler

arXiv:2610.36991v1cs.AIcs.CLcs.IR

TL;DR

Dense retrieval can return redundant passages and miss cross-chunk evidence needed for multi-hop reasoning. SpectRAG combines hybrid seeding, a weighted chunk graph, graph expansion and propagation, and token-budgeted context selection. It reports broader evidence recovery and strongest generation metrics on MultiHopRAG, with moderate generation margins.

  • Problem

    Independently ranked dense retrieval can be redundant and miss bridge evidence or structural relations when answers depend on multiple chunks.

    Source: §1 · p. 2, §1.2 · p. 3

  • Method

    SpectRAG seeds candidates with dense retrieval, then uses a weighted chunk graph and spectral structure for expansion, relevance propagation, and token-budgeted context selection.

    Source: §2.5 · p. 6, §3.8 · p. 11, §8 · p. 24

  • Results

    On MultiHopRAG, SpectRAG achieves the highest overall recall and Recall@10 and the strongest EM, F1, and answer-containment scores, with moderate generation margins.

    Source: §8 · p. 24

  • Takeaways & Limitations

    The findings support graph-spectral structure as a useful retrieval signal beyond local vector similarity, especially for broad evidence recovery and relational reasoning.

    Source: §8 · p. 24

    The manuscript is a methodological proposal, and its experiment tables specify a reporting format whose numeric values should be populated only after experiments run.

    Source: §4 · p. 12

Abstract

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Retrieval-augmented generation (RAG) systems ground large language models (LLMs) by retrieving external evidence and conditioning generation on the retrieved context. Although dense retrieval is effective for local semantic matching, independently ranked retrieval can return redundant passages, miss cross-chunk dependencies, and provide incomplete evidence for multi-hop reasoning. We propose SpectRAG, a spectral graph-augmented retrieval framework that combines hybrid candidate seeding, weighted chunk graph construction, graph-based expansion, spectral relevance propagation, and token-budgeted context selection. Document chunks are represented by dense semantic embeddings and graph-spectral coordinates derived from a weighted chunk graph whose edges encode semantic similarity, document adjacency, section hierarchy, shared entities, citation links, and similarity between LLM-generated utility questions. At query time, SpectRAG builds a high-recall seed set using exact inner-product search and hybrid relevance signals, expands it over the chunk graph, re-scores candidates using graph proximity and spectral information, and assembles the final context under a fixed token budget. The goal is not merely to retrieve individually similar chunks, but to construct a context that is relevant, diverse, structurally connected, and sufficient for grounded reasoning. Experiments on MultiHopRAG, UltraDomain, and long-document question-answering settings show that SpectRAG improves broad evidence recovery and achieves competitive generation quality against dense, hybrid, HyDE, LightRAG, and NaiveRAG baselines. The results further indicate that graph-spectral structure is particularly useful for inference-oriented and cross-document retrieval, while highlighting trade-offs in early precision, computational cost, and domain-dependent performance.

1 Introduction

Independently ranked dense retrieval can return redundant passages and miss bridge evidence or corpus structure needed for multi-hop reasoning. SpectRAG combines dense seeding with graph-aware context selection to address these limits.

1 Introduction

  • The introduction distinguishes individual top-k ranking from context-set retrieval, which seeks chunks that together provide sufficient evidence for generation.The stated contributions also include an evaluation protocol for multi-hop and long-document QA and an ablation study of pipeline components.Source: §1 · p. 2, §1.3 · p. 3

1.1 Motivation Behind The Study

  • SpectRAG uses a high-recall candidate pool, then expands through graph neighborhoods, re-scores candidates, and selects context under a token budget.The selection aims to recover bridge evidence and reduce redundant context.Source: §1.1 · pp. 2–3, §1.3 · p. 3, §1.2 · p. 3

1.2 Limitations of Top-k Dense Retrieval

  • Dense top-k retrieval can waste limited context on redundant passages, miss bridge evidence, and ignore structural relationships among chunks.These limits matter when answers require evidence distributed across passages, documents, or reasoning steps.Source: §1 · p. 2, §1.2 · p. 3

1.3 Contributions

  • SpectRAG combines dense search with weighted chunk graphs, graph expansion, relevance diffusion, and cluster-aware selection to build a final context.Chunks have dense embeddings and graph-spectral coordinates; the graph can incorporate semantic, adjacency, hierarchy, entity, citation, and utility-question signals.Source: §1.3 · pp. 3–4

2 Related Work

The related-work discussion moves from independently ranked RAG toward context-set and graph-aware retrieval. SpectRAG frames its objective as selecting a compact, relevant, diverse, and connected set of chunks for generation.

2.1 Retrieval-Augmented Generation

  • Traditional RAG retrieves passages through sparse, dense, or combined methods, but independently ranked passages may be inadequate when evidence spans chunks, documents, or structural relations.The generator uses retrieved passages as context, making the quality of the set relevant as well as individual passage relevance.Source: §2.1 · p. 4

2.2 Diversity-Aware and Context-Set Retrieval

  • Context-set retrieval selects passages jointly to preserve relevance, cover evidence, avoid repetition, and provide sufficient, coherent context.The text connects this need to multi-hop and long-document reasoning, where answers may depend on links across the corpus.Source: §2.2 · pp. 4–5

2.3 Graph-Enhanced Retrieval and GraphRAG

  • GraphRAG represents corpus structure, while CrossAug addresses cross-chunk relations that may be absent when relations are extracted within individual chunks [7].The cited GraphRAG approach extracts an entity graph, forms communities, and generates summaries for global questions [12].Source: §2.3 · p. 5

2.4 Weighted Chunk Graph

  • SpectRAG’s weighted chunk graph connects chunks through semantic similarity, adjacency, hierarchy, entity overlap, utility-question similarity, and citation or dependency links.The normalized Laplacian supplies spectral coordinates and a diffusion operator used during query-time retrieval.Source: §2.4 · pp. 5–6

2.5 Context-Set Retrieval Objective

  • SpectRAG formulates retrieval as selecting a compact set of k chunks for joint utility rather than choosing the individually highest-scoring chunks.Its set objective combines relevance with redundancy, coverage, and graph connectivity; setting λ, γ, and η to zero recovers independent dense selection.Source: §2.5 · p. 6

2.6 Terms of the Context-Set Objective

  • The objective’s relevance reflects direct query similarity and graph position, while redundancy penalizes overlap and coverage rewards distinct evidence aspects.Connectivity measures relationships among selected chunks; dense and hybrid retrieval seed candidates before graph expansion, re-scoring, and token-budgeted selection.Source: §2.6 · p. 7

3 Spectral Graph-Augmented Retrieval

SpectRAG separates corpus indexing from query-time retrieval, constructing a weighted graph and spectral coordinates offline. Online, it seeds candidates, expands and re-scores them using graph structure, then selects context under a token budget.

3.1 Overview of SpectRAG

  • Offline indexing chunks documents, computes embeddings and edge signals, builds and sparsifies a weighted graph, and stores graph and spectral artifacts for reuse.The stage runs once per collection; query-time retrieval uses the precomputed artifacts.Source: §3.1 · p. 7, Table 1 · p. 8
  • Online retrieval fuses dense, BM25, and utility-question signals for seeds, expands them through two-hop graph traversal, re-scores by relevance and proximity, and selects context within a token budget.The final context is grouped by source document and passed to the generator with ranked source metadata.Source: §3.1 · p. 7

3.2.1 Nodes and edge signals

  • The chunk graph uses dense embeddings as nodes and combines six normalized edge signals: semantic similarity, adjacency, section hierarchy, entities, utility questions, and citations.These signals connect chunks through both textual similarity and structural or functional relations.Source: §3.2.1 · pp. 7–8

3.2.2 Weight fusion and sparsification

  • The six signals are fused into edge weights, and edges below threshold τ are discarded to keep graph size O(k_g n).The weights α_r may use fixed priors or be auto-calibrated per corpus.Source: §3.2.2 · p. 8

3.2.3 Spectral coordinates

  • SpectRAG uses the symmetric normalized Laplacian’s smallest non-trivial eigenvectors to assign spectral coordinates that reflect graph-community proximity.The Laplacian also serves as the diffusion operator for relevance propagation.Source: §3.2.3 · p. 9

3.3 Documents Chunking

SpectRAG adapts chunking to document structure or sentence-level semantic breaks, then uses graph-Laplacian coordinates to represent corpus structure separately from textual meaning.

3.3 Documents Chunking

  • Structured documents are split along their hierarchy, while unstructured documents use sentence-embedding distance breakpoints; chunks are capped at 1,200 tokens with 100-token overlap.Chunks under 32 tokens are joined to the previous chunk, and tables are serialized to Markdown without splitting rows.Source: §3.3 · pp. 9–10

3.4 Laplacian Spectral Coordinates

  • The 32-dimensional spectral coordinates encode a chunk’s position in graph communities rather than its text semantics, complementing dense embeddings that represent content.Chunks in the same graph community can be close in spectral space even when their surface text differs.Source: §3.4 · p. 10, Figure 4 · p. 10

3.5 Initial Dense Retrieval

Dense retrieval deliberately supplies a broad, high-recall seed pool rather than the final context; graph expansion can recover structurally connected evidence missed by query-nearest-neighbor search.

3.5 Initial Dense Retrieval

  • Dense retrieval provides plausible, individually relevant chunks as a high-recall seed set, not the final context.The final context is selected later through graph expansion, spectral diffusion, and token-budgeted selection.Source: §3.5 · pp. 10–11
  • The candidate budget K exceeds the final context budget k so the seed set is sufficiently broad.Over-retrieval is deliberate because expansion can only recover evidence reachable from the seeds, making seed recall an upper bound on pipeline recall.Source: §3.5 · p. 10, §3.6 · p. 11

3.6 Graph Expansion

  • Graph expansion targets evidence structurally connected to query-relevant chunks but outside the query’s embedding neighborhood.Such evidence may be important for multi-hop reasoning despite lacking direct semantic similarity to the query.Source: §3.6 · p. 11

3.7 Spectral Diffusion of Query Relevance

SpectRAG diffuses query relevance across the chunk graph, with a scale parameter controlling how far relevance spreads and approximations available for large corpora.

3.7 Spectral Diffusion of Query Relevance

  • The diffused relevance signal is s′ = exp(−tLsym)s, with t controlling the diffusion scale.The equation propagates the initial relevance signal through the graph.Source: §3.7 · p. 11
  • Small t keeps relevance local, whereas large t spreads it across broader graph regions.Source: §3.7 · p. 11
  • For large corpora, Equation 17 can be approximated with truncated Chebyshev polynomials, personalized PageRank-style iteration, or repeated smoothing.Source: §3.7 · p. 11

3.8 Token-Budgeted and Cluster-Aware Context Selection

SpectRAG assembles a context under a fixed token budget, balancing relevance with graph proximity, cluster and document coverage, and redundancy control.

3.8 Token-Budgeted and Cluster-Aware Context Selection

  • The final context is selected under a maximum token budget B rather than as a fixed number of chunks.The design accounts for the generator’s limited context window and allocates available tokens across evidence sources.Source: §3.8 · p. 11
  • Candidate utility combines re-scored relevance and seed-set proximity with spectral-cluster and document coverage gains, minus redundancy.Token-normalized utility can account for chunk length; ρ controls length normalization, from utility-only selection at ρ = 0 to utility per token at ρ = 1.Source: §3.8 · pp. 11–12
  • Selection protects a core of high-confidence chunks, adds lower-ranked candidates subject to precision and coverage criteria, then backfills if budget remains.Source: §3.8 · p. 12
  • The online pipeline fuses dense, BM25, and utility-question rankings, expands two hops, re-scores candidates, and selects context up to B tokens.The current implementation typically produces about 10–15 chunks under a budget of about 12k tokens.Source: §3.8 · p. 12

4 Experiments

The experiments assess retrieval, answer quality, and index cost across multi-hop and domain-diverse settings. Reported results show stronger evidence retrieval than LightRAG on MultiHopRAG, comparable objective answer accuracy, and favorable index size.

4.1 Research Questions

  • The experiments ask about graph index cost, holistic answer quality, objective answer accuracy, and the ranking of gold evidence.Evaluation spans MultiHopRAG and four UltraDomain subsets—agriculture, computer science, legal, and mixed—using precision, recall, and F1 among its metrics.Source: §4.1 · p. 12, §4.2 · p. 13

4.3 Implementation Parameters and Details

  • Two chunking settings use 256-token chunks with 64-token overlap and 1,200-token chunks with 100-token overlap; both use the same hybrid-to-budgeted retrieval pipeline.The settings test finer-grained evidence composition against retention of richer local document context.Source: §4.3 · p. 13

4.4 Baselines

  • Baselines include NaiveRAG, BM25-plus-dense HybridRAG, entity-and-relation-graph LightRAG, and hypothetical-document-embedding HyDeRAG.Source: §4.4 · p. 13

4.5 Retrieval and Answer Correctness Metrics

  • Retrieval precision, recall, and F1 are measured against annotated evidence; answer-level measures include EM, token F1, and judge-rated comprehensiveness, diversity, empowerment, and overall quality.Ground-truth measures apply to MultiHop-RAG and UltraDomain; open-ended sensemaking questions without references receive only preference-based measures, and the measure families are reported separately.Source: §4.5.1 · p. 14, §4.5.2 · p. 15, §4.5.3 · p. 15

4.6 Preliminary Generation-Level Evaluation

  • In a preliminary UltraDomain pairwise evaluation against NaiveRAG, SpectRAG outperformed it across all dimensions, with a 55.0% margin for diversity.The evaluation sampled 20 questions per domain and used an LLM judge; values above 50% indicate an advantage for SpectRAG.Source: §4.6 · p. 15
  • On MultiHopRAG, SpectRAG’s index is 46 MB versus LightRAG’s 274 MB, while its Recall@5 is 65.2 versus 49.5 and answer accuracy is comparable.Table 4 reports per-corpus graph size and index cost.Source: §4.7 · pp. 15–16, Table 4 · p. 16
  • On 2,556 MultiHopRAG gold-answer questions, SpectRAG’s EM 72.0 and F1 72.4 exceed NaiveRAG’s EM 65.2 and F1 65.6, and are on par with LightRAG.SpectRAG’s retrieval advantage over LightRAG yields only a small answer-accuracy gain in these results.Source: §4.9 · p. 16
  • Against LightRAG, SpectRAG raises MRR from 61.5 to 70.4 and Recall@5 from 49.2 to 64.7 on MultiHopRAG.The passage also reports higher recall at every cutoff and higher MRR than NaiveRAG.Source: §4.10 · p. 16

5 Results and Analysis

SpectRAG combines stronger evidence retrieval with lower index cost on MultiHopRAG and competitive answer quality across the evaluated settings. Its retrieval gains are broad, while answer-accuracy gains are modest overall and clearest on inference questions; diversity remains its strongest qualitative advantage.

5.1 Main Results

  • SpectRAG matches LightRAG’s objective answer accuracy on MultiHopRAG while retrieving gold evidence more effectively at substantially lower index cost, and wins UltraDomain pairwise judgments against NaiveRAG, HyDE, and Hybrid.It remains competitive with LightRAG on UltraDomain and shows an advantage in answer diversity.Source: §5.1 · p. 17

5.2 Retrieval-Level Results

  • MRR is 70.4 for SpectRAG versus 61.5 for LightRAG, and Recall@2/@5/@10 is 39.1/64.7/84.0 versus 31.2/49.2/61.8.Recall@5 also favors SpectRAG on comparison (72.0 versus 54.8), inference (53.7 versus 38.8), and temporal (69.5 versus 55.5) questions.Source: §5.2 · p. 17, Table 6 · p. 18

5.3 Generation-Level Results

  • EM is 71.2, F1 is 71.6, and contains is 71.6 for SpectRAG, the highest overall accuracy on every metric among five systems.The margin over LightRAG and Hybrid, both near 70.6, is narrow; the gap over NaiveRAG (67.8) and HyDE (65.2) is larger.Source: Table 7 · p. 18, §5.3 · p. 18
  • Inference accuracy is 95.1 for SpectRAG, while comparison and temporal results cluster tightly and LightRAG is marginally ahead at 66.4 and 44.9.On null questions, SpectRAG scores 83.1 versus 89.7 for vector baselines and 87.4 for Hybrid; broader retrieval tends to surface candidate evidence for unanswerable queries.Source: §5.3 · pp. 18–19, Table 8 · p. 19

5.4 Diversity, Redundancy, and Connectivity Analysis

  • Across two substantially different signal weightings, diversity remains SpectRAG’s strongest dimension; the utility-question-weighted configuration also produces slight overall and empowerment leads over LightRAG.In configuration 2, SpectRAG wins empowerment and overall at 51.2, while losing comprehensiveness narrowly at 49.4.Source: §5.4 · p. 19
  • Diversity is SpectRAG’s strongest dimension against every baseline under configuration 1, with average win rates of 64.1 against NaiveRAG, 71.5 against HyDE, 60.6 against Hybrid, and 55.0 against LightRAG.Against LightRAG, it is close to even on comprehensiveness, empowerment, and overall quality, but wins on diversity.Source: §5.4 · p. 19, Table 9 · p. 20

6 Discussion

SpectRAG’s strongest retrieval advantage is broad evidence recovery, while generation and pairwise quality gains are more modest and depend on task and corpus. The discussion explains how weighted chunk-graph structure supports connected context selection and describes practical deployment and inspection features.

6 Discussion

  • On MultiHopRAG, SpectRAG achieves the highest overall recall and Recall@10, while Hybrid leads Recall@2, Recall@5, and MRR.The pattern reflects a broader candidate pool rather than optimization solely for nearest-neighbor ranking.Source: §6 · p. 20
  • On MultiHopRAG, SpectRAG obtains the highest EM, F1, and answer-containment scores, with modest margins over compared systems.Better retrieval coverage does not automatically produce substantially better generation; the LLM must integrate evidence and follow the reasoning path.Source: §6 · pp. 20–21
  • SpectRAG scores highest on inference and null questions, while comparison and temporal results are mixed and LightRAG is slightly better.The discussion also reports lower memory cost than LightRAG, attributed to a more compact graph with fewer nodes and edges.Source: §6 · p. 21
  • Across domains and signal configurations, SpectRAG generally receives favorable judge win rates against NaiveRAG, HyDE, and Hybrid, especially for diversity and empowerment.Against LightRAG it is competitive and often stronger in diversity, but does not consistently dominate, particularly in CS; outcomes depend on corpus structure, baseline strength, and signal weighting.Source: §6 · pp. 21–22, Table 10 · p. 21
  • In one anomaly-detection case, SpectRAG is preferred for comprehensiveness, diversity, empowerment, and overall quality.The judged explanation contrasts broader coverage of methods, domains, evaluation strategies, and visualization tools with LightRAG’s more compact synthesis.Source: §6 · p. 22

6.1 Why Spectral Structure Helps

  • SpectRAG’s weighted chunk graph combines semantic similarity, adjacency, section hierarchy, entity co-occurrence, citation relations, and utility-question similarity.Low-frequency Laplacian coordinates describe global connectivity and communities, helping cluster-aware selection avoid domination by one local neighborhood; diffusion can raise the relevance of connected bridge evidence.Source: §6.1 · p. 22

6.2 Practical Deployment in RAG Pipeline and Framework

  • Embeddings, graph construction, Laplacian computation, and spectral coordinates can be precomputed and cached offline.At query time, the pipeline retrieves seeds, expands neighborhoods, diffuses relevance in the candidate subgraph, and selects context.Source: §6.2 · p. 22
  • The graph-view interface displays chunks as nodes and relation signals as edges, with node layout and edge colors showing graph organization and dominant relation types.The visualization can help identify dense neighborhoods, bridge nodes, isolated regions, and inter-document connections before retrieval and context selection.Source: §6.2 · pp. 22–23, Figure 5 · p. 23

7 Limitations and Threats to Validity

The reported results have boundaries involving retrieval-to-generation transfer, task dependence, signal-weight sensitivity, chunking choices, and computational scalability.

Retrieval–generation gap

  • Retrieval coverage does not always yield proportional answer gains because generators may misuse evidence, ignore bridge passages, or react to context ordering.The authors advise interpreting retrieval-level and generation-level metrics separately.Source: §7 · p. 23

Task-dependent performance

  • SpectRAG performs strongly on inference questions, but results are weaker or mixed for comparison, temporal, and null questions.The authors identify evidence connection and synthesis as a favorable task fit, with precise temporal ordering, direct comparison, and abstention calibration as less favorable settings.Source: §7 · p. 23

Signal-weight sensitivity

  • Performance varies with the relative weights assigned to graph signals, and a configuration that works for one corpus may not suit another.The authors describe this as a threat to external validity.Source: §7 · p. 23

Chunking sensitivity

  • Chunk size and overlap affect graph topology, retrieval, redundancy, and available local context, so chunking should be treated as an experimental variable.Larger chunks preserve more local context but may reduce the benefit of graph-based composition.Source: §7 · pp. 23–24

Computational scalability

  • Exact inner-product search avoids approximation error but costs more query time, while spectral computation can be expensive on large graphs.Large-scale deployment may require sparse graph construction, approximate eigensolvers, graph coarsening, caching, or approximate vector indexes.Source: §7 · p. 24

8 Conclusion

SpectRAG uses graph-spectral signals to build diverse, connected context sets, with its strongest benefits in broad evidence recovery and relational reasoning. Results support its use as a complement to existing retrieval strategies, while identifying areas for further evaluation and optimization.

8 Conclusion

  • SpectRAG targets the gap between individually similar passages and context sets that are diverse, connected, and evidence-complete.This distinction matters in multi-hop and cross-document settings where answers may depend on evidence distributed across passages, documents, or structural relations.Source: §8 · p. 24
  • The framework combines dense candidate seeding, weighted chunk-graph construction, neighborhood expansion, spectral relevance propagation, and token-budgeted context selection.It uses dense retrieval as a high-recall entry point, then applies graph-spectral signals to recover supporting evidence, reduce redundancy, and improve structural coherence.Source: §8 · p. 24
  • SpectRAG achieves the highest overall recall and Recall@10 on MultiHopRAG and the strongest EM, F1, and answer-containment scores among compared systems, with moderate generation margins.Improved evidence coverage does not automatically yield large answer-quality gains unless the generator can use the selected evidence effectively.Source: §8 · p. 24
  • Across most domains and signal combinations, SpectRAG outperforms NaiveRAG, HyDE, and Hybrid on diversity, empowerment, and total performance, while comparisons with LightRAG are mixed.Its aggregate advantage supports a complementary role where evidence diversity and connectivity must be preserved.Source: §8 · p. 24
  • The findings support graph-spectral structure as a useful retrieval signal beyond local vector similarity, while motivating larger-corpus and broader-domain evaluation.Future work also includes human preference studies, stronger graph-enhanced baselines, scalable indexing, signal-weight optimization, and investigation of temporal reasoning and context ordering.Source: §8 · p. 24

Code Availability

The paper states that SpectRAG's source code, configuration files, evaluation scripts, and documentation will be publicly available in a GitHub repository.

Code Availability

  • The repository is identified as https://github.com/SightAndCite/SpectRAG and is stated to include experiment configurations, dependency information, and reproduction instructions.The source code, evaluation scripts, and documentation are also listed as planned repository contents.Source: Code Availability · pp. 24–25

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