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

cs.AIOct 27, 2026

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

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

Organizations: Mitsubishi Electric US Cambridge, 5900-A Katella Avenue California 90630, USA · Mitsubishi Electric Innovation Center (MELIC) Cambridge, MA 02139, USA · Institute of Graduate Programs, Dept. of Computer Engineering, Karabuk University, Karabuk, 78050, Turkey

Abstract

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.

Figures & tables

Figure 1: Top-k paradigm vs. our SpectRAG framework

Figure 2: Documents are chunked into token-based passages (1–2) and encoded as dense embeddings (3). Rather than treating chunks as independent vectors, SpectRAG connects them with edges derived from six complementary evidence signals—semantic similarity, document adjacency, section hierarchy, shared entities, citations, and utility-question similarity (4).

Step	What it does	Output
Chunking	Splits documents into structural (heading-aware) or semantic chunks measured with tiktoken (1200 tokens, 100 overlap). Extracts tables. Never cuts mid-sentence.	Chunk objects with text, position, section path, and references
Embedding	Encodes each chunk with nomic-embed-text (768-dimensional), using the model’s search_document: task prefix. Builds a FAISS flat index over L2-normalized vectors for approximate nearest-neighbor search.	chunk.embedding per chunk & faiss.index on disk
Edge signals	Runs six extractors to find relationships between chunks. Entity edges use gpt-4o-mini concept extraction by default, & utility-question edges use gpt-4o-mini ; both store per-chunk outputs for query-time reuse. Concepts are disk-cached.	Six lists of RawEdge(i, j, weight) & chunk. utility_questions
Graph build	Combines all six signals using configurable weights, either fixed priors or auto-calibrated per corpus. Drops edges below the sparsification threshold.	Weighted graph $G=(V,E,W)$
Spectral decomp	Computes the normalized Laplacian $L=I-D^{-1/2}WD^{-1/2}$ . Extracts the 32 smallest eigenvectors. Each chunk gets a 32-dimensional coordinate encoding its position in the graph’s community structure.	chunk.spectral_coords (32-dimensional) per chunk
Neo4j write	Writes all chunks as nodes and edges with per-signal attributes to Neo4j via batched Cypher.	Persistent graph in Neo4j

Table 1: Offline SpectRAG pipeline—runs once per document set

Stage	What it does	Output
Hybrid seed retrieval	Fuses three rankings with reciprocal rank fusion (RRF): dense FAISS cosine, utility-question matching (query to stored questions), & BM25 lexical retrieval. The full relevance vector consumed downstream is hybrid (dense & BM25), so lexical precision reaches later stages.	Seed set $S_{0}$ (20 chunks) & hybrid relevance scores for all chunks
Graph expansion	Performs breadth-first search from $S_{0}$ in Neo4j, using two hops and a cap of 200 nodes. Fetches the candidate subgraph.	Candidate set $S_{1}$ ( $\leq 200$ chunks) and subgraph
Proximity re-scoring	Blends relevance with graph proximity as $(1-\alpha)\cdot\mathrm{relevance}+\alpha\cdot\mathrm{proximity}$ , where proximity in hybrid mode is the mean of spectral eigenspace closeness and Personalized PageRank from the seeds over the real weighted subgraph.	Re-scored candidate set $S_{2}$
Token-budget selection	Fills an approximately 12k-token budget with relevant chunks: a protected core, a tail precision floor, document-coverage tie-break, and backfill so the budget is never starved. Alternative modes include anchor_expand_ce , protected_mmr , and mmr .	Final context set $C$ (adaptive, approximately 10–15 chunks)
Generation	Formats $C$ grouped by source document and sends it to gpt-4o-mini with a synthesis-oriented, grounded prompt and temperature 0.	Answer string and ranked source metadata

Table 2: Online SpectRAG pipeline—runs per query.

Figure 3: Overview of the SpectRAG pipeline.

Figure 4: Sparse lexical vectors (top) allocate one dimension per vocabulary term and match exact words; dense embeddings (middle, 768-d) encode meaning in every dimension and support similarity search via FAISS. Bottom: SpectRAG’s spectral coordinates ( $d=32$ ), derived from the smallest eigenvectors of the normalized graph Laplacian, encode a chunk’s position in the corpus graph’s community structure rather than its textual semantics.

Parameter	Setting	Related stage
Chunking	Structural or semantic chunking with tiktoken ; 1200-token chunks and 100-token overlap; sentence boundaries and tables are preserved.	Offline chunking
Embedding model	nomic-embed-text , 768-dimensional embeddings, with the search_document: prefix for indexed chunks.	Offline embedding
Edge extraction	Six edge-signal extractors: semantic, document adjacency, section hierarchy, entity/concept, utility-question, and citation/dependency signals.	Offline edge signals
LLM-assisted extraction	gpt-4o-mini for concept extraction, utility-question generation, and answer generation; gpt-4o for judging when evaluation requires an LLM judge.	Offline and generation
Graph and spectral index	Weighted graph $G=(V,E,W)$ with sparsified edges; normalized Laplacian $L=I-D^{-1/2}WD^{-1/2}$ ; 32 spectral coordinates per chunk.	Graph build and spectral decomp
Seed retrieval	RRF over dense FAISS cosine, BM25 lexical retrieval, and utility-question matching; seed set size is 20 chunks.	Online stage 1

Table 3: Implementation parameters aligned with the SpectRAG pipelines

Corpus	System	Nodes	Edges	E/N	Graph	Node
					File	Red.
Agriculture	LightRAG	1,236	1,083	0.88	1.08 MB	—
	SpectRAG	239	476	1.99	0.14 MB	$5.2\times$
CS	LightRAG	1,327	1,036	0.78	1.06 MB	—
	SpectRAG	461	2,608	5.66	0.72 MB	$2.9\times$
Legal	LightRAG	5,615	6,784	1.21	6.80 MB	—

Table 4: Per-corpus graph size and index cost.

Field	Content
Query	How can anomaly detection techniques be applied in various domains to identify outliers?
SpectRAG answer	Frames anomaly detection as a versatile toolset applied through several themes: understanding the dataset (categorical, ordinal, or continuous) to guide method choice; statistical methods (z-scores, p-values, standard-deviation thresholds); machine-learning approaches (K-means clustering, supervised learning on labeled data); domain-specific applications in finance (fraud), healthcare (rare conditions), network security (intrusions), and manufacturing (predictive maintenance); evaluation and validation via precision, recall, F1, and cross-validation; and visualization tools (scatter plots, box plots, heat maps) for inspecting distributions.
LightRAG answer	Synthesizes anomaly detection across fields through big data and machine learning (real-time pattern flagging for finance and network security); statistical analysis (z-scores, box plots, interquartile range for healthcare); data mining (clustering to surface outliers in marketing); optimization methods (refining operations-research models); and real-time applications (streaming detection in telecommunications). Concludes that the techniques are versatile across finance, healthcare, marketing, and operations research.
Comprehensiveness	Winner: SpectRAG (position-sensitive; split on swap). More detailed exploration covering a wider range of methods, applications, and evaluation strategies.
Diversity	Winner: SpectRAG (confirmed both orderings). Richer variety of perspectives across multiple domains and specific techniques within each.
Empowerment	Winner: SpectRAG (confirmed both orderings). Detailed explanations and examples that help the reader understand how the techniques are applied.

Table 5: CS-domain qualitative case study: query, answers, and LLM-judge verdict.

System	Recall	R@2	R@5	R@10	MRR
LightRAG	65.6	31.2	49.2	61.8	61.5
Hybrid	76.1	46.3	68.0	76.1	79.1
HyDE	64.1	36.1	58.2	64.1	65.5
NaiveRAG	69.5	40.9	62.4	69.5	72.8
SpectRAG	91.8	39.1	64.7	84.0	70.4

Table 6: Retrieval ranking quality on MultiHopRAG.

System	EM	F1	Contains
HyDE	65.2	65.6	65.4
NaiveRAG	67.8	68.3	68.3
Hybrid	70.6	71.1	71.0
LightRAG	70.5	70.9	70.8
SpectRAG	71.2	71.6	71.6

Table 7: Overall answer accuracy on MultiHopRAG dataset.

Type	SpectRAG	LightRAG	Hybrid	HyDE	NaiveRAG
Comparison	62.7	66.4	63.1	55.7	59.8
Inference	95.1	92.2	92.2	87.0	87.7
Temporal	43.9	44.9	42.7	35.8	40.1
Null	83.1	72.8	87.4	89.7	89.7

Table 8: Per-type answer accuracy on MultiHopRAG.

Baseline: NaiveRAG
Dimension	Agriculture		CS		Legal		Mix		Average
	Base	SpectRAG	Base	SpectRAG	Base	SpectRAG	Base	SpectRAG	Base	SpectRAG
Comprehensiveness	43.8	56.2	37.5	62.5	51.3	48.7	37.5	62.5	42.5	57.5
Diversity	32.5	67.5	21.3	78.7	52.5	47.5	37.5	62.5	35.9	64.1
Empowerment	40.0	60.0	32.5	67.5	51.3	48.7	33.8	66.2	39.4	60.6
Overall	40.0	60.0	35.0	65.0	51.3	48.7	35.0	65.0	40.3	59.7

Table 9: Win rates (%) of baselines versus SpectRAG across four domains and four dimensions (signal configuration 1: semantic 0.300, section 0.250, entity 0.200, adjacency 0.084, utility question 0.083, citation 0.083)

Baseline: NaiveRAG
Dimension	Agriculture		CS		Legal		Mix		Average
	Base	SpectRAG	Base	SpectRAG	Base	SpectRAG	Base	SpectRAG	Base	SpectRAG
Comprehensiveness	43.8	56.2	41.2	58.8	53.7	46.3	43.8	56.2	45.6	54.4
Diversity	37.5	62.5	26.2	73.8	55.0	45.0	41.2	58.8	40.0	60.0
Empowerment	40.0	60.0	36.3	63.7	51.3	48.7	41.2	58.8	42.2	57.8
Overall	41.2	58.8	36.3	63.7	52.5	47.5	42.5	57.5	43.1	56.9

Table 10: Win rates (%) of baselines versus SpectRAG across four domains and four dimensions (signal configuration 2: semantic 0.150, section 0.200, entity 0.250, adjacency 0.100, utility question 0.280, citation 0.020)

Figure 5: Example graph-view interface of the proposed SpectRAG framework. Nodes represent document chunks and edges represent weighted relation signals, including semantic similarity, section relations, entity overlap, adjacency, utility-question similarity, and citation links.

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Retrieval-Augmented Generation (RAG) mitigates hallucinations in Large Language Models (LLMs) by grounding the generation process on external knowledge. However, standard RAG approaches struggle with multi-hop reasoning. While recent graph-based RAG methods improve the retrieval of interconnected chunks, they often rely on computationally expensive and error-prone LLM-based extraction pipelines. To address these issues, we propose TIGRAG (Token-Induced GraphRAG), an efficient graph-augmented RAG framework based on a token co-occurrence Knowledge Graph. TIGRAG directly models topological relationships between tokens using sliding-window co-occurrence statistics, thus enabling scalable graph construction. During inference, it combines graph-based semantic expansion and neural reranking to retrieve interconnected evidence for multi-hop reasoning. Specifically, it introduces an iterative entity-driven retrieval strategy that progressively expands the query using bridging entities extracted from previously retrieved contexts. We evaluated TIGRAG on three widely adopted multi-hop Question Answering (QA) benchmarks. Experimental results demonstrated that our framework consistently outperforms dense retrieval and graph-based RAG methods in both retrieval and downstream QA tasks, while substantially reducing indexing time, inference latency, and prompt footprint.

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