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Dense Expands, Sparse Anchors: Channel-Asymmetric Query Expansion for Hybrid Retrieval

Chunran Zhang

arXiv:2608.15851v1cs.IRcs.CL

TL;DR

Hybrid retrieval evaluations can make query-expansion gains depend on a fixed fusion cutoff and overlook how much ranked evidence each channel requires. DESA addresses this with channel-asymmetric expansion and complete-list replay evaluation, improving retrieval effectiveness while reducing access depths across seven BEIR datasets.

  • Problem

    Fixed top-L fusion entangles the fused result with per-channel access depth, so expansion effects may change or reverse across cutoffs.

  • Method

    DESA adds orthogonal semantic residuals to dense queries and score-product anchors generated lexical cues within the original sparse support, evaluated with complete-list fusion and replay stopping depths.

  • Results

    Across seven BEIR datasets, DESA improves macro nDCG@10 and Recall@20 by 3.82% and 2.38% while reducing dense and sparse replay stopping depths by 36.90% and 36.56%.

  • Takeaways & Limitations

    The findings support assigning semantic expansion to dense retrieval and anchored lexical reordering to sparse retrieval in hybrid query expansion.

  • Takeaways & Limitations

    The evaluation covers seven English BEIR datasets, two generators, two dense encoders, BM25, and equal-weight RRF, so results may differ for other languages, retrievers, or fusion rules.

Abstract

from arXiv · show

LLM-based query expansion improves retrieval by generating document-like passages. In hybrid retrieval, however, most evaluations fuse fixed top-$L$ dense and sparse rankings. Because the cutoff controls both which cross-channel contributions enter fusion and how much of each ranking is accessed, gains measured at one $L$ can change or reverse at another. We separate these effects by evaluating retrieval effectiveness under complete-list fusion and recording the policy-specific per-channel replay stopping depths at which its ordered top-$K$ is certified. We then introduce DESA (Dense Expansion and Sparse Anchoring), a channel-asymmetric query expansion method. An LLM generates complementary reference passages; orthogonal residual expansion adds their new semantic directions to the dense query, while score-product anchoring incorporates their lexical cues into sparse retrieval without broadening the original query's lexical support. Across seven BEIR datasets, DESA improves nDCG@10 and Recall@20 over the unexpanded query by 3.82% and 2.38%, while reducing dense and sparse access depths by 36.90% and 36.56%. With equal dataset weighting, 63.31% of queries become shallower in both channels. However, both depths increase with Contriever on Touché-2020. These results support channel-specific integration of generated passages and joint evaluation of retrieval effectiveness and access depth.

1 Introduction

Hybrid retrieval evaluations at a fixed top-L cutoff conflate fusion contributions with ranking access depth, so DESA evaluates complete-list fusion and channel-specific certification depths. DESA improves retrieval effectiveness while reducing dense and sparse access requirements across seven BEIR datasets.

  • Introduction: Fixed top-L evaluation confounds which documents enter hybrid fusion with how deeply each channel is read, making gains conditional on L.Complete-list fusion plus sound replay records the per-channel depths needed to certify the same ordered top-K.
  • Introduction: Retriever-dependent effects motivate channel asymmetry: on NFCorpus, symmetric expansion reduced dense depth but increased sparse depth because generated terms broadened nonzero sparse matches.Mechanism experiments find sparse anchoring contributes most effectiveness gains, while the dense residual further reduces decisive ranked evidence.
  • Introduction: DESA adds orthogonal residual semantic directions to dense queries while using score-product anchoring to incorporate lexical cues without broadening sparse support.The LLM generates complementary reference passages around the original information need.
  • Introduction: 3.82% and 2.38% gains in macro nDCG@10 and Recall@20 accompany 36.90% and 36.56% reductions in dense and sparse access depths, respectively.With equal dataset weighting, 63.31% of queries become shallower in both channels.

2 Related Work

Prior query-expansion methods enrich queries, representations, term weights, or rank fusion with generated document-like content, while hybrid evaluations often depend on fixed top-L cutoffs. DESA instead constrains the same generated passages asymmetrically, expanding dense semantic coverage while anchoring sparse retrieval to the original lexical support.

  • Prior query expansion: LLM-based expansion adds document-like language through hypothetical documents, pseudo-documents, alternative evidence, or multiple references (Gao et al., 2023; Wang et al., 2023; Jagerman et al., 2023; Zhang et al.HyDE encodes a generated hypothetical document for dense retrieval, whereas Query2doc appends a pseudo-document for sparse and dense retrieval.
  • Evaluation perspective: Fixed top-L evaluation makes measured expansion effects conditional on the cutoff because L controls both accessed rankings and cross-channel contributions in hybrid fusion.The paper therefore separates complete-list retrieval effectiveness from channel access depth, following EAHR (Zhang, 2026).
  • Integration strategies: Expansion can enter retrieval through query text, dense representations, term weights, or rank fusion, as illustrated by Query2doc, MuGI, Word2Passage, and Exp4Fuse.These approaches modify query text, pool multiple-reference representations, reweight generated terms, or combine original and expanded rankings (Wang et al., 2023; Zhang et al., 2024; Choi et al., 2025; Liu and Zhang, 2025).
  • DESA positioning: DESA differs from heterogeneous fusion methods by modifying dense and sparse rankings before fusion, expanding dense semantic coverage while keeping sparse retrieval anchored to the original lexical support.MoR weights sparse and dense retrievers, whereas QuDAR adaptively fuses four rankings from original and expanded queries (Kalra et al., 2025).

3 DESA

DESA generates complementary reference passages that preserve the query’s intent while varying its expression, then integrates them asymmetrically: orthogonal semantic residuals expand dense retrieval, whereas score-product anchoring enriches sparse ranking without adding expansion-only matches. Complete-list equal-weight RRF fusion evaluates the resulting rankings, while bound-based replay records the channel depths needed to certify the final top-K.

  • Reference generation: DESA generates short reference passages that introduce aliases, technical terms, or paraphrases while preserving the query’s entities, relations, numbers, polarity, temporal conditions, scope, and information need.The prompt prohibits broader information needs and invented answers, so passages vary expression rather than intent.
  • Dense expansion: Dense expansion removes each reference representation’s component parallel to the original query and adds the orthogonal residual, introducing new semantic directions while keeping the expanded query within 45° of the original.If references contribute no orthogonal component, the dense representation remains unchanged.
  • Sparse anchoring: Sparse anchoring multiplies original and expanded sparse scores, allowing generated terms to reorder documents in the original lexical support while assigning zero anchored score to expansion-only matches.If the expanded score is only a positive multiple of the original, the sparse order is unchanged.
  • Fusion and evaluation: DESA fuses complete dense and sparse rankings with equal-weight RRF and evaluates effectiveness directly on the resulting ordered target top-K.Documents absent from a channel contribute zero to the fusion score.
  • Access-depth evaluation: Bound-based replay progressively reveals both rankings until unread documents cannot change the target top-K’s membership or order, recording the required dense and sparse stopping depths.At each step, replay reads from the channel with the larger next-item contribution bound, breaking ties in favor of dense retrieval.

4 Experiments

The experiments test cutoff sensitivity, DESA’s retrieval effectiveness and channel access depth, and the robustness and contributions of its dense and sparse operators. Evaluations use complete-list fusion for the main comparisons across seven BEIR datasets, with controlled baselines and matched statistical procedures.

  • Experimental scope: Experiments evaluate whether DESA improves retrieval effectiveness while reducing dense and sparse replay stopping depths across seven BEIR datasets.Effectiveness uses nDCG@10 and Recall@20; access uses dense and sparse depths LD and LS, including the proportion of queries whose two depths both decrease.
  • Cutoff sensitivity: Cutoff sensitivity is tested by fusing dense and sparse rankings at L ∈ {10, 20, 50, 100, 200, 500, 1000} and comparing results with complete-list fusion.The analysis measures metric values, ordering changes across cutoffs, top-20 reproducibility, and strict reversals in expansion judgments relative to Original.
  • Baselines: DESA is compared with Original, Shared expansion, HyDE, Query2doc, MuGI, and QuDAR-simple to separate channel asymmetry from generic generative expansion.Shared expansion applies the same references directly to both channels, while the other baselines use distinct dense, sparse, or rank-fusion pipelines.
  • Operator analysis: A matched 2 × 2 operator study isolates orthogonal residual expansion for dense retrieval and score-product anchoring for sparse retrieval, individually and in combination.Additional analyses relate vector-angle changes, sparse top-20 turnover, relevant-document movement, effectiveness, and access depth.
  • Robustness: Robustness tests vary reference count, anchoring controls, RRF constants, the generator, the dense encoder, and nested TREC-COVID corpus sizes.The corpus-scale analysis uses strict subsets of TREC-COVID that retain judged relevant documents while increasing the document collection.
  • Evaluation protocol: Results are reported per dataset and as equal-dataset macro averages using draw-averaged queries, stratified bootstrap confidence intervals, and Holm-corrected paired randomization tests.The primary comparisons are DESA against Original and Shared expansion, with corrections applied separately across effectiveness and access metrics.

5 Results

Across seven BEIR datasets, DESA improves retrieval effectiveness over Original while reducing dense and sparse replay access, with gains driven by complementary channel-specific operators. Its advantages persist against external baselines and most tested settings, although fixed cutoffs can change query-level judgments and Contriever on Touché-2020 increases access depth.

  • Cutoff sensitivity: Fixed L = 50 changes 6.95% of nDCG judgments and 18.84% of Recall judgments, including strict gain–loss reversals for 3.07% and 3.06% of cases.Thus, cutoff choice can change whether expansion is judged beneficial for an individual query rather than merely perturbing ranking.
  • 5 Results: 3.82% higher nDCG@10 and 2.38% higher Recall@20 than Original accompany 36.90% and 36.56% lower dense and sparse access depths, with 63.31% of queries shallower in both channels.Under complete-list fusion, DESA reaches .4747 nDCG@10 and .4695 Recall@20 in the seven-dataset comparison.
  • Operator ablation: Sparse anchoring supplies most effectiveness gains, while dense residual expansion adds complementary depth reductions; together, both operators produce the full DESA improvements.Sparse anchoring alone improves nDCG and Recall by 3.11% and 2.01%, while dense residual expansion alone improves them by 1.08% and 1.11%.
  • External comparisons: DESA matches QuDAR-simple without significant effectiveness differences while using 64.16% fewer mean available entries, and exceeds HyDE, MuGI, and Query2doc in effectiveness with lower access depths.Relative to HyDE, DESA gains 15.39% nDCG and 7.32% Recall; relative to MuGI, it gains 3.56% and 2.15%; relative to Query2doc, it gains 0.40% and 0.43%.
  • Robustness: DESA retains effectiveness gains across tested generators, dense encoders, and corpus sizes, but Contriever on Touché-2020 is the only observed setting where access depth increases.On NFCorpus, DESA preserves original sparse support, reduces sparse depth by 23.15%, and reduces dense depth by 15.03%.

6 Conclusion

DESA treats dense and sparse retrieval asymmetrically: generated passages add semantic directions to dense queries while anchoring sparse ranking within the original lexical support. Across seven BEIR datasets, this design improves retrieval effectiveness and reduces the replay depth required to certify fused top-K results.

  • Method: DESA uses orthogonal residual expansion to add complementary semantic directions to dense queries and score-product anchoring to reorder documents within the original sparse support.Both operators use the same generated reference passages, preserving the sparse query’s lexical support while enriching dense semantics.
  • Evaluation: Complete-list fusion separates retrieval effectiveness from cutoff choice by recording the per-channel replay stopping depths needed to certify the ordered top-K.This evaluation avoids tying measured effects to a fixed top-L cutoff that simultaneously controls channel contributions and ranking access.
  • Operator analysis: Sparse anchoring provides the more consistent effectiveness improvement, while dense residual expansion adds further gains and reduces the ranked evidence required for fusion.Together, the operators implement DESA’s division of labor: dense expands semantic coverage, while sparse anchors ordering without broadening lexical support.

Limitations

The evaluation is limited in scope and its replay-depth measure does not equal end-to-end latency. Remaining uncertainties include score-function assumptions, generated-reference quality, incomplete relevance pools, and broader retrieval architectures.

  • Evaluation scope: The evaluation covers seven English BEIR datasets, two generators, two dense encoders, BM25, and equal-weight RRF, so results may differ across languages, learned sparse retrievers, or fusion rules.Score-product anchoring also assumes a non-negative sparse scoring function.
  • Efficiency measure: Replay stopping depth measures ranked evidence needed to certify fused top-K rather than wall-clock latency, while end-to-end efficiency also depends on generation, encoding, indexing, and the retrieval interface.
  • Data and architecture boundaries: Generated references may contain irrelevant or unsupported expressions, and pooled relevance judgments may omit relevant documents outside existing pools.Broader retrieval architectures and online incremental retrieval remain needed to clarify these boundaries.

A Reproducibility Details … A.3 Baseline Reproduction

The appendix specifies reproducible generation, query-construction, retrieval, replay, and baseline-reproduction settings. It fixes model revisions, decoding and validation procedures, DESA’s dense and sparse integrations, and comparison-method implementations.

  • A Reproducibility Details: The reproducibility appendix records the generation, query-construction, retrieval, and replay settings required to reproduce the experiments.
  • A.1 Complementary Reference Generation: Qwen2.5-7B-Instruct uses a fixed revision, BF16 MLX-LM execution, deterministic batch seeding, and decoding with temperature 0.7, top-p 0.9, top-k 20, and 256-token maximum.Queries are identifier-sorted and processed in batches of eight.
  • A.1 Complementary Reference Generation: The reference generator returns exactly five complementary one-sentence passages that preserve query constraints while adding aliases, terminology, and paraphrases without broadening the information need.XGrammar validation rejects empty, duplicate, or placeholder passages; invalid output is retried once before falling back to the unexpanded query.
  • A.1 Complementary Reference Generation: Mistral-7B-Instructv0.3 is reproduced at a fixed revision using the same decoding, batching, and validation settings as the primary generator.
  • A.2 Query Construction: Orthogonal residual expansion uses float32, whereas shared expansion averages and normalizes query–reference representations without removing the component parallel to the original query.
  • A.2 Query Construction: DESA’s sparse query appends selected references to one original-query copy, then combines separate original and expanded BM25 scores through a document-wise product.The appendix also defines binary-mask and references-only ablations and notes that DESA does not repeat the original query or use MuGI’s repetition coefficient.
  • A.3 Baseline Reproduction: HyDE, Query2doc, and MuGI are reproduced with distinct generation counts, dense representations, and sparse concatenation or repetition rules.HyDE generates eight hypothetical documents; Query2doc generates one pseudo-document; MuGI generates five pseudo-references and is reproduced without pseudo-relevance-feedback calibration.

A.4 Retrieval Implementation … B.1 Properties of the Channel Operators

The retrieval pipeline fixes encoder, indexing, replay, and artifact-recording details, while channel operators provide certified access depths and preserve key dense and sparse properties.

  • A.4 Retrieval Implementation: BGE-small-en-v1.5 and Contriever use fixed revisions, normalized embeddings, and specified query encoding, while Pyserini builds corpus-specific Lucene indexes.BGE queries use a fixed search prefix and 512-token maximum; BM25 statistics are computed separately for each dataset and TREC-COVID snapshot.
  • A.5 Access-Depth Replay: Replay certifies ordered top-20 membership and order by bounding unread channel contributions, recording the stopping depths (L_D, L_S).The replay reads the channel with the larger bound, breaking ties toward dense, and stops once lower and upper bounds certify the result.
  • A.6 Artifact Traceability: Generation and query records preserve outputs, settings, hashes, rankings, effectiveness, replay traces, and access depths for reproducible reconstruction.A locked Python environment, Java checks, and a hash manifest cover code, configurations, prompts, inputs, models, generations, and rankings.
  • B.1 Properties of the Channel Operators: Unit-normalized contextual vectors and orthogonal projection ensure the dense residual construction does not increase vector norm.The construction uses the triangle inequality and projection non-expansion, yielding ∥z∥≤1.
  • B.1 Properties of the Channel Operators: Sparse score-product anchoring preserves the original lexical support because nonnegative scores intersect supports and the expanded query includes the original query.Thus supp(s_o) ⊆ supp(s_r), while zero residuals leave the original dense vector unchanged.
  • B.1 Properties of the Channel Operators: Positive rescaling of sparse scores leaves anchored rankings unchanged, including proportional expansions where squaring is strictly increasing on positive scores.Multiplying either sparse score vector by a positive global constant only rescales all anchored scores.

B.2 Mechanism Diagnostics · C Additional Experimental Results

DESA’s diagnostics show modest dense-query rotation and sparse-ranking turnover without universal thresholds linking either mechanism to effectiveness or access depth. Exact sparse-support preservation holds on six datasets, while Touché-2020 has a small export-related exception.

  • B.2 Mechanism Diagnostics: 11.98° mean dense angle and 26.15% average sparse top-20 turnover quantify the realized channel-specific changes across seven datasets.The maximum dense angle is 27.87°, below the analytic 45° bound; one invalid-generation fallback leaves 11,327 query–draw pairs.
  • B.2 Mechanism Diagnostics: Figure 4 visualizes query-level dense-angle and sparse-turnover distributions across three generation draws and seven datasets.Boxes show interquartile ranges and medians; whiskers extend to 1.5 times the interquartile range, with outliers omitted.
  • B.2 Mechanism Diagnostics: Relevant-document reciprocal-rank gain correlates more strongly with sparse-only nDCG gain than overall turnover, .391 versus .078.Dense-angle correlations with nDCG gain and depth reduction are .010 and .011, and within-dataset quartiles show no monotonic diagnostic–outcome relation.
  • B.2 Mechanism Diagnostics: The diagnostics support no universal angle or turnover threshold for predicting effectiveness or access-depth changes.Neither dense angle nor sparse turnover exhibits a monotonic relationship with effectiveness or access depth within datasets.
  • B.2 Mechanism Diagnostics: Exact sparse-support preservation holds for six datasets under a non-negative additive scorer and complete score export.Table 4 reports support-retention diagnostics from frozen query constructions and rankings, with the displayed macro rounding to 100.0000%.
  • B.2 Mechanism Diagnostics: Touché-2020 retains 99.99990% of sparse support on average and 99.99881% at minimum despite omitted extremely low-scoring tail documents.The exception affects 23 of 147 query–draw pairs, which are retained without claiming exact support preservation for the Lucene export.

C.1 Additional Ablations and Robustness · C.2 Matched Operator and QuDAR Controls

Additional ablations show that preserving original sparse-score magnitudes, using more references, and testing alternative generators affect DESA’s effectiveness and replay depths. Matched controls compare operator variants and DESA against QuDAR under shared references and standardized inference conditions.

  • C.1 Additional Ablations and Robustness: 1.91% higher nDCG@10 and 17.23%/18.14% lower dense/sparse replay stopping depths result from increasing references from one to three.Using five references adds 0.35% nDCG@10 and 0.43% Recall@20, with further dense/sparse reductions of 3.83%/3.40%.
  • C.1 Additional Ablations and Robustness: 1.54% lower macro nDCG@10 and 0.74% lower Recall@20 follow binary masking, which preserves sparse support but removes original-score magnitude.
  • C.1 Additional Ablations and Robustness: With Mistral, all four sampled datasets retain non-negative effectiveness changes and 7.12–47.61%/7.16–47.62% dense/sparse depth reductions, although 10% of sampled ArguAna queries fall back.
  • C.1 Additional Ablations and Robustness: Contriever improves both metrics on all four datasets but raises Touché-2020 dense/sparse depths by 14.29%/4.34%, while nested TREC-COVID gains and reductions remain positive but non-monotonic.
  • C.2 Matched Operator and QuDAR Controls: Matched operator controls share references, keep the other channel at Original, and average three draws within each query before inference.Tables 6 and 7 report these matched controls; Holm correction covers nDCG and Recall within each control pair.
  • C.2 Matched Operator and QuDAR Controls: DESA and QuDAR show no statistically significant paired difference under matched-reference RRF: −.00145 nDCG and −.00188 Recall, with pHolm=.3966 and .1668.The comparison uses top-1000 original-sparse, expanded-sparse, original-dense, and expanded-dense rankings with k=60.
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