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Finding the Right Balance: Relevance and Diversity in LLM Retrieval

Guillaume Brouillette, Faustin Kagabo, Usef Faghihi, Nadia Ghazzali

arXiv:2610.09412v1cs.IRcs.CL

TL;DR

RAG studies disagree on whether retrieval diversification improves answer quality. This paper tests diversification across redundancy regimes and introduces a query-adaptive rule based on the effective distinctness of nearest-neighbor selections and the query’s evidence requirement. Diversification harms clean-pool outcomes but helps on redundant multi-evidence tasks, supporting selective rather than routine use.

  • Problem

    Prior studies disagree on whether retrieval diversification improves retrieval and answer quality in RAG.

    Source: §1 · p. 1

  • Method

    The paper analyzes redundancy regimes and diversifies when the effective number of distinct documents in nearest-neighbor top-k falls below the query’s evidence requirement.

    Source: §1 · p. 2, §4.3 · p. 8

  • Results

    On clean pools, diversifiers generally degrade relevance, coverage, and answer quality, while on redundant multi-evidence tasks they overtake nearest-neighbor selection.

    Source: §1 · p. 3, §9 · p. 24

  • Takeaways & Limitations

    Diversification should be used selectively according to observable pool redundancy and the query’s evidence requirement.

    Source: §9 · p. 24

    The evidence requirement is treated as a static workload property read from gold annotations, which deployment does not have per query.

    Source: §7.4 · p. 22

Abstract

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Retrieval diversification is widely available in retrieval-augmented generation (RAG) frameworks, yet prior studies disagree on whether it improves retrieval and answer quality. We show that its effectiveness varies primarily with candidate-pool redundancy, in a pattern consistent with the number of distinct evidence pieces a query requires. Using controlled near-duplicate injection and production-style overlapping chunking, we find that diversification harms relevance, evidence coverage and answer quality on clean pools, but becomes beneficial on multi-evidence tasks when redundancy causes nearest-neighbor retrieval to select repeated passages. We therefore introduce a query-adaptive rule that diversifies only when the effective number of distinct documents in the nearest-neighbor top-$k$ selection falls below the query's evidence requirement. Computed from existing embeddings, the rule captures most of the achievable gain, transfers across datasets and encoders and automatically reduces to nearest-neighbor retrieval for single-evidence queries. We also introduce RNG-Score, a geometric reranker with an exact nearest-neighbor fallback whose margin indicates duplicate structure. Overall, we conclude that diversification should be used selectively, based on observable redundancy and evidence requirements.

1 Introduction

The paper asks when retrieval diversification helps in RAG, where prior findings conflict. It organizes the answer around candidate-pool redundancy and proposes a query-adaptive rule, alongside a geometric reranker with a nearest-neighbor fallback.

1 Introduction

  • The analysis treats candidate-pool redundancy as the observable variable and uses a diagnostic from system embeddings, thresholded by the query’s evidence requirement, to decide whether to diversify.The study is scoped to instrumental diversity, where diversity matters through the final answer rather than being rewarded in its own right.Source: §1 · p. 2
  • RNG-Score is a geometric reranker whose margin can diversify or exactly fall back to nearest-neighbor ranking, while also providing an offline readout of duplicate structure.The two-sided fallback lets validation tuning express “do not diversify.”Source: §1 · p. 2
  • Diversify when the effective number of distinct documents in nearest-neighbor top-k falls below the query’s evidence requirement; the rule switches off for single-evidence retrieval.It stays within a one-point clean-pool cost tolerance on most evaluated sweeps and transfers without retuning across encoders, datasets, redundancy mechanisms, and selection sizes.Source: §1 · p. 2
  • The regime analysis manipulates and measures pool redundancy directly, including near-duplicate injection and production-style overlapping chunking, on a common measured-redundancy axis.The study also includes a weak-versus-strong pipeline contrast.Source: §1 · p. 2
  • On clean pools, classical diversifiers lower relevance and coverage; as redundancy grows, nearest-neighbor coverage collapses and the decision rule tracks the upper envelope.The clean-pool result is significant on the primary coverage endpoint of the headline benchmark.Source: Figure 1 · p. 2, §1 · p. 3
  • Per-query oracle bounds show that clean-pool gains from routing among evaluated policies are at most marginal, while available headroom grows with measured redundancy.The oracle is an upper reference across the evaluated methods and operating points.Source: §1 · p. 3

2 Background and Related Work

The background places diversification within staged RAG retrieval, where selecting documents from a candidate pool is a shared pipeline step. Prior work gives mixed reasons to diversify, motivating evaluation that separates geometric spread from task-relevant evidence coverage and relates the RNG idea to the paper’s reranker.

2.1 Modern RAG pipelines

  • RAG pipelines retrieve a finite candidate pool, then refine it before generation; diversification is orthogonal to retriever and reranker choices because each pipeline ultimately selects k documents.First-stage retrieval may be sparse, dense, or hybrid, and refinement may use rerankers, cross-encoders, or late-interaction models.Source: §2.1 · p. 3

2.2 The case for diversity in RAG

  • RAG diversification studies report gains in some settings, but prior evaluations often entangle selection with extra LLM calls or use pools redundant by construction, leaving nonredundant pools with state-of-the-art encoders unisolated.The paper also distinguishes diversity as an instrumental means to answer quality from settings where diversity itself receives evaluation credit.Source: §2.2 · pp. 3–4, §2.4 · p. 4

2.3 The case against diversity in RAG

  • Other controlled evaluations find no consistent advantage for novelty-based diversification over nearest-neighbor retrieval, and geometric spread may select passages that do not contain needed answers.Prior work distinguishes geometric novelty from genuine coverage of query aspects.Source: §2.3 · p. 4

2.4 Diversification in recommendation

  • Recommendation and search-result diversification typically evaluate diversity intrinsically, rewarding coverage or dissimilarity; the paper instead studies instrumental-credit settings where diversity matters through the final answer.Controlled comparisons in recommendation report coverage gains under that intrinsic-credit protocol.Source: §2.4 · p. 4

2.5 Diversity evaluation metrics

  • Average pairwise distance and Vendi score measure geometric spread, while α-NDCG, ERR-IA, and Subtopic Recall reward coverage of distinct query facets and penalize redundant coverage.Disagreement between metric families can diagnose spread without coverage; the annotation-free measures also serve as pool redundancy diagnostics.Source: §2.5 · pp. 4–5

2.6 Relative neighborhood graphs

  • In the RNG, a pair is connected when no third point lies in its open lune; this paper softens that query-centered test into a cumulative penalty for ranking a fixed pool.The paper distinguishes this reranking use from prior graph pruning and hard-constraint constructions.Source: §2.6 · p. 5, Figure 2 · p. 5

3 The Relative-Neighborhood Score

The RNG-Score reranks a fixed candidate pool by balancing query relevance against geometric redundancy, with a nearest-neighbor fallback. Its behavior targets semantic near-duplicates, not exact copies, and can be adapted to different query–document distances.

3.1 Setup

  • For a fixed query, the finite candidate pool V comes from a first-stage retriever, with m ≫ k but small enough for pairwise reranking.The distance need only be a symmetric, nonnegative dissimilarity; exact-distance ties do not obstruct one another, so coincident duplicates can both be selected.Source: §3.1 · p. 6

3.2 Definition

  • The RNG-Score adds obstruction penalties to query distance when closer candidates sit near enough to make a candidate look redundant, then selects the k lowest scores.The score's reranking cost is O(m^2D); at m = 100, k = 5, and D = 1024, a pass averages 230 µs per query.Source: §3.2 · p. 6
  • On a two-evidence HotpotQA query, the RNG-Score keeps one sibling-article representative and recovers the second gold document, while MMR disperses onto less relevant material.The table compares k-NN, RNG-Score, and MMR for a query needing the 1925 Birthday Honours and George V.Source: §3.2 · p. 6, Table 1 · p. 7

3.3 Properties and instantiation

  • At both extremes of its margin, the RNG-Score reduces exactly to k-NN, but interior margins can reorder selections adversely because the score uses no relevance labels.Unlike Maxmin and DPP, it has a relevance-only operating point at both margin extremes; MMR has one at λ = 1.Source: §3.3 · p. 7
  • The score suppresses strictly closer near-copies but does not suppress exactly coincident copies, so its redundancy gains target perturbed semantic duplicates rather than byte-exact duplication.The paper identifies hash-level deduplication as an upstream option for byte-exact copies.Source: §3.3 · p. 7
  • The RNG-Score can accommodate settings where query–document distance differs from embedding-space distance, including cross-encoders, and can also take a kernel as input.Source: §3.3 · p. 7

4 Redundancy Diagnostics and the Decision Rule

The section defines pool- and query-level redundancy diagnostics from embeddings already held by the retrieval system, then uses a query-level threshold to decide when to diversify. The threshold is tied to the query's evidence requirement, and free tuning recovers a value near that requirement.

4.1 Near-duplicate pair fraction

  • PoolRedundancy measures the fraction of passage pairs whose cosine similarity exceeds 0.95, using embeddings already held by the system without relevance judgments or gold answers.Because the cutoff depends on the encoder's similarity scale and the fraction grows quadratically with duplicate-cluster size, comparisons should hold encoder and pool size fixed.Source: §4 · p. 7, §4.1 · p. 8

4.2 Effective size of the nearest-neighbor selection

  • T(q) measures the effective number of geometrically distinct embeddings in the k-NN selection, not the number of semantically distinct evidence pieces it covers.It costs one k × k eigendecomposition on embeddings already in memory; at k = 5 and D = 1024, the full trigger averages 20.5 µs per query.Source: §4.2 · p. 8

4.3 The decision rule

  • The rule diversifies when the effective distinct-document count T(q) falls below τ = min{h, k}; when h = 1, it reduces to k-NN by construction.Here h is the number of distinct evidence pieces a query needs; gold-derived h is treated as an oracle analysis, while relevant-document count is only a proxy for evidence multiplicity on graded-relevance tasks.Source: §4.3 · p. 8
  • At k = 5 and k = 10, freely tuned thresholds recover τ* ≈ h, with a wide plateau of equivalent thresholds around it.Source: §4.3 · p. 9
  • The pool-level redundancy crossover corresponds to the query-level trigger rate rising from under 16% to over 80% of queries below τ.The pair-fraction diagnostic is measured over m documents, while τ tests the k ≪ m documents selected for an individual query.Source: §4.3 · p. 9

5 Experimental Setup

The experiments compare retrieval selection under shared candidate pools across datasets with different evidence requirements, then test how redundancy, decision rules, and answer generation affect outcomes.

5.1 Research questions

  • The five research questions test clean-pool diversification, manipulated redundancy, oracle headroom, query-level decisions, and answer quality under redundancy.RQ1 also asks whether geometric diversification improves standard benchmarks over nearest-neighbor selection.Source: §5.1 · p. 9

5.2 Datasets

  • Datasets span multi-hop QA, single-answer controls, and BEIR tasks ranging from mostly single-evidence SciFact to multi-evidence FiQA-2018 and saturated TREC-COVID.HotpotQA questions require two supporting paragraphs from distinct articles; MuSiQue varies from two to four supporting passages.Source: §5.2 · p. 9

5.3 Models

  • The encoder comparisons use bge-m3, Qwen3-Embedding-4B, and lightweight all-MiniLM-L6-v2; answer generation uses flan-t5-base and, in specified analyses, Qwen3.8-27B.The cross-encoder pipeline uses bge-reranker-v2-m3.Source: §5.3 · p. 10

5.4 Baselines

  • Baselines include MMR, Maxmin, greedy DPP, and RNG-Score; among the evaluated grids, RNG-Score alone can express a no-diversification fallback.MMR reproduces k-NN at λ = 1, represented by the k-NN row rather than an interior grid point.Source: §5.4 · p. 10

5.5 Evaluation metrics

  • Evaluation separates relevance, annotation-free spread, intent-aware coverage, and generation quality using Recall, NDCG, APD, Vendi, α-NDCG, S-Recall, EM, and F1.Recall@k includes gold passages missing from the first-stage pool, whereas S-Recall@k counts only retrievable subtopics.Source: §5.5 · p. 10
  • The study reports worst-case downside against k-NN and minimax regret against a common per-regime oracle; both measures depend on the evaluated method grids.The two measures answer different questions and can order methods differently.Source: §5.5 · pp. 10–11

5.6 Protocol

  • Each reranker selects from the same first-stage candidate pool; default pool size is 100, with k = 5 for QA and k = 10 for BEIR.Hyperparameters are selected on held-out validation data; reported comparisons use test queries and, unless noted, three seeds.Source: §5.6 · p. 11
  • Redundancy is varied through identity-preserving near-duplicate injection and overlapping sliding-window chunks while candidate-pool size is held fixed.The decision rule compares the effective number of distinct selected documents with the query’s evidence requirement; its oracle comparisons use gold access.Source: §5.6 · p. 12

6 Results

Across the evaluated settings, diversification is costly on clean pools but can help when redundancy crowds out distinct evidence. A frozen query-level rule tracks the better fixed policy and its retrieval gains carry over to answer quality.

6.1 RQ1: Diversification on standard benchmarks

  • On clean HotpotQA pools, fixed-pressure diversifiers lose 0.7–33.0 S-Recall@5 points; after a cross-encoder, CE top-k wins every fixed-pressure comparison.The tuned RNG-Score is within the materiality tolerance of k-NN on the clean HotpotQA comparison.Source: §6.1 · pp. 13–14, Table 2 · p. 13, Table 4 · p. 14
  • Across five BEIR tasks, fixed-pressure diversifiers lose on both NDCG@10 and α-NDCG@10, while tuned RNG-Score stays within one point of k-NN on the three replicated tasks.The replicated-task conclusions are exploratory because those query sets are small.Source: §6.1 · p. 13, Table 3 · p. 13

6.2 RQ2: Manipulating pool redundancy

  • At ρ = 0.1, tuned MMR improves HotpotQA S-Recall@5 over k-NN by +1.83 points; at ρ = 1, MMR gains +22.2 points and RNG-Score +12.7.The MMR paired effect changes from −0.02 points at ρ = 0.05 to +1.83 at ρ = 0.1, bracketing the crossover.Source: §6.2 · p. 15, Table 6 · p. 15
  • With overlapping chunks, k-NN falls by up to 4.0 S-Recall points, while relevance-aware diversifiers hold flat or improve; greedy DPP gains 7.2 points on 2WikiMultiHopQA and 9.9 on MuSiQue.On saturated TREC-COVID, k-NN coverage does not collapse, yet tuned RNG-Score leads it by 4.6 points at the highest overlap.Source: §6.2 · p. 16, Table 8 · p. 18

6.3 RQ3: Oracle headroom

  • Oracle headroom grows with redundancy on multi-evidence tasks but stays low on single-evidence SciFact; on clean HotpotQA it improves over k-NN on only 5.8% of queries.At ρ = 1, the oracle improves on 34.8% of FiQA-2018 queries and over half of HotpotQA queries.Source: §6.3 · p. 17, Figure 6 · p. 18

6.4 RQ4: The decision rule

  • The frozen rule captures 60% of all-methods oracle headroom and 91% of per-level tuned-selector gain, staying within 0.7 points of k-NN on clean levels and within 0.3 points of always-MMR from ρ = 0.1.The rule diversifies when the effective number of distinct selected documents falls below the evidence requirement.Source: §6.4 · p. 18, Table 9 · p. 19
  • Without retuning, the rule transfers across encoders, k, redundancy mechanisms, and datasets; it is exactly k-NN on single-hop NQ-Open and gains under redundancy on nearly every multi-evidence sweep.The reported exceptions to staying within one point on clean pools are FiQA-2018 and saturated TREC-COVID sweeps.Source: §6.4 · p. 19

6.5 RQ5: Answer quality under redundancy

  • At ρ = 1, MMR beats k-NN by +4.7 EM points on HotpotQA, while the decision rule stays within 0.2 EM points of the better policy at every level.The Qwen3.8-27B comparison retains the same clean-versus-heavy redundancy pattern, with the rule within 0.1 points of the better fixed policy at both endpoints.Source: §6.5 · pp. 19–20, Table 11 · p. 20

7 Discussion

The discussion reconciles mixed findings by linking diversification’s value to candidate-pool redundancy, and argues for selective use with a reachable nearest-neighbor fallback. It also identifies evidence multiplicity as the rule’s threshold and the RNG-Score margin as a diagnostic of duplicate structure.

7.1 Reconciling the literature

  • Findings that diversification helps or does not help arise in different redundancy regimes, so neither conclusion transfers across regimes without qualification.The discussion associates positive findings with redundant pools and negative findings with nonredundant pools.Source: §7.1 · p. 21

7.2 Clean pools resist diversification

  • On clean pools, geometric spread can conflict with coverage-aware metrics, and the all-methods oracle suggests little gain over nearest-neighbor retrieval.The discussion recommends treating spread metrics as descriptive and reporting coverage-aware metrics when labels permit.Source: §7.2 · pp. 21–22

7.3 Reading the regime from the RNG-Score

  • A small negative RNG-Score margin signals duplicate-scale structure, while fallback-region or seed-unstable margins indicate little reliable structure to remove.Margin sign changes differ across encoders because duplicate pairs occupy different scales relative to query–document distances.Source: §7.3 · p. 22

7.4 Deploying the rule

  • The decision rule adapts to redundancy, but its threshold uses evidence multiplicity treated as a workload property that deployments must know or estimate.Behavior with an estimated rather than annotated evidence requirement remains untested.Source: §7.4 · p. 22

7.5 A reachable fallback as a design requirement

  • Because fixed diversification strength interacts unpredictably with pool geometry, the discussion argues that every diversifier should have a reachable relevance-only fallback.A fallback can be structural, as with RNG-Score margin extremes, or operational, by gating diversification on a redundancy trigger.Source: §7.5 · p. 23

8 Limitations

The authors qualify their conclusions by noting limits in statistical coverage, redundancy realism, rule deployment, task scope, generation evaluation, and baseline selection.

Statistical coverage

  • Some result families are descriptive, BEIR conclusions are exploratory at 50–300 queries, and transfer sweeps share queries and corpora rather than providing independent validation.The authors say dataset-level generalization would require hierarchical analysis or more independently sampled corpora.Source: §8 · p. 23

Redundancy realism

  • Redundancy tests use sentence-shuffled copies and natural chunk overlap, leaving injected paraphrases, independent production corpora, and injection-protocol sensitivity untested.Chunking also uses an optimistic coverage convention and is not paired with generation.Source: §8 · p. 23

Scope of the rule and its guarantees

  • The rule assumes task-specific evidence multiplicity, and its behavior with estimated rather than annotated evidence requirements is untested.Transfer evidence at k = 10 covers only the specified HotpotQA injection replica and three BEIR sweeps; margin tuning also needs adequate validation data.Source: §8 · p. 23

Task and domain scope

  • The study covers English factoid, multi-hop QA, and BEIR-style retrieval, leaving multilingual retrieval, summarization, and exploratory search untested or out of scope.The authors explicitly exclude open-ended information seeking where answer diversity or comprehensiveness has independent value.Source: §8 · p. 23

Generation

  • Generation results rely on Qwen3.8-27B for specified settings but use flan-t5-base alone for intermediate injection levels and remaining datasets.Prompt-format sensitivity and variability across splits and injection draws are untested for the single-run results.Source: §8 · p. 23

Baselines

  • The comparison uses classical fixed-pressure diversifiers, leaving adaptive and Vendi-objective selectors on the same pools and quality-weighted DPPs for future work.Source: §8 · p. 23

9 Conclusion

The conclusion finds that diversification’s value depends on candidate-pool redundancy: fixed-pressure methods often harm clean-pool retrieval, while relevance-aware diversifiers outperform nearest-neighbor selection on redundant multi-evidence tasks. It presents a query-level rule and RNG-Score as practical tools for selective diversification and safe fallback.

9 Conclusion

  • On clean pools, fixed-pressure diversifiers usually degrade relevance, coverage-aware diversity, and answer quality; on redundant multi-evidence tasks, relevance-aware diversifiers overtake nearest-neighbor selection.The latter advantage is wide under injection and smaller under chunk overlap.Source: §9 · pp. 23–24
  • The Vendi score of a query’s nearest neighbors supports a rule that diversifies when the score falls below the query’s evidence requirement.The rule stays within a one-point clean-pool materiality tolerance except on FiQA-2018 and saturated TREC-COVID, and recovers most of the value of perfect regime knowledge on redundant pools.Source: §9 · p. 24
  • Misspecification downside spans 10–33 coverage points, while RNG-Score’s provable nearest-neighbor limits anchor tuning to the relevance-only baseline and its tuned margin turns negative with duplicate structure.Source: §9 · p. 24
  • The full evaluation pipeline and per-run result files are available on GitHub.Source: §9 · p. 24

A Theoretical properties

The appendix establishes properties of the RNG-Score, including conditions for recovering nearest-neighbor rankings and guarantees for validated tuning. It also specifies limits on what monotonicity and finite-sample fallback claims imply.

Score properties

  • RNG-Score adds hinge penalties over closer competitors, and each candidate’s score is nondecreasing in the margin parameter.That pointwise monotonicity does not imply monotonicity of rankings, selected-set diversity, or task utility.Source: A Theoretical properties · p. 31

Exact recovery condition

  • A candidate’s score equals its query distance exactly when every closer competitor is at least its query distance plus the margin away from it.Source: A Theoretical properties · p. 31

Similarity invariance

  • Under an injective similarity transformation that scales all distances by the same positive factor, the score scales and its induced ordering is preserved.The margin must scale with the distances as well; scaling only part of the construction does not preserve the score.Source: A Theoretical properties · p. 31

Negative-margin fallback

  • At sufficiently negative margins, RNG-Score ranking coincides with nearest-neighbor ranking; under cosine distance, γ ≤ −2 guarantees this fallback on every finite pool.A smaller-magnitude endpoint such as γ = −0.5 has no uniform guarantee, even where it reproduces k-NN empirically.Source: A Theoretical properties · pp. 31–32

Positive-margin fallback

  • At sufficiently positive margins, the score ordering also coincides with nearest-neighbor ranking when query distances are pairwise distinct.Source: A Theoretical properties · p. 32

Validated fallback

  • If a finite tuning grid contains a margin that reproduces k-NN on every validation pool, the selected grid member cannot score worse on validation than k-NN.The finite-sample population bound additionally assumes independent validation units and a grid fixed independently of them; it does not cover distribution shift.Source: A Theoretical properties · pp. 32–33

B Cross-encoder dissimilarity

The cross-encoder adaptation applies RNG-Score using cross-encoder relevance for query-candidate comparisons and embedding-space distances for candidate-pair geometry. Tested distance normalizations yield similar tuned F1 results, and tuned margins reach or approach nearest-neighbor fallback limits across the evaluated datasets.

B Cross-encoder dissimilarity

  • The construction requires only a symmetric nonnegative dissimilarity, allowing distinct candidates to have zero query distance when their relevance scores equal one.Unlike a metric, the dissimilarity need not separate distinct points or satisfy the triangle inequality.Source: B Cross-encoder dissimilarity · p. 33
  • The adaptation sets query-candidate dissimilarity to one minus cross-encoder relevance and applies RNG-Score to that construction.The paper describes this as a symmetric nonnegative dissimilarity on the query and candidate set.Source: B Cross-encoder dissimilarity · p. 33
  • Cross-encoder scores determine relevance ordering, while embedding-space distances provide document-document comparisons and the pool radius.The closer competitors of a candidate are exactly those ranked above it by the cross-encoder.Source: B Cross-encoder dissimilarity · p. 33
  • All five tested distance variants land within half an F1 point of one another at their tuned margins, suggesting normalization has little impact on results.The variants include sigmoidal and reciprocal normalizations, relevance-scaled distance, and raw cosine distance.Source: B Cross-encoder dissimilarity · p. 33
  • Tuned margins reach or approach fallback limits on every dataset, reproducing the cross-encoder ranking exactly on 2WikiMultiHopQA at γ = −0.3.The reported tuned margins are −0.5 on HotpotQA, −0.3 on 2WikiMultiHopQA, −0.35 on NQ-Open, and +1.1 on MuSiQue.Source: B Cross-encoder dissimilarity · p. 33

C Kernelization

Kernelization lets the RNG-Score operate using kernel evaluations rather than explicit coordinates. The construction uses the same kernel input for DPP comparison, but applies local obstruction scoring instead of global log-determinant inference.

C Kernelization

  • Any positive-semidefinite kernel induces the symmetric nonnegative dissimilarity required by RNG-Score, whose hinge terms depend only on kernel evaluations.The squared distance is dK(x, y) = K(x, x) + K(y, y) − 2K(x, y), so explicit coordinates are unnecessary.Source: C Kernelization · p. 34
  • With the same kernel input, DPP performs global log-determinant inference while RNG-Score performs local obstruction scoring.The binary lune condition is invariant under squaring, so kernelization changes soft penalty weighting but not the obstruction graph.Source: C Kernelization · p. 34
  • For unit-normalized embeddings, the linear-kernel distance is twice the cosine distance, adding information when vector norms carry information.Source: C Kernelization · p. 34

D Statistical procedure

The statistical procedure tests whether diversification's paired effect against k-NN changes with redundancy, using query-clustered bootstrap uncertainty and Holm adjustment. Across thirteen sweeps, the interaction is positive and significant after adjustment except for MMR under SciFact injection; the authors also identify limits to the uncertainty estimates and small-set conclusions.

D Statistical procedure

  • The primary test compares each method's heavy-minus-clean change in paired S-Recall effect against k-NN, with uncertainty estimated by query-clustered bootstrap.Whole query trajectories are resampled 1,999 times; seed observations are averaged within query because test splits share queries.Source: D Statistical procedure · p. 34
  • Holm step-down adjustment controls familywise error separately for each sweep's method-by-level effects and primary interactions.The adjusted values determine reported significance; raw values are retained in the released archive.Source: D Statistical procedure · p. 34
  • Across thirteen sweeps, every diversifier's heavy-minus-clean interaction is positive and Holm-significant except MMR under SciFact injection.The exception is consistent with the evidence-multiplicity interpretation because single-hop SciFact offers no evidence to recover through added redundancy.Source: D Statistical procedure · p. 34, Table 12 · p. 35
  • Fixed-pool re-executions supply the interaction results and the displayed injection and chunk-overlap sweep tables, while other tables and figures use original runs.On small-pool sweeps, freezing candidate counts shifts some k-NN levels substantially, while paired interactions remain positive and significant.Source: D Statistical procedure · p. 34
  • Some families and non-HotpotQA cross-encoder comparisons are descriptive, and original runs did not serialize embedding tensors, post-encoder rankings, or answer strings.The complete archive of contrasts, intervals, p-values, improved/tied/harmed fractions, and an independent validator is released with the code.Source: D Statistical procedure · p. 35
  • Intervals do not account for residual dependence between queries sharing source documents, and conclusions on small BEIR sets are exploratory.The query is the finest resampling unit; the reporting tolerance is not an equivalence test.Source: D Statistical procedure · p. 35

E Single-stage comparisons on the remaining QA datasets

Single-stage reranking on natural QA pools shows dataset-dependent results, with mild diversification gains on MuSiQue and results near or below k-NN elsewhere. Within MuSiQue, tuned RNG-Score gains increase with query hop count.

E Single-stage comparisons on the remaining QA datasets

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