Finding the Right Balance: Relevance and Diversity in LLM Retrieval

Guillaume Brouillette; Faustin Kagabo; Usef Faghihi; Nadia Ghazzali

cs.IROct 7, 2026

Finding the Right Balance: Relevance and Diversity in LLM Retrieval

Authors: Guillaume Brouillette, Faustin Kagabo, Usef Faghihi, Nadia Ghazzali

Organizations: Université du Québec à Trois-Rivières, Trois-Rivières, Canada

Abstract

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.

Figures & tables

Figure 1 : The paper’s central result: coverage of three policies on HotpotQA fullwiki as measured pool redundancy grows under controlled injection. Nearest-neighbor selection, the framework default, collapses past the shaded crossover bracket (measured redundancy between

0.0012

and

0.0030

, Section 6.2 ). Diversifying hurts on clean pools and the decision rule of Section 4.3 tracks the upper envelope of both.

Panel of Figure 2 — Figure 2 : ( 2(a) ) The open lune of $x$ and $y$ (shaded) is the intersection of the two open balls of radius $d(x,y)$ centered at $x$ and $y$ ; $z_{1}$ lies inside it and obstructs the pair $\{x,y\}$ , so that pair is not an edge of the RNG , while $z_{2}$ does not. ( 2(b) ) The RNG of a planar point set, with an edge between exactly the pairs whose lune is empty.

Panel of Figure 3 — Figure 3 : One candidate pool, three computed top- $5$ selections (filled blue = selected, open = unselected, $\blacksquare=q$ ). ( 3(a) ) $k$ -NN spends the whole budget on a tight cluster of near-duplicates; ( 3(b) ) the RNG-Score keeps one cluster representative and disperses to nearby distinct points; ( 3(c) ) MMR pushes further out onto less relevant points.

rank	$k$ -NN	RNG-Score ( $\gamma{=}0$ )	MMR ( $\lambda{=}0.5$ )
1	1925 Birthday Honours	1925 Birthday Honours	1925 Birthday Honours
2	1915 Birthday Honours	David Lloyd George	Edward VII
3	1924 Birthday Honours	1915 Birthday Honours	George Champagne
4	1926 Birthday Honours	Henry V, Holy Roman Emperor	Julius Meinl V
5	1927 Birthday Honours	George V	A. Thynn, Marquess of Bath

Table 1: A HotpotQA fullwiki query needing two pieces of evidence ( 1925 Birthday Honours and George V , in bold).

Method	Recall@5	NDCG@5	$\alpha$ -NDCG@5	S-Recall@5	APD	Vendi	EM	F1
$k$ -NN	74.8	73.9	76.5	78.7	0.450	3.08	50.8	63.6
MMR ( $\lambda=0.3$ )	45.3	53.3	55.4	48.1	0.630	4.00	36.4	47.8
MMR ( $\lambda=0.5$ )	55.6	60.3	62.5	58.6	0.574	3.73	41.6	53.5
MMR ( $\lambda=0.7$ )	69.2	70.0	72.5	72.8	0.505	3.38	47.6	59.9
MMR ( $\lambda=0.9$ )	74.1	73.5	76.1	78.0	0.463	3.16	50.3	62.9
Maxmin	42.9	51.7	53.8	45.7	0.625	3.85	36.0	47.4

Table 2: Controlled reranking on HotpotQA (MDR top-100 pools, bge-m3 ,

m=100

k=5

; clean level of the sweep of Section 6.2 , on its grids). The four left metrics are objectives (best in bold, second best underlined); APD and Vendi are descriptive spread statistics, not objectives; EM and F1: one deterministic Qwen3.8-27B run, seed-

0

test split (

5{,}924

queries).

Method	SciFact	FiQA	TREC-COVID	ArguAna	Touché
$k$ -NN	64.1 / 64.1	41.7 / 46.7	66.1 / 70.2	38.3 / 38.3	25.2 / 27.8
MMR	52.9/52.9	29.6/33.0	37.0/40.3	0.2/0.2	10.9/12.9
Maxmin	49.4/49.4	27.2/30.2	46.7/52.0	0.9/0.9	9.2/11.7
Greedy DPP	56.0/56.0	30.9/34.4	39.8/43.8	1.0/1.0	11.0/13.2
RNG-Score	63.4 / 63.5	41.7 / 46.8	65.6 / 69.6	26.4 / 26.4	17.8 / 19.6

Table 3: NDCG@10 /

\alpha

-NDCG@10 on five BEIR tasks ( bge-m3 ,

k=10

; MMR at

\lambda=0.5

; best in bold, second best underlined). SciFact, FiQA and TREC-COVID are seed-replicated; conclusions on these small query sets are exploratory (Appendix D ). ArguAna and Touché are single-run.

Dataset	Method (post-CE)	Recall@5	NDCG@5	EM	F1
HotpotQA	CE top- $k$	89.6	87.9	41.0	53.3
	CE+ MMR	84.6	83.4	38.2	50.0
	CE+ DPP	80.0	80.8	36.2	47.7
	CE+ RNG-Score	89.6	87.9	41.0	53.3
2WikiMultiHopQA	CE top- $k$	90.6	90.3	31.3	37.9
	CE+ MMR	71.0	76.3	25.0	29.6

Table 4: Cross-encoder pipelines,

k=5

( MMR at its best

\lambda=0.7

; CE+ RNG-Score is the tuned dissimilarity variant of Appendix B ; the non-HotpotQA datasets are single-run). Best per dataset and column in bold; a tie occupies both ranks, so cells below a tied best are not underlined.

	$\rho=0$ (clean)		$\rho=1$ (redundant)
Method	best	worst	best	worst	max. downside	minimax regret
$k$ -NN	78.7		52.6		22.0	22.2
MMR	78.0	48.1	74.6	53.5	30.6	6.3
Maxmin	45.7	45.7	50.6	50.6	33.0	33.6
Greedy DPP	69.1	69.1	72.1	72.1	9.6	10.0
RNG-Score	79.0	74.8	65.2	52.8	3.9	9.5

Table 5: Misspecification downside ( 5.1 ) and common-oracle minimax regret ( 5.2 ) on HotpotQA, with the best and worst S-Recall@5 over each method’s grid on clean and heavily redundant pools (the

k

-NN row of the downside column is constructed against the best tuned method per regime and is not directly comparable to the others). Lower is better in the last two columns. Query-bootstrap

95\%

intervals (computed, like the regret column, from query-level test means, hence a few tenths off the displayed seed-mean cells): downside MMR

[30.2,31.5]

, Maxmin

[32.6,34.0]

, DPP

[9.2,10.3]

, RNG-Score

[3.5,4.4]

; regret

k

-NN

[21.6,22.8]

, MMR

[5.9,6.8]

, Maxmin

[32.9,34.3]

, DPP

[9.6,10.6]

, RNG-Score

[8.9,10.0]

. Best per column in bold, second best underlined.

Method	$\rho{=}0$	$0.025$	$0.05$	$0.1$	$0.15$	$0.25$	$0.5$	$1.0$
	0	.0006	.0012	.0030	.0054	.012	.042	.147
$k$ -NN	79.0	77.3	76.9	71.4	62.1	54.5	53.0	52.7
MMR ( $\lambda^{*}$ )	78.2	77.0	76.9	73.2	73.3	73.5	73.9	74.9
Maxmin	45.7	46.1	46.2	46.7	47.1	47.5	48.6	51.8
Greedy DPP	69.2	69.5	69.9	70.3	70.6	70.8	71.3	72.4
RNG-Score ( $\gamma^{*}$ )	79.2	77.8	77.8	76.5	74.7	71.7	68.1	65.4

Table 6: Redundancy-injection sweep, HotpotQA ( bge-m3 ,

k=5

); S-Recall@5, operating points tuned per

\rho

. Second header row: measured pool redundancy ( 4.1 ). Best per column in bold, second best underlined.

Panel of Figure 4 — Figure 4 : The HotpotQA injection sweep under three encoders: S-Recall vs measured near-duplicate pair fraction ( 4.1 ), on common axes (log-scaled with the clean level kept on-axis).

Panel of Figure 5 — Figure 5 : The BEIR injection sweeps ( bge-m3 , $k=10$ , three seeds): S-Recall@10 vs measured near-duplicate pair fraction ( 4.1 ), on common axes. Single-evidence SciFact ( 5(a) ) stays flat across the sweep; multi-evidence FiQA-2018 ( 5(b) ) reproduces the multi-hop collapse-and-crossover pattern.

Sweep	$\rho{=}0$	$0.025$	$0.05$	$0.1$	$0.15$	$0.25$	$0.5$	$1.0$
HotpotQA, bge-m3	$+0.2$	$-0.3$	$-0.3$	$-0.2$	$-0.2$	$-0.2$	$-0.2$	$-0.2$
HotpotQA, Qwen3-Embedding-4B	$+0.3$	$\pm$	$\pm$	$-0.2$	$-0.1$	$-0.1$	$-0.1$	$-0.1$
HotpotQA, all-MiniLM-L6-v2	$+0.3$	$+0.3$	$+0.2$	$+0.2$	$+0.2$	$\pm$	$-0.1$	$-0.1$
SciFact, bge-m3	$-0.2$	$\pm$	$\pm$	$-0.3$	$\pm$	$\pm$	$\pm$	$\pm$
FiQA-2018, bge-m3	$-0.2$	$\pm$	$-0.2$	$-0.2$	$-0.2$	$-0.2$	$-0.2$	$-0.2$

Table 7: Validation-selected RNG-Score margins

\gamma^{*}

per injection level: modal value across the three seeds where the seeds agree in sign,

\pm

where they do not.

Method	HotpotQA	2Wiki	MuSiQue	SciFact	NQ-Open	TREC-COVID
hops	2	2	2–4	1	1	sat.
red .75	.001	.011	.015	.002	.005	.006
$k$ -NN	78.1 /75.0	88.5 /87.4	74.1/73.2	77.2 /73.2	92.1/89.7	21.8 /23.1
Maxmin	46.5/48.3	74.7/83.6	56.9/69.5	57.8/62.2	86.8/87.6	14.9/21.9
Greedy DPP	69.5/70.9	87.2/ 94.4	76.2/ 86.1	73.3/74.1	91.6/92.0	18.6/25.9
MMR ∗	77.6/ 76.6	88.2/91.5	76.3 /85.0	77.0 / 76.1	92.8 / 93.0	21.4 / 27.2

Table 8: Chunk-overlap sweep ( bge-m3 ,

k=5

;

k=10

for SciFact and TREC-COVID; 2Wiki abbreviates 2WikiMultiHopQA). Each cell reports the row method’s S-Recall@

k

on the non-overlapping pool / at overlap

0.75

(tuned operating points per level); the header rows give each dataset’s hop count and measured redundancy ( 4.1 ) at overlap

0.75

. Best per dataset in bold, second best underlined (ties both bold and occupying both ranks). The NQ-Open sweep is single-run; conclusions on the small SciFact and TREC-COVID query sets are exploratory (Appendix D ); saturated TREC-COVID (mean

493

relevant documents per query) has no hop count.

Panel of Figure 6 — Figure 6 : Oracle headroom: percentage of test queries on which the all-methods oracle beats $k$ -NN (HotpotQA, 2Wiki and MuSiQue at $k=5$ ; SciFact, FiQA-2018 and TREC-COVID at $k=10$ ; three seeds throughout). ( 6(a) ) Injection sweeps vs injected fraction $\rho$ (log-scaled axis with the clean level kept on-axis); ( 6(b) ) Chunk-overlap sweeps vs overlap.

Panel of Figure 7 — Figure 7 : The decision rule on the HotpotQA sweep. ( 7(a) ) Pooled validation S-Recall@5 as the trigger threshold $\tau$ varies continuously. ( 7(b) ) The frozen rule per injection level (log-scaled $\rho$ axis, ticks at the sweep levels).

Reference bounds (not deployable policies)
Selector	$\rho{=}0$	$0.025$	$0.05$	$0.1$	$0.15$	$0.25$	$0.5$	$1.0$	pool
always $k$ -NN	78.7	77.0	76.7	71.1	62.0	54.5	52.9	52.6	65.7
always $D^{*}$	72.8	72.7	73.0	73.0	73.1	73.3	73.7	74.6	73.3
rule	78.7	76.9	76.0	72.9	73.1	73.2	73.5	74.3	74.8
trigger %	0.7	3.3	15.5	81.0	87.8	90.0	91.4	92.9
per-level tuned	78.9	77.6	77.5	76.2	74.5	73.3	73.7	74.6	75.8

Table 9: The frozen rule (

\tau=h=2

D^{*}=\textsc{MMR}(0.7)

) per injection level, S-Recall@5. “Per-level tuned” knows the regime; the oracle is the all-methods per-query bound of Section 6.3 ; the trigger rate is the fraction of queries on which the rule diversifies. Among the three policies, best in bold, second best underlined.

Different encoder (injection)
Transfer target	clean $\Delta$	heavy $\Delta$	pooled $\Delta$
Qwen3-Embedding-4B	$-0.3$	$+22.5$	$+9.8$
all-MiniLM-L6-v2	$-0.2$	$+13.6$	$+5.9$
Different $k$ (injection)
HotpotQA ( $k{=}10$ )	$\phantom{-}0.0$	$+24.1$	$+5.7$
Different mechanism (chunk overlap)

Table 10: Transfer of the frozen rule (

\tau=\min\{h,k\}

with gold

h

, an oracle analysis;

D^{*}=\textsc{MMR}(0.7)

) to further sweeps with no retuning, grouped by what each sweep changes relative to the tuning sweep ( bge-m3 HotpotQA injection). Each

\Delta

is the rule’s S-Recall@

k

minus

k

-NN’s at the same sweep level, averaged over seeds (positive favors the rule): clean

\Delta

is the worst

\Delta

over the near-clean levels (

\rho\leq 0.05

on injection sweeps, overlap

\leq 0.25

on chunking sweeps), heavy

\Delta

the

\Delta

at the heaviest level (

\rho=1

, respectively overlap

0.75

) and pooled

\Delta

the difference with all levels pooled.

Panel of Figure 8 — Figure 8 : Exact match vs injected redundancy on ( 8(a) ) HotpotQA and ( 8(b) ) 2WikiMultiHopQA, generator flan-t5-base . Log-scaled $\rho$ axis with ticks at the sweep levels.

	HotpotQA		2WikiMultiHopQA
Method	$\rho{=}0$	$\rho{=}1$	$\rho{=}0$	$\rho{=}1$
$k$ -NN	50.8 / 63.6	41.7/53.6	63.4 / 71.8	49.5/56.5
MMR ( $\lambda{=}0.7$ )	47.6/59.9	47.8 / 60.5	59.3/67.5	55.5 / 63.5
rule ( $\tau{=}h$ )	50.8 / 63.6	47.8 / 60.4	63.4 / 71.9	55.4 / 63.4

Table 11: Answer quality (EM/F1) at the clean and heaviest injection levels, generator Qwen3.8-27B (a single run per dataset). Best in bold, second best underlined.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Mechanism	MMR ∗	Maxmin	Greedy DPP	RNG-Score
HotpotQA	injection	$+23.0$ ( $+22.5$ )	$+32.4$ ( $+31.8$ )	$+29.5$ ( $+28.9$ )	$+12.5$ ( $+12.1$ )
HotpotQA	chunk overlap	$+2.1$ ( $+1.8$ )	$+4.8$ ( $+4.4$ )	$+4.4$ ( $+4.0$ )	$+3.0$ ( $+2.7$ )
2WikiMultiHopQA	injection	$+22.0$ ( $+21.7$ )	$+27.4$ ( $+26.8$ )	$+24.3$ ( $+23.9$ )	$+12.1$ ( $+11.8$ )
2WikiMultiHopQA	chunk overlap	$+4.3$ ( $+4.0$ )	$+9.9$ ( $+9.5$ )	$+8.3$ ( $+7.9$ )	$+6.0$ ( $+5.7$ )
MuSiQue	injection	$+23.8$ ( $+23.0$ )	$+31.6$ ( $+30.3$ )	$+27.5$ ( $+26.6$ )	$+17.3$ ( $+16.5$ )
MuSiQue	chunk overlap	$+9.6$ ( $+8.7$ )	$+13.5$ ( $+12.2$ )	$+10.8$ ( $+9.9$ )	$+9.9$ ( $+9.1$ )

Appendix

Table 12: Primary test: heavy-minus-clean change of each method’s paired S-Recall effect against

k

-NN, in percentage points (one-sided

95\%

lower bound in parentheses). All entries are significant after Holm adjustment except the one marked

\dagger

Dataset	red 0	$k$ -NN	Maxmin	DPP	MMR ∗	RNG-Score ∗
2WikiMultiHopQA	0.0006	85.7	69.3	84.4	85.5	85.8
MuSiQue	0.0011	69.2	48.4	71.3	71.3	71.7
NQ-Open	0.0007	92.1	86.8	91.6	92.8	92.9

Appendix

Table 13: Single-stage reranking on the natural pools of the remaining QA datasets (S-Recall@5, bge-m3 , single run each; red 0 = measured pool redundancy ( 4.1 ); tuned operating points

\lambda=0.9/0.9/0.7

and

\gamma=-0.3/0.1/-0.1

for 2WikiMultiHopQA/MuSiQue/NQ-Open). Best in bold, second best underlined.

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