OPERA: Online Data Pruning for Efficient Retrieval Model Adaptation

OPERA: Online Data Pruning for Efficient Retrieval Model Adaptation Haoyang Fang, Shuai Zhang, Yifei Ma, Hengyi Wang, Cuixiong Hu, Katrin Kirchhoff, Bernie Wang, George Karypis Amazon Web Services haoyfang,shuaizs,yifeim,yuyawang@amazon.com Abstract Domain-specific finetuning is essential for dense retrievers, yet not all training pairs contribute equally to the learning process. We introduce OPERA, a data pruning framework that exploits this heterogeneity to improve both the effectiveness and efficiency of retrieval model adaptation. We first investigate static pruning (SP), which retains only high-similarity query-document pairs, revealing an intrinsic quality-coverage tradeoff: ranking (NDCG) improves while retrieval (Recall) can degrade due to reduced query diversity. To resolve this tradeoff, we propose a two-stage dynamic pruning (DP) strategy that adaptively modulates sampling probabilities at both query and document levels throughout training, prioritizing high-quality examples while maintaining access to the full training set. Evaluations across eight datasets spanning six domains demonstrate the effectiveness of both approaches: SP improves ranking over standard finetuning (NDCG@10 +0.5%), while DP achieves the strongest performance on both ranking (NDCG@10 +1.9%) and retrieval (Recall@20 +0.7%), with an average rank of 1.38 across all methods. These findings scale to Qwen3-Embedding, an LLM-based dense retriever, confirming architecture-agnostic benefits. Notably, DP reaches comparable performance in less than 50% of the training time required by standard finetuning. 1 Introduction Dense retrievers have advanced information retrieval (Izacard et al., 2021; Reimers and Gurevych, 2019; Karpukhin et al., 2020; Xiao et al., 2023; Muennighoff et al., 2024; Wang et al., 2022; Lee et al., 2024), substantially outperforming traditional sparse methods (Robertson et al., 2009; Ramos and others, 2003). Built on pretrained language models (Vaswani et al., 2017; Devlin et al., 2018; Jiang et al., 2023), these models achieve strong zero-shot performance across diverse benchmarks (Thakur et al., 2021; Muennighoff et al., 2022). Nevertheless, achieving optimal performance on specific downstream tasks still requires domain-specific finetuning (Thakur et al., 2022; Howard and Ruder, 2018). Data pruning and coreset selection have shown promise for improving training efficiency in neural networks (Toneva et al., 2018; Marion et al., 2023; Sorscher et al., 2022; Killamsetty et al., 2021), and dynamic pruning methods have further demonstrated that adjusting data selection during training can maintain performance while reducing computation (Qin et al., 2023; Li et al., 2024; Huang et al., 2024). However, these methods are designed for standard classification or generation tasks where training samples are treated as independent, identically distributed instances. Dense retriever finetuning is fundamentally different: it employs a two-stage contrastive sampling framework (Xiao et al., 2023; Chen et al., 2024; Zhang et al., 2023) where queries are first sampled, and then positive and negative documents are selected for each query. This hierarchical structure means that data quality operates at two distinct granularities (query relevance and document relevance), creating unique challenges that existing pruning methods do not address. To our knowledge, no prior work has studied data pruning specifically for dense retriever finetuning. A detailed discussion of related work is provided in Appendix A. We introduce OPERA, a framework that exploits the heterogeneous quality of training data (Tirumala et al., 2024; Abbas et al., 2023) to improve domain adaptation for dense retrievers. Our investigation begins with static pruning (SP), which retains only the highest-similarity query-document pairs for training. This simple strategy reveals a key insight: quality-based filtering consistently improves ranking metrics (NDCG) but can degrade retrieval coverage (Recall), because pruning disproportionately removes queries with fewer high-quality documents, breaking the balanced sampling that retrievers rely on for broad coverage. This quality-coverage tradeoff is intrinsic to the two-stage sampling structure of retrieval training and motivates the need for a more nuanced approach. To resolve this tradeoff, we propose dynamic pruning (DP), which maintains the complete training set while adaptively adjusting sampling probabilities at both query and document levels. Unlike InfoBatch (Qin et al., 2023), which uses a fixed loss-average threshold and rescales gradients to maintain unbiasedness, our approach implements dynamic thresholds that evolve throughout training via cosine scheduling, and preserves original learning rates to emphasize high-quality training signals. Rather than employing hard exclusions, DP assigns reduced but nonzero sampling probabilities to lower-quality examples, ensuring continued data diversity while prioritizing informative instances. Concretely, our dynamic pruning framework combines three components: (1) hierarchical pruning at both query and document granularities, reflecting the two-stage sampling structure; (2) dynamic threshold scheduling that progressively sharpens selection as model representations improve; and (3) soft pruning mechanisms that modulate sampling probabilities rather than discarding data. We evaluate OPERA on eight datasets spanning nutrition (Boteva et al., 2016; Thakur et al., 2021), medicine (Rekabsaz et al., 2021), finance (Maia et al., 2018; Thakur et al., 2021), non-factoid QA (Hashemi et al., 2020), factoid QA (Joshi et al., 2017; Karpukhin et al., 2020; Yang et al., 2018; Thakur et al., 2021), and fact verification (Thorne et al., 2018; Thakur et al., 2021), including both datasets seen and unseen during pretraining. Our contributions are: • We identify a quality-coverage tradeoff unique to retrieval’s two-stage sampling: static quality filtering improves ranking but degrades recall. This finding holds across encoder-only (BGE) and LLM-based (Qwen3-Embedding) retrievers. • We propose dynamic pruning with hierarchical scheduling that resolves this tradeoff, improving both ranking and recall while halving convergence time. We provide an efficient formulation compatible with fixed-iteration training frameworks. • We validate OPERA across 8 datasets, 6 domains, and 2 architectures (encoder-only BGE and decoder-based Qwen3-Embedding), with theoretical guarantees on when pruning outperforms standard finetuning. 2 Methodology 2.1 Preliminary: Standard Finetuning (FT) Given a dataset Q with n queries where each query q∈Qq∈ Q has mqm_q positive documents, we adopt a contrastive learning framework with two-stage sampling (Xiao et al., 2023). For each training step, we first uniformly sample queries from Q. Then, for each sampled query, we randomly select one positive document d from its mqm_q positive documents and one negative document through hard negative mining for loss computation. The sampling probabilities are: Pt​(q)=1/n,Pt​(d|q)=1/mqP_t(q)= 1n, P_t(d|q)= 1m_q (1) Note that for notational simplicity, we omit the time step t for the following equations. 2.2 Static Pruning (SP) To understand how data quality affects retrieval finetuning, we begin with a straightforward approach inspired by Sorscher et al. (2022): retaining only the highest-quality training pairs. We compute cosine similarity between each query-document pair using the pretrained model and retain only the top fraction of pairs for training. Mathematically, we use an indicator function I to mark whether a query or query-document pair is kept: I=1,if kept0,if prunedI= cases1,&if kept\\ 0,&if pruned cases (2) This adjusts our sampling probabilities to: P​(q)=∑dId∑q∑dId,P​(d|q)=Id∑IdP(q)= _dI_d _q _dI_d, P(d|q)= I_dΣ I_d (3) In practice, we select top k​∑mqkΣ m_q query-document pairs with highest similarity scores for training, where k is the data retention rate: k=∑q∑dId∑mqk= _q _dI_dΣ m_q (4) Crucially, quality-based filtering breaks the uniform query sampling that standard finetuning relies on: queries with more high-similarity documents are overrepresented, while queries with fewer such documents may be excluded entirely. This improves ranking (e.g., NDCG) by focusing on well-matched pairs, but can degrade recall by reducing coverage of the query space. This quality-coverage tradeoff is intrinsic to the two-stage sampling structure of retrieval training and motivates the dynamic approach described in Section 2.3. Alternative scoring metric. We also evaluate consistency-based scoring (CBS) (Wang et al., 2022), which ranks each positive pair against random negatives and retains pairs that consistently rank highly, adapted to our finetuning setting. CBS and cosine similarity yield comparable results (Appendix D.1), but CBS is incompatible with DP as it requires re-embedding all negative documents after each model update. We therefore adopt cosine similarity as the default metric for both SP and DP. 2.3 Dynamic Pruning (DP) Algorithm 1 Dynamic Pruning procedure OPERA αs←query strength start _s strength start αe←query strength end _e strength end rs←query ratio startr_s ratio start βs←doc strength start _s strength start βe←doc strength end _e strength end vs←doc ratio startv_s ratio start ve←doc ratio endv_e ratio end n←size of datasetn of dataset tm​a​x←max training stepst_max training steps n0=⌊n⋅(1−rs)/αs+rs⋅n⌋n_0= n·(1-r_s)/ _s+r_s· n for each iteration do t←current training stept training step Update q ⊳ Query scores Update p ⊳ Pos. scores SampleQuery​() SampleQuery() SampleDocument​() SampleDocument() end for end procedure procedure SampleQuery α←αe+(1+cos⁡(ttm​a​x​π))⋅(αs−αe)2α← _e+ (1+ ( tt_maxπ))·( _s- _e)2 r←α⋅n0−n(α−1)⋅nr← α· n_0-n(α-1)· n qt​o​p←Top r Queriesq_top $r$ Queries qr​e​m←q​u​e​r​i​e​s∖qt​o​pq_rem← queries q_top qr​a​n​d←Random Select n0−r from qr​e​mq_rand Select $n_0-r$ from $q_rem$ q′←qt​o​p∪qr​a​n​dq ← q_top∪ q_rand Sample from q′q end procedure procedure SampleDocument β←βe+(1+cos⁡(ttm​a​x​π))⋅(βs−βe)2β← _e+ (1+ ( tt_maxπ))·( _s- _e)2 v←ve+(1+cos⁡(ttm​a​x​π))⋅(vs−ve)2v← v_e+ (1+ ( tt_maxπ))·(v_s-v_e)2 Calculate the threshold T at cutoff v w=(>T)⋅(β−1)+1w=(p>T)·(β-1)+1 w=n​o​r​m​a​l​i​z​e​(w)w=normalize(w) Sample documents with weights w end procedure The quality-coverage tradeoff identified in SP arises because hard pruning permanently discards data, reducing the diversity of training signals. Dynamic Pruning (DP) resolves this tradeoff by replacing hard exclusions with soft sampling modulation: high-quality examples receive elevated sampling probabilities, while lower-quality examples remain accessible with reduced frequencies. This preserves the broad data coverage needed for recall while concentrating training effort on informative instances. The sampling process, detailed in Algorithm 1, consists of two components. For query sampling, we combine top-scoring queries with randomly selected low-scoring queries to maintain diversity. In document sampling, we assign sampling weights to documents based on their quality while ensuring all documents maintain a non-zero probability of selection. The sampling probabilities for queries and query-document pairs are defined as: P(q)=1(1+α)​n−n0,if low qualityα(1+α)​n−n0,if high quality,P(d|q)=1[1−(1−β)​rq]​mqif low qualityβ[1−(1−β)​rq]​mq,if high qualityP(q)= cases 1(1+α)n-n_0,&if low quality\\ α(1+α)n-n_0,&if high quality cases , P(d|q)= cases 1[1-(1-β)r_q]m_q&if low quality\\ β[1-(1-β)r_q]m_q,&if high quality cases (5) Here, n0n_0 represents a fixed virtual dataset size, ensuring compatibility with training frameworks that require a static dataset size. rqr_q is the fraction of high-quality positive pairs for each query. α and β are sampling strength parameters that vary during training: α​(t)=αe+(1+cos⁡(ttm​a​x​π))⋅(αs−αe)2α(t)= _e+ (1+ ( tt_maxπ))·( _s- _e)2 (6) where αs _s and αe _e denote the start and end sampling strengths respectively, and tm​a​xt_max is the maximum training steps. Similarly, β follows the same cosine decay schedule. Update Interval To mitigate the computational overhead associated with frequent score updates and pruning operations, we introduce an update interval parameter IuI_u. We update the query scores q every IuI_u iterations, while maintaining the per-iteration random selection of d due to its negligible computational cost. Our empirical analysis demonstrates that this optimization reduces additional computation time from 4.5% to 1.64% over the baseline, without impacting performance. The effects of varying IuI_u are examined in Section 3.4.2. 2.4 Theoretical Analysis: When Does Pruning Help? We formalize the conditions under which data pruning outperforms standard finetuning. In dense retrieval, a query q and its positive document d are encoded into normalized embeddings eq,ed∈ℝhe_q,e_d ^h, with cosine similarity s​(eq,ed)=eqT​eds(e_q,e_d)=e_q^Te_d. We analyze SP and DP by studying how each method’s sampling strategy affects the optimal query embedding when some positive labels are noisy. Throughout the analysis, we consider a single query q. Lemma 1. Let u,v∈ℝnu,v ^n be unit vectors with u≠vu≠ v, and k∈(0,1)k∈(0,1). Define f​(k)=(k​u+(1−k)​v)T​u‖k​u+(1−k)​v‖.f(k)= (ku+(1-k)v)^Tu\|ku+(1-k)v\|. Then f′​(k)>0f (k)>0 for all k∈(0,1)k∈(0,1). Proof. Direct computation yields f′​(k)=(1−(uT​v)2)​(1−k)‖k​u+(1−k)​v‖3.f (k)= (1-(u^Tv)^2)(1-k)\|ku+(1-k)v\|^3. Since u≠v⟹uT​v<1u≠ v u^Tv<1, and k<1k<1, thus f′​(k)>0f (k)>0. ∎ Theorem 1. Let mqm_q be the total number of documents labeled as positive for query q, and mq+m_q^+ be the number of correctly labeled documents (mq+≤mqm_q^+≤ m_q). Assume correctly labeled documents have embedding mean direction μ1∈ℝh _1 ^h, noisy (false-positive) documents have mean direction μ2∈ℝh _2 ^h, and negative documents have mean 0∈ℝh0 ^h. For simplicity, we consider only the bias in the estimated query embedding and dismiss variance. For SP, r documents are selected (γ​rγ r correctly labeled) for uniform sampling. For DP, s documents are selected (ρ​sρ s correctly labeled) with probability β times higher than the remaining mq−sm_q-s documents (β>1β>1). Define EFTE^FT, ESPE^SP, EDPE^DP as the expected cosine similarity between the optimal query embedding and true-positive documents under each strategy. Then: ES​P>EF​T⇔γ>mq+mqE^SP>E^FT γ> m_q^+m_q (7) and similarly for DP. Additionally, when γ=ργ=ρ: ES​P>ED​P.E^SP>E^DP. (8) Proof. Under FT, the model maximizes ℒF​T=∑i=1mqs​(eq,edi)L^FT= _i=1^m_qs(e_q,e_d_i), yielding: eqFT e_q^FT =C1​(mq+mq​μ1+(1−mq+mq)​μ2) =C_1\! ( m_q^+m_q _1+(1- m_q^+m_q) _2 ) (9) and similarly for SP and DP: eqSP=C2​(γ​μ1+(1−γ)​μ2),eqDP e_q^SP=C_2(γ _1+(1-γ) _2), e_q^DP =C3((ρs(β−1)+mq+)μ1 =C_3((ρ s(β\!-\!1)+m_q^+) _1 +((1−ρ)s(β−1)+mq−mq+)μ2) +((1\!-\!ρ)s(β\!-\!1)+m_q\!-\!m_q^+) _2) (10) where C1,C2,C3C_1,C_2,C_3 are normalization constants. By Lemma 1: γ>mq+mq⇔s​(eqSP,μ1)>s​(eqFT,μ1)⇔ES​P>EF​Tγ> m_q^+m_q s(e_q SP, _1)>s(e_q FT, _1) E^SP>E^FT (11) and similarly for DP. Comparing SP and DP when γ=ργ=ρ: ES​P>ED​P⇔γ>mq+mqE^SP>E^DP γ> m_q^+m_q (12) ∎ Theorem 1 provides a general justification for quality-based pruning: any scoring function that identifies true positives at a rate higher than the dataset’s base rate (mq+/mqm_q^+/m_q) will improve learned query representations. Under equal selection quality, SP outperforms DP because it completely excludes noisy samples rather than merely down-weighting them. However, as training progresses, DP can surpass SP through improved sampling quality (ρ) and strength (β) enabled by dynamic threshold scheduling. This motivates a two-stage approach: applying SP first to discard strong noise, followed by DP to refine on the filtered data. The empirical validation is presented in Section 3.5. 3 Experiments To evaluate our proposed OPERA approach, we design a series of experiments addressing six key research questions: • RQ1: How does OPERA compare to FT and other pruning methods across domains? • RQ2: Can OPERA’s findings scale to LLM-based dense retrievers? • RQ3: How effective is OPERA in handling noisy training data? • RQ4: How does OPERA affect convergence speed and training efficiency? • RQ5: What is the computational overhead of OPERA, and how can it be optimized? • RQ6: How does DP’s sampling behavior evolve during training? We evaluate our methods on eight datasets spanning six domains: NFCorpus (Boteva et al., 2016) (nutrition), TripClick head/torso (Rekabsaz et al., 2021) (medical), FiQA (Maia et al., 2018) (finance), ANTIQUE (Hashemi et al., 2020) (non-factoid QA), TriviaQA (Joshi et al., 2017) and HotpotQA (Yang et al., 2018) (factoid QA), and FEVER (Thorne et al., 2018) (fact verification). FEVER and HotpotQA were seen during bge-large-en-v1.5 pretraining (Xiao et al., 2023), while the others are unseen. See Appendix C.1 for more datasets statistics. 3.1 Implementation Details We used the bge-large-en-v1.5 model (Xiao et al., 2023) (335M parameters) as our primary dense retriever. All hyperparameters were selected to optimize the FT baseline performance and used without any additional tuning for all other methods, ensuring a fair comparison. We also compare against Random Pruning (RP), which retains the same fraction of data as SP but selects pairs randomly; RP consistently underperforms all other methods and is therefore excluded from the main results table but included in the efficiency analysis (Figure 1) and the full results in Appendix E. Dataset-specific hyperparameters are detailed in Appendix C.2. For LLM-based retriever experiments (Section 3.2.2), we use Qwen3-Embedding-0.6B with hyperparameters similarly optimized for its FT baseline; implementation details are provided in Appendix C.3. 3.2 Main Results Table 1: OPERA vs. baselines on bge-large-en-v1.5. Best in bold, second-best underlined. †Datasets seen during pretraining. NDCG@10 Recall@20 OPERA OPERA Domain Dataset PT FT IB SP DP PT FT IB SP DP Nutrition NFCorpus 0.451 0.466 0.470 0.491 0.480 0.232 0.300 0.304 0.267 0.304 Medical TripClick (h) 0.219 0.298 0.295 0.270 0.309 0.189 0.242 0.244 0.219 0.252 TripClick (t) 0.208 0.245 0.248 0.236 0.249 0.334 0.398 0.396 0.373 0.400 Finance FiQA 0.489 0.514 0.514 0.516 0.524 0.602 0.639 0.640 0.630 0.639 Non-Factoid QA ANTIQUE 0.543 0.575 0.572 0.564 0.590 0.414 0.405 0.398 0.428 0.413 Factoid QA TriviaQA 0.487 0.481 0.482 0.501 0.491 0.429 0.458 0.460 0.445 0.460 HotpotQA† 0.790 0.806 0.806 0.803 0.812 0.807 0.836 0.835 0.781 0.838 Fact Verif. FEVER† 0.868 0.892 0.893 0.915 0.902 0.950 0.960 0.961 0.950 0.962 Average 0.507 0.535 0.535 0.537 0.545 0.495 0.530 0.530 0.512 0.534 Avg. Rank (Unseen) 4.67 3.33 3.00 2.67 1.33 4.50 2.83 2.33 3.50 1.83 Avg. Rank (Seen) 5.00 3.50 2.50 2.50 1.50 4.00 2.50 2.50 5.00 1.00 Avg. Rank (Overall) 4.75 3.38 2.88 2.63 1.38 4.38 2.75 2.38 3.88 1.63 PT: Pretrained, IB: InfoBatch, SP: Static Pruning, DP: Dynamic Pruning. † Datasets seen in pretraining. Table 2: OPERA vs. baselines on Qwen3-Embedding-0.6B. Best in bold, second-best underlined. NDCG@10 Recall@20 OPERA OPERA Domain Dataset PT FT IB SP DP PT FT IB SP DP Nutrition NFCorpus 0.441 0.479 0.478 0.487 0.479 0.211 0.314 0.308 0.265 0.311 Non-Factoid QA ANTIQUE 0.518 0.496 0.506 0.540 0.520 0.398 0.340 0.329 0.396 0.353 Factoid QA TriviaQA 0.467 0.489 0.484 0.493 0.504 0.403 0.462 0.453 0.421 0.461 Average 0.475 0.488 0.489 0.507 0.501 0.337 0.372 0.363 0.361 0.375 3.2.1 bge-large-en-v1.5 We conduct a comparative analysis of SP and DP against the pretrained model (Xiao et al., 2023), standard finetuning (FT) (Xiao et al., 2023), and InfoBatch (Qin et al., 2023). The evaluation metrics are NDCG (Järvelin and Kekäläinen, 2002; Thakur et al., 2021; Muennighoff et al., 2022) and Recall (Zhan et al., 2021; Chen et al., 2024), assessed at the top 10 and 20 retrievals, respectively, with all methods trained for an equivalent number of iterations. SP confirms the quality-coverage tradeoff in the previous section: it outperforms FT and InfoBatch in NDCG@10 across unseen, seen, and all datasets on average (average rank: 2.63), achieving the best NDCG@10 on NFCorpus (0.491), TriviaQA (0.501), and FEVER (0.915). As expected from our analysis, this comes at the cost of recall, as SP’s Recall@20 average rank drops to 3.88, because a priori removal of training pairs reduces query diversity. Despite this, SP offers substantial data efficiency: it drops 75% of pairs yet improves ranking, and subsequent analysis demonstrates even faster convergence and effective denoising capabilities. DP resolves the quality-coverage tradeoff, achieving the best performance on both metrics. It achieves the highest average rank on NDCG@10 (1.38) and Recall@20 (1.63), consistently outperforming other methods for both unseen (NDCG@10: 1.33, Recall@20: 1.83) and seen (NDCG@10: 1.50, Recall@20: 1.00) datasets. DP achieves the highest NDCG@10 on 6 of 8 datasets and the highest Recall@20 on 5 of 8. By replacing hard exclusions, DP maintains the broad data coverage needed for recall while concentrating training effort on informative instances. An ablation of DP’s hierarchical design is presented in Section 3.3, with additional analysis on the static pruning data retention rate in Appendix D.2. 3.2.2 Qwen3-Embedding-0.6B To investigate whether OPERA generalizes beyond encoder-only models, we evaluate on Qwen3-Embedding-0.6B (Zhang et al., 2025), a decoder-based LLM embedding model that employs last-token pooling and instruction-based query encoding, representing a fundamentally different architecture from the CLS-pooling encoder model used above. Due to the higher computational cost and potential data leakage from large-scale pretraining, we use a higher learning rate (1e-5 vs. 1e-6) with only 2,000 iterations (vs. 8,000–32,000 for BGE). Note that this setting is inherently less favorable to DP, which benefits from more iterations to dynamically adjust sampling rates. We evaluate on datasets with fewer than 1M documents (NFCorpus, ANTIQUE), with the exception of TriviaQA (21M documents), included to demonstrate scalability. We exclude FiQA, as the pretrained Qwen3-Embedding model already outperforms all finetuned methods on this dataset (NDCG@10: 0.511, Recall@20: 0.633), likely due to high-quality financial domain data in its pretraining corpus. As with the BGE experiments, all hyperparameters were first optimized for the vanilla FT baseline, and OPERA’s pruning methods were applied without additional tuning. Table 2 presents the results. Despite the limited training budget, SP achieves the best average NDCG@10 (0.507), while DP achieves the best average Recall@20 (0.375), reproducing the same quality-coverage pattern observed with bge-large-en-v1.5: SP excels at ranking due to its focus on high-quality examples, while DP maintains stronger recall through soft pruning. Notably, even under conditions unfavorable to dynamic pruning (few iterations, high learning rate), DP still outperforms baselines on average, achieving NDCG gains similar to SP while preserving and improving recall, confirming that OPERA’s benefits extend to LLM-based retrievers. Detailed results are provided in Appendix F. 3.3 Ablation: Hierarchical Query-Document Pruning Table 3: Ablation of hierarchical pruning. Recall@20 is 0.639 for all; Recall@10 shown to differentiate. Method NDCG@10 Recall@10 FT 0.514 0.547 DP w/ Query Sel. 0.517 0.556 DP w/ Doc Sel. 0.516 0.549 DP w/ Both 0.524 0.559 Table 4: Computational overhead of DP with varying query update intervals (IuI_u) on FiQA. Method I_u Iters/sec Speed Diff (%) NDCG@10 Recall@20 FT – 2.43 0.00 0.514 0.639 InfoBatch – 2.42 -0.30 0.514 0.640 DP 1 2.32 -4.49 0.524 0.639 DP 10 2.37 -2.51 0.519 0.646 DP 100 2.39 -1.64 0.522 0.635 A key design choice in DP is operating at two granularities, query selection and document selection, reflecting the two-stage sampling structure of retrieval training. To validate this design, we ablate each component on FiQA (Maia et al., 2018) (Table 4). Query selection alone (NDCG@10: 0.517, Recall@10: 0.556) and document selection alone (NDCG@10: 0.516, Recall@10: 0.549) both improve over FT (NDCG@10: 0.514, Recall@10: 0.547), confirming that both granularities carry complementary signal. Their combination achieves the highest scores on both metrics (NDCG@10: 0.524, Recall@10: 0.559). This supports our core argument that retrieval-specific data pruning must account for the query-document hierarchy. An additional ablation on the static pruning data retention rate is provided in Appendix D.2. 3.4 Efficiency Analysis 3.4.1 Convergence Speed Figure 1: Training efficiency on ANTIQUE (unseen) and FEVER (seen). RP and SP use retention rate k=0.25k=0.25. Figure 1 illustrates the training efficiency on both the unseen ANTIQUE dataset (Hashemi et al., 2020) and the FEVER dataset (Thorne et al., 2018) seen during pretraining. We evaluate SP and DP against FT and alternative pruning approaches across multiple training iterations. To ensure a fair comparison, we conducted separate experiments for each iteration count without using checkpoints, maintaining full learning rate scheduling in all experiments. Note that for DP, each run produces a fundamentally different sampling trajectory due to the dependence of the cosine schedule on tm​a​xt_max, yet DP consistently outperforms baselines across all iteration counts, demonstrating robustness to these scheduling variations. Both pruning strategies demonstrate substantial efficiency gains. On FEVER, while FT and InfoBatch (Qin et al., 2023) require 16,000 iterations to achieve optimal NDCG@10, DP achieves comparable results in fewer than 8,000 iterations, and SP reaches this level in fewer than 500 iterations. SP shows particularly rapid convergence in early training stages and consistently outperforms baseline approaches on NDCG@10, while DP demonstrates robustness across both NDCG@10 and Recall@20. Although DP introduces a small per-iteration overhead (4.5%), this is offset by requiring fewer than 50% of the training iterations to reach peak performance, making DP more efficient overall. 3.4.2 Computation Overhead Table 4 compares the computational costs of DP with varying query update intervals (IuI_u). With the most frequent updates (Iu=1I_u=1), DP processes 2.32 iterations per second compared to FT’s 2.43, a 4.49% reduction. Setting Iu=100I_u=100 reduces this to 1.64% while maintaining comparable performance (NDCG@10 = 0.522, Recall@20 = 0.635), and Iu=10I_u=10 achieves the highest Recall@20 (0.646) with only 2.51% overhead. The document update interval has negligible computational impact. Table 5: Denoising evaluation on ANTIQUE with noisy positive samples. SPk: retention rate k; SPk+DP: two-stage pipeline. Best in bold, second-best underlined. Metric Baselines OPERA (Individual) OPERA (Two-Stage) Pretrained FT InfoBatch SP.25 SP.5 SP.75 DP SP.25+DP SP.5+DP SP.75+DP NDCG@10 0.543 0.570 0.567 0.560 0.560 0.582 0.587 0.560 0.567 0.582 Recall@20 0.414 0.395 0.390 0.430 0.430 0.419 0.411 0.426 0.433 0.422 3.5 Denoising Capability We evaluate OPERA’s robustness to label noise by introducing noisy samples into the ANTIQUE (Hashemi et al., 2020) training set. Specifically, we include documents with lower relevance levels (level 2, which “does not answer the question”) as positives, simulating real-world scenarios with imperfect annotations. The detailed setup is provided in Appendix C.4. Table 5 presents the results. Consistent with Theorem 1, which predicts that pruning outperforms FT when selection quality exceeds random, a clear divergence emerges between ranking and retrieval metrics under noisy conditions: while NDCG@10 improves from 0.543 (Pretrained) to 0.570 (FT), Recall@20 degrades from 0.414 to 0.395, indicating that retrieval effectiveness is more sensitive to false-positive training signals than ranking performance. Among individual methods, DP achieves the highest NDCG@10 (0.587), while SP yields substantially better Recall@20 (0.430) than both FT (0.395) and DP (0.411). This advantage of SP in noisy settings motivates the two-stage approach: applying SP first to filter out noisy samples, followed by DP on the filtered data. The combined SP.5+DP achieves the best overall Recall@20 (0.433). Notably, SP.75+DP outperforms all baselines on both metrics (NDCG@10: 0.582, Recall@20: 0.422), confirming that OPERA provides an effective denoising mechanism for dense retriever finetuning. 3.6 Sampling Weight Visualization To analyze how DP allocates training focus over time, we visualize the evolution of sampling probabilities on the FiQA (Maia et al., 2018) dataset (Figure 2). Unlike curriculum learning (Bengio et al., 2009), which imposes a fixed easy-to-hard ordering and may exclude examples at certain stages, DP keeps all examples accessible throughout training while continuously re-evaluating and adjusting their sampling weights as model representations evolve. Figure 2(a) shows the probability distribution grouped by query. Crucially, nearly all queries maintain nonzero sampling probabilities throughout training, demonstrating that DP preserves broad query coverage unlike SP, which would exclude many queries entirely. The variation in intensity reflects quality-aware up-weighting while maintaining the diversity needed for recall. Figure 2(b), sorted by initial probabilities, reveals how DP dynamically redistributes attention: initially high-probability examples may decrease in importance while previously low-priority examples gain prominence. This demonstrates DP’s ability to discover valuable training examples beyond what the pretrained model initially favors, shifting focus toward examples more informative for domain-specific adaptation. (a) Grouped by query (b) Sorted by initial prob. Figure 2: DP sampling probability evolution. Color: black (low) to yellow (high). 4 Conclusion We presented OPERA, a data pruning framework for domain adaptation of dense retrievers. Our investigation revealed a quality-coverage tradeoff intrinsic to the two-stage query-document sampling structure of retrieval training: static pruning (SP) improves ranking by focusing on high-quality pairs but reduces retrieval coverage, while dynamic pruning (DP) resolves this tradeoff through soft sampling modulation, achieving the best performance on both ranking and retrieval metrics across most evaluation settings while halving convergence time. Both approaches demonstrate effective denoising capability, especially when combined in a two-stage pipeline. Experiments on Qwen3-Embedding-0.6B provide evidence that these findings generalize beyond encoder-only architectures. In practice, the choice depends on the application: SP is suited for ranking-focused scenarios where training speed is paramount, DP is preferred when both ranking and retrieval performance matter, and SP followed by DP is recommended when training data contains known label noise. 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Contents 1 Introduction 2 Methodology 2.1 Preliminary: Standard Finetuning (FT) 2.2 Static Pruning (SP) 2.3 Dynamic Pruning (DP) 2.4 Theoretical Analysis: When Does Pruning Help? 3 Experiments 3.1 Implementation Details 3.2 Main Results 3.2.1 bge-large-en-v1.5 3.2.2 Qwen3-Embedding-0.6B 3.3 Ablation: Hierarchical Query-Document Pruning 3.4 Efficiency Analysis 3.4.1 Convergence Speed 3.4.2 Computation Overhead 3.5 Denoising Capability 3.6 Sampling Weight Visualization 4 Conclusion References A Related Work A.1 Dense Retrieval Models A.2 Data Pruning in Neural Networks A.3 Curriculum Learning B Theoretical Analysis C Experimental Setup C.1 Dataset Statistics C.2 Dataset-specific Hyperparameters C.3 Qwen3-Embedding-0.6B Implementation Details C.4 Denoising Experiment Setup D Additional Experiments D.1 Consistency-Based Score Analysis D.2 Static Pruning Data Retention Rate E Detailed bge-large-en-v1.5 Results F Detailed Qwen3-Embedding-0.6B Results G Limitations Appendix A Related Work A.1 Dense Retrieval Models Recent advances in dense retrieval have demonstrated significant improvements over traditional sparse retrieval methods. These models leverage pretrained language models (Devlin et al., 2018; Jiang et al., 2023; Touvron et al., 2023) to generate robust embeddings in various retrieval tasks (Muennighoff et al., 2022; Thakur et al., 2021). While models like NV-Embed-v1 (Lee et al., 2024) with 7B parameters have pushed performance boundaries, a more compact model family such as BGE (Xiao et al., 2023; Chen et al., 2024) offers an attractive balance between computational efficiency and effectiveness. Our work is based on the bge-large-en-v1.5 model (Xiao et al., 2023), for its favorable balance between computational efficiency and strong performance, as well as its open source training and evaluation process, which enables reproducibility and practical deployment. This choice allows us to conduct extensive experiments on various data pruning strategies while maintaining manageable computational requirements. More recently, LLM-based embedding models such as Qwen3-Embedding (Zhang et al., 2025) have further advanced the state of the art by adapting large language models directly for embedding generation, achieving strong retrieval performance across diverse tasks, though at substantially higher computational cost. A.2 Data Pruning in Neural Networks Data pruning has emerged as a promising approach to improve training efficiency while maintaining or enhancing model performance (Yang et al., 2022; Raju et al., 2021; Toneva et al., 2018; He et al., 2024b; Dong et al., 2023). Recent innovations have shown that data pruning can surpass traditional power law scaling, improving efficiency with minimal performance degradation (Sorscher et al., 2022). Previous work in this area can be categorized into two main approaches: Static Pruning Traditional static pruning methods select a fixed subset of training data before the training process begins (Toneva et al., 2018; Killamsetty et al., 2021; Mirzasoleiman et al., 2020). While these approaches can reduce training time, they often struggle with generalization across different architectures and datasets. In the context of dense retrievers, (Wang et al., 2022) introduced the consistency-based filter for pretraining, which retains only high-quality text pairs based on their ranking against random documents. Our work extends these ideas to the domain adaptation setting, where different considerations apply due to the distinct nature of the training data. Dynamic Pruning More recent approaches have explored dynamic data selection during training (Raju et al., 2021; He et al., 2024a; Qin et al., 2023; Li et al., 2024; Huang et al., 2024; Xiao et al., 2024). InfoBatch (Qin et al., 2023) notably achieves training acceleration through unbiased dynamic pruning, adjusting sampling probabilities based on training loss. However, these methods primarily focus on maintaining model performance while improving convergence speed. In contrast, our approach demonstrates that careful selection of query-document pair can simultaneously enhance both training efficiency and model performance. To the best of our knowledge, there is no prior work discussing data pruning for dense retrievers during the finetuning stage, where the query is selected regardless of its relevant documents. Therefore, we will compare our approach with our implementation of InfoBatch (Qin et al., 2023) which prunes on the query level. A.3 Curriculum Learning Curriculum learning has emerged as a promising approach to train neural networks by presenting training examples in a meaningful order. The idea of curriculum learning was formalized in (Bengio et al., 2009), where it showed that gradually increasing the difficulty of training examples could lead to better generalization and faster convergence. In natural language processing, CL has been applied to machine translation (Platanios et al., 2019), question answering (Sachan and Xing, 2016), language modeling (Graves et al., 2017), etc. Several approaches have been proposed for automatically determining the difficulty of training examples and generating curricula. Self-paced learning (Kumar et al., 2010) allows the model to automatically select its own curriculum based on the loss of training examples. Other works have explored the use of teacher-student frameworks (Matiisen et al., 2019), where a teacher model determines the curriculum for a student model. Our dynamic pruning framework incorporates curriculum learning principles through its evolving threshold scheduling, which gradually adjusts both the ratio and sampling strength of training instances as the model’s representations become more refined. However, a key distinction is that OPERA selects examples based on data quality (query-document similarity) rather than difficulty. These are distinct axes: a high-similarity query-document pair can be easy or hard depending on the negative mining strategy, and a difficult example is not necessarily high-quality. This quality-based perspective, combined with the hierarchical query-document sampling structure specific to retrieval, differentiates our approach from standard curriculum learning. Appendix B Theoretical Analysis The full theoretical analysis, including Lemma 1, Theorem 1, and their proofs, is presented in Section 2.4 of the main paper. Appendix C Experimental Setup C.1 Dataset Statistics Table 6 presents detailed statistics for all eight evaluation datasets. The datasets vary significantly in scale, ranging from NFCorpus with 3,633 documents to TriviaQA with over 21 million documents. Training set sizes span from 2,426 queries (ANTIQUE) to 109,810 queries (FEVER), while the number of positive query-document pairs ranges from 14,166 (FiQA) to 741,436 (TriviaQA), reflecting diverse annotation densities across domains. FEVER and HotpotQA were previously seen by the pretrained model during its initial training, while the remaining six datasets are unseen. Table 6: Dataset statistics. #pos: number of positive query-document pairs. †Datasets seen during pretraining. Dataset Domain #Docs Train Test #q #pos #q #pos NFCorpus Nutrition 3,633 2,590 110,575 323 12,334 TripClick (h) Medical 1,523,878 3,529 55,663 1,175 32,067 TripClick (t) Medical 1,523,878 105,964 424,820 1,175 6,202 FiQA Finance 57,638 5,500 14,166 648 1,706 ANTIQUE Non-Factoid QA 403,666 2,426 19,813 200 2,976 TriviaQA Factoid QA 21,015,324 78,785 741,436 8,837 82,658 HotpotQA† Factoid QA 5,233,329 85,000 170,000 7,405 14,810 FEVER† Fact Verif. 5,416,568 109,810 140,085 6,666 7,937 † Datasets seen by the pretrained model. C.2 Dataset-specific Hyperparameters Table 7 summarizes the dataset-specific hyperparameters used during training. All hyperparameters were optimized based on the vanilla FT baseline performance. Table 7: Dataset-specific hyperparameters, optimized for the FT baseline. Dataset Negative Mining k Training Mining Range Iters NFCorpus Random — 0.25 32,000 TripClick (h) Hard 100–1,100 0.25 32,000 TripClick (t) Hard 100–1,100 0.25 32,000 FiQA Hard 10–100 0.50 8,000 TriviaQA Random — 0.25 16,000 ANTIQUE Hard 50–500 0.25 16,000 FEVER Hard 10–200 0.25 32,000 HotpotQA Hard 10–200 0.25 32,000 The model finetuning process uses a learning rate of 1e-6 with a linear scheduler and operates on a per-device train batch size of 8, yielding a total batch size of 64. Training uses FP16 precision with a maximum gradient norm of 1.0, no warmup, and no weight decay. The temperature is set to 0.02, and the system leverages cross-device negatives during training. The maximum query and passage length are set to 128 and 512 tokens, respectively. All embeddings are normalized. FiQA (Maia et al., 2018)’s data retention ratio k is set to 0.5 to accommodate its smaller dataset size. For dynamic pruning, we initialize the query cutoff ratio (rsr_s) at 0.25, and use sampling strengths of 2 and 5 for the starting (αs _s) and ending (αe _e) values, respectively. The document level includes an initial cutoff ratio (vsv_s) of 0.25, a terminal cutoff ratio (vev_e) of 0.5, and a constant sampling strength (β) of 5. All cutoff schedulers follow a cosine schedule. C.3 Qwen3-Embedding-0.6B Implementation Details For the Qwen3-Embedding-0.6B experiments, we use a learning rate of 1e-5 (10× higher than the BGE experiments) and train for 2,000 iterations across all datasets. The higher learning rate and reduced iteration count reflect the substantially higher computational cost of LLM-based retrievers and the potential data leakage from Qwen3-Embedding’s large-scale pretraining corpus. We use a per-device batch size of 2, yielding a total batch size of 16, with gradient accumulation steps of 4 to achieve an effective batch size of 64. Training uses BF16 precision with the same temperature (0.02) and contrastive learning setup as the BGE experiments. The maximum query and passage lengths are set to 128 and 512 tokens, respectively, with instruction-based query encoding following the Qwen3-Embedding default prompts. The static pruning retention rate k is set to 0.25 for all datasets. Dynamic pruning uses the same hyperparameters as the BGE experiments. Full results are provided in Appendix F. C.4 Denoising Experiment Setup The ANTIQUE dataset (Hashemi et al., 2020) defines relevance levels as follows: • Level 1: Completely out of context or does not make any sense (4.6% of the training data) • Level 2: Does not answer the question, or provides an unreasonable answer, but is not out of context (23.1% of the training data) • Level 3: Can be an answer to the question, but is not sufficiently convincing (29.5% of the training data) • Level 4: Looks reasonable and convincing, with high quality (42.8% of the training data) Our experimental setup is designed as follows: • Test set: We maintain the standard evaluation criterion, considering only documents with relevance levels of 3 and 4 as positive samples (Hashemi et al., 2020). • Training set: Documents with relevance levels of 2, 3, and 4 were treated as positive samples. The inclusion of level 2 documents, which are documented as insufficient answers, deliberately introduces noise into the positive samples. We did not include level 1 documents as positive samples since they represent a small portion (4.6%) of the training data and are more like random noise, which differs from real-world scenarios where noisy samples are typically hard negatives that share some relevance with the query. Appendix D Additional Experiments D.1 Consistency-Based Score Analysis Table 8: SP with cosine similarity vs. CBS as pruning metric. Best per row in bold. Dataset Metric SP SP (CBS) NFCorpus NDCG@10 0.491 0.463 Recall@20 0.267 0.305 FiQA NDCG@10 0.511 0.514 Recall@20 0.620 0.635 ANTIQUE NDCG@10 0.564 0.577 Recall@20 0.428 0.403 FEVER NDCG@10 0.915 0.894 Recall@20 0.950 0.961 Average NDCG@10 0.620 0.612 Recall@20 0.566 0.576 The consistency-based filter was introduced in (Wang et al., 2022) as a quality control mechanism for large-scale pretraining. The core insight is that high-quality training pairs should maintain relevance compared to random documents: the method ranks each positive pair against random negatives and retains only those that consistently rank highly. We adapt this to our finetuning context with three modifications: (1) we leverage the pretrained checkpoint directly instead of training on noisy data, (2) we reduce the random document pool from one million to ten thousand to match the smaller scale of downstream tasks, and (3) we replace the static top-k threshold with a reciprocal rank metric (CBS) for percentage-based filtering. We sample random negatives from positive documents of other queries to avoid additional embedding computation. We compare SP using CBS with SP using cosine similarity. Cosine similarity directly measures the semantic relationship between queries and documents, while CBS evaluates pairs based on their relative ranking against random samples. Table 8 presents the comparative performance across these datasets. SP uses cosine similarity as the similarity metric for pruning, while SP (CBS) uses CBS. In the nutrition dataset NFCorpus, SP achieves optimal NDCG@10 (0.491), while SP (CBS) leads in Recall@20 (0.305). FiQA demonstrates marginal improvements with SP (CBS) on both metrics (NDCG@10: 0.514, Recall@20: 0.635). For ANTIQUE, SP (CBS) leads in NDCG@10 (0.577), while SP with cosine similarity achieves higher Recall@20 (0.428). In FEVER, SP excels in NDCG@10 (0.915), while SP (CBS) shows superior Recall@20 (0.961). Overall, SP achieves better NDCG@10 (0.620) while SP (CBS) performs better on Recall@20 (0.576). However, CBS is incompatible with DP as it requires computationally expensive recalculation of embeddings on all negative documents after each model update. We therefore adopt cosine similarity as the default pruning metric for both SP and DP. D.2 Static Pruning Data Retention Rate Figure 3: Effect of SP data retention rate k on NFCorpus. SP improves NDCG@10 over FT at all retention rates. We evaluate the effects of varying data retention rates (k) in Static Pruning (SP) through comprehensive experiments on NFCorpus (Boteva et al., 2016). The experimental setup comprises six configurations: standard finetuning (FT) as baseline (k=1k=1) and SP with k=0.75,0.5,0.25,0.1,0.05k=0.75,0.5,0.25,0.1,0.05. The results, presented in Figure 3, demonstrate that SP consistently surpasses FT in terms of NDCG@10 across all retention rates. The optimal performance was achieved at k=0.25k=0.25, achieving a peak NDCG of 0.491. Notably, even with minimal data retention (5%), SP maintains superior performance with an NDCG of 0.482 compared to FT (0.466). As expected, Recall@20 shows a monotonic decrease as the retention rate reduces from 100% to 5%, which aligns with the reduced data visibility. These findings highlight SP’s data efficiency and indicate the potential for computational resource optimization while maintaining or enhancing ranking performance. Appendix E Detailed bge-large-en-v1.5 Results We present full evaluation results for bge-large-en-v1.5 across all eight datasets at multiple training iterations (0 to 32,000). Each table reports NDCG, Recall, and Success at cutoffs of 10, 20, 100 for all methods: FT, RP (Random Pruning with the same retention rate as SP), InfoBatch, SP, and DP. The subscript in RP and SP denotes the data retention rate k (e.g., RP25 retains 25% of training pairs selected randomly, SP25 retains the top 25% by similarity). FiQA additionally includes SP50 and RP50 variants due to its smaller dataset size. Results are shown for NFCorpus (Table 9), FiQA (Table 10), ANTIQUE (Table 11), TriviaQA (Table 12), TripClick head (Table 13), TripClick torso (Table 14), FEVER (Table 15), and HotpotQA (Table 16). Appendix F Detailed Qwen3-Embedding-0.6B Results We present comprehensive evaluation results for Qwen3-Embedding-0.6B across four datasets at 2,000 training iterations: NFCorpus (Table 17), FiQA (Table 18), ANTIQUE (Table 19), and TriviaQA (Table 20). We report all evaluation metrics (MRR, NDCG, Recall, and Success at cutoffs of 1, 5, 10, 20, 50, 100) for each configuration. The pretrained model results are iteration-independent and shown as a reference in each table. Notably, for FiQA (Table 18), the pretrained model outperforms all finetuned methods across all metrics, suggesting that Qwen3-Embedding’s pretraining corpus already contains high-quality financial domain data. Appendix G Limitations We identify several directions for future work. Our LLM-based experiments use Qwen3-Embedding-0.6B as initial evidence; extending to larger models (4B, 8B parameters) and additional model families would strengthen the generalizability claim, though we note that the consistent quality-coverage tradeoff pattern across two architecturally distinct models (encoder-only BGE and decoder-based Qwen3) suggests the underlying principle is architecture-agnostic. Our evaluation covers eight English-language text retrieval datasets across six domains; applying OPERA to multilingual and multimodal retrieval settings is a natural extension. While we report results under identical hyperparameters (optimized for the FT baseline of BGE) but use a higher learning rate for Qwen3 due to the substantially higher computational cost of LLM-based retrievers, we do not report variance across random seeds due to the computational cost of running all method-dataset combinations multiple times; however, the consistency of improvements across eight diverse datasets provides evidence of robustness beyond what single-dataset variance estimates would capture. Finally, OPERA’s dynamic pruning hyperparameters (sampling strengths, cutoff ratios, and scheduling) were not tuned due to computational constraints; exploring different configurations or adaptive scheduling strategies may yield further gains. Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.45101 0.45101 0.45101 0.45101 0.45101 500 0.45608 0.45768 0.46132 0.47209 0.46939 1000 0.46758 0.46583 0.46669 0.47429 0.47479 2000 0.47059 0.46631 0.47209 0.47979 0.47418 4000 0.47465 0.47516 0.47438 0.48804 0.48388 8000 0.47471 0.45486 0.47866 0.49103 0.49008 16000 0.4802 0.43449 0.48371 0.48671 0.48067 32000 0.46565 0.42648 0.46965 0.49128 0.48019 Recall@10 0 0.18786 0.18786 0.18786 0.18786 0.18786 500 0.19205 0.19057 0.1934 0.19968 0.19693 1000 0.20346 0.19951 0.20231 0.198 0.20538 2000 0.20952 0.20231 0.20912 0.20422 0.20623 4000 0.21562 0.20594 0.21102 0.20835 0.21765 8000 0.21083 0.20026 0.21204 0.21186 0.21774 16000 0.21814 0.18932 0.22421 0.20753 0.22189 32000 0.22654 0.18213 0.23186 0.21049 0.2272 Success@10 0 0.75542 0.75542 0.75542 0.75542 0.75542 500 0.74923 0.73994 0.74613 0.75851 0.75851 1000 0.75542 0.74613 0.75232 0.75542 0.76471 2000 0.76161 0.75542 0.76161 0.76471 0.76161 4000 0.7709 0.77709 0.76471 0.77709 0.77709 8000 0.77709 0.76471 0.78019 0.78019 0.7678 16000 0.76471 0.73684 0.76161 0.76471 0.78019 32000 0.75851 0.72446 0.74923 0.75232 0.74613 NDCG@20 0 0.46963 0.46963 0.46963 0.46963 0.46963 500 0.47225 0.47045 0.47562 0.48777 0.4863 1000 0.48135 0.47612 0.48132 0.493 0.49069 2000 0.48129 0.48145 0.4836 0.50005 0.48827 4000 0.48389 0.48097 0.48472 0.50418 0.49289 8000 0.48058 0.46252 0.48539 0.50196 0.50145 16000 0.48987 0.44691 0.49305 0.50082 0.49279 32000 0.476 0.43441 0.48058 0.4989 0.49261 Recall@20 0 0.23235 0.23235 0.23235 0.23235 0.23235 500 0.24643 0.23986 0.24754 0.24674 0.25311 1000 0.25214 0.24472 0.2516 0.25396 0.25597 2000 0.2572 0.25875 0.25863 0.25857 0.25766 4000 0.2667 0.25901 0.26489 0.26086 0.26595 8000 0.27199 0.25249 0.27128 0.25804 0.27595 16000 0.29227 0.24643 0.29663 0.26297 0.292 32000 0.30031 0.24182 0.30361 0.2671 0.30398 Success@20 0 0.80495 0.80495 0.80495 0.80495 0.80495 500 0.79876 0.79567 0.80186 0.80186 0.81115 1000 0.79567 0.78947 0.79567 0.81734 0.80805 2000 0.79876 0.80495 0.79876 0.81734 0.80186 4000 0.81734 0.80805 0.80805 0.80805 0.81424 8000 0.81115 0.80805 0.82353 0.81424 0.81424 16000 0.82353 0.78328 0.82663 0.81115 0.81734 32000 0.79567 0.76161 0.79257 0.80186 0.80805 NDCG@100 0 0.5908 0.5908 0.5908 0.5908 0.5908 500 0.59424 0.59384 0.59712 0.60724 0.60158 1000 0.60187 0.5992 0.60232 0.60983 0.60755 2000 0.60681 0.60372 0.60681 0.61762 0.6134 4000 0.61242 0.61026 0.61227 0.62192 0.62047 8000 0.61675 0.5967 0.62023 0.6202 0.62778 16000 0.61673 0.58437 0.61839 0.62012 0.61766 32000 0.60532 0.57457 0.60861 0.61819 0.61702 Recall@100 0 0.36386 0.36386 0.36386 0.36386 0.36386 500 0.39106 0.39251 0.39036 0.38694 0.39014 1000 0.40479 0.4013 0.40445 0.3935 0.40153 2000 0.4134 0.40905 0.41078 0.39942 0.41369 4000 0.43184 0.42072 0.43176 0.40591 0.4305 8000 0.46136 0.43142 0.46095 0.40966 0.45188 16000 0.48035 0.43325 0.47794 0.41957 0.47781 32000 0.50295 0.42943 0.49731 0.42292 0.49686 Success@100 0 0.89474 0.89474 0.89474 0.89474 0.89474 500 0.89783 0.89474 0.89783 0.89474 0.88854 1000 0.89164 0.89474 0.89474 0.89783 0.88854 2000 0.90093 0.89783 0.89474 0.90402 0.89783 4000 0.90402 0.90093 0.89474 0.89783 0.90712 8000 0.89474 0.89474 0.89474 0.88545 0.89783 16000 0.88235 0.89164 0.87926 0.89783 0.89783 32000 0.88854 0.88854 0.88545 0.89164 0.89783 Table 9: Full Results on NFCorpus. Metric #iterations FT RP50 InfoBatch SP25 SP50 DP NDCG@10 0 0.48919 0.48919 0.48919 0.48919 0.48919 0.48919 500 0.5073 0.50502 0.50971 0.50296 0.50469 0.50404 1000 0.5085 0.50659 0.50761 0.50241 0.50876 0.50655 2000 0.51277 0.50653 0.51195 0.50229 0.51293 0.51212 4000 0.5148 0.5026 0.51559 0.51047 0.51555 0.51812 8000 0.51359 0.50572 0.5137 0.511 0.5162 0.52418 16000 0.50859 0.49985 0.50758 0.51213 0.51463 0.51715 Recall@10 0 0.51432 0.51432 0.51432 0.51432 0.51432 0.51432 500 0.53982 0.53969 0.53958 0.53143 0.5367 0.54259 1000 0.54812 0.5451 0.54982 0.53329 0.54211 0.54512 2000 0.559 0.54228 0.55506 0.53052 0.54561 0.5546 4000 0.55662 0.54005 0.55558 0.54067 0.54815 0.56327 8000 0.54711 0.53811 0.54964 0.53731 0.54906 0.55887 16000 0.54124 0.52443 0.53852 0.54046 0.5469 0.55478 Success@10 0 0.72685 0.72685 0.72685 0.72685 0.72685 0.72685 500 0.74383 0.74383 0.74691 0.73611 0.74228 0.74846 1000 0.75154 0.74537 0.75 0.74074 0.74691 0.74846 2000 0.7608 0.74383 0.75772 0.73457 0.74846 0.7608 4000 0.76235 0.75 0.76389 0.74074 0.75 0.76543 8000 0.75463 0.75154 0.75926 0.73457 0.74537 0.76389 16000 0.74691 0.74074 0.74537 0.73765 0.74383 0.76389 NDCG@20 0 0.52218 0.52218 0.52218 0.52218 0.52218 0.52218 500 0.54164 0.5384 0.54391 0.53541 0.53779 0.53734 1000 0.54275 0.54106 0.54071 0.53541 0.54142 0.54203 2000 0.54417 0.54016 0.54539 0.53641 0.54587 0.54416 4000 0.54578 0.53642 0.54629 0.54136 0.54946 0.54855 8000 0.54723 0.54071 0.54671 0.54296 0.54924 0.5539 16000 0.54209 0.53193 0.54116 0.54289 0.54821 0.54795 Recall@20 0 0.60161 0.60161 0.60161 0.60161 0.60161 0.60161 500 0.63196 0.62872 0.63162 0.61578 0.62241 0.63024 1000 0.6369 0.63292 0.6364 0.61609 0.62523 0.63847 2000 0.63903 0.62874 0.64027 0.61811 0.62882 0.63727 4000 0.63808 0.63194 0.63514 0.62047 0.63412 0.64222 8000 0.63933 0.63279 0.63994 0.61994 0.63041 0.63909 16000 0.62971 0.61118 0.63012 0.61941 0.63243 0.63809 Success@20 0 0.79321 0.79321 0.79321 0.79321 0.79321 0.79321 500 0.81636 0.81327 0.81636 0.80093 0.81019 0.81481 1000 0.82407 0.82253 0.82407 0.80401 0.81019 0.82716 2000 0.82562 0.81327 0.82407 0.80556 0.81944 0.82562 4000 0.82099 0.81481 0.8179 0.8071 0.82407 0.82407 8000 0.8287 0.81327 0.82562 0.80864 0.81944 0.82099 16000 0.8179 0.80247 0.81481 0.8071 0.8179 0.82253 NDCG@100 0 0.57052 0.57052 0.57052 0.57052 0.57052 0.57052 500 0.58557 0.58211 0.58748 0.57741 0.58011 0.58142 1000 0.58628 0.58487 0.58404 0.57796 0.58414 0.58462 2000 0.58806 0.58638 0.58894 0.57922 0.58792 0.58797 4000 0.59107 0.58097 0.59279 0.58342 0.59066 0.59249 8000 0.59063 0.58115 0.5907 0.58538 0.59152 0.59951 16000 0.58399 0.57598 0.58324 0.58426 0.58982 0.59 Recall@100 0 0.77048 0.77048 0.77048 0.77048 0.77048 0.77048 500 0.78785 0.78461 0.78634 0.75805 0.76858 0.78739 1000 0.79259 0.79034 0.79133 0.76416 0.77228 0.7897 2000 0.7951 0.7905 0.79659 0.76461 0.77901 0.79448 4000 0.79596 0.78875 0.79938 0.76684 0.78161 0.79421 8000 0.79368 0.77385 0.79628 0.76688 0.78176 0.80139 16000 0.7764 0.76227 0.77643 0.76078 0.77788 0.78376 Success@100 0 0.89506 0.89506 0.89506 0.89506 0.89506 0.89506 500 0.90586 0.89969 0.90432 0.89352 0.89815 0.90586 1000 0.90895 0.90586 0.90586 0.89506 0.89969 0.90432 2000 0.90895 0.90741 0.90895 0.89352 0.90432 0.90586 4000 0.90895 0.90278 0.91204 0.89815 0.90432 0.90741 8000 0.91049 0.8966 0.91358 0.89969 0.90432 0.91358 16000 0.90123 0.8966 0.89969 0.89506 0.90278 0.90586 Table 10: Full Results on FiQA. Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.54361 0.54361 0.54361 0.54361 0.54361 500 0.51341 0.50884 0.51514 0.555 0.54143 1000 0.53297 0.52488 0.53106 0.56221 0.54905 2000 0.55202 0.54677 0.55086 0.56385 0.56028 4000 0.57041 0.56046 0.5673 0.56475 0.5814 8000 0.5756 0.55501 0.56865 0.56304 0.58932 16000 0.57495 0.55635 0.57182 0.56404 0.58987 32000 0.5704 0.54994 0.56128 0.56153 0.5803 Recall@10 0 0.3187 0.3187 0.3187 0.3187 0.3187 500 0.30215 0.30074 0.30394 0.32731 0.3211 1000 0.31274 0.30605 0.31297 0.33135 0.32435 2000 0.31647 0.3128 0.31478 0.33139 0.32999 4000 0.32797 0.31715 0.32603 0.33024 0.33619 8000 0.32685 0.30934 0.32143 0.32961 0.33503 16000 0.32654 0.30758 0.32119 0.33087 0.33564 32000 0.3201 0.303 0.31485 0.32149 0.3269 Success@10 0 0.915 0.915 0.915 0.915 0.915 500 0.915 0.915 0.91 0.925 0.92 1000 0.92 0.93 0.925 0.925 0.92 2000 0.93 0.93 0.93 0.925 0.925 4000 0.93 0.93 0.93 0.925 0.94 8000 0.94 0.925 0.935 0.925 0.935 16000 0.94 0.92 0.93 0.925 0.94 32000 0.93 0.92 0.935 0.92 0.935 NDCG@20 0 0.58938 0.58938 0.58938 0.58938 0.58938 500 0.55908 0.55891 0.56392 0.60371 0.58903 1000 0.58022 0.57683 0.57841 0.60726 0.59685 2000 0.60082 0.59966 0.59985 0.60895 0.60292 4000 0.61127 0.60587 0.61113 0.61126 0.62214 8000 0.61673 0.6027 0.61021 0.60916 0.63131 16000 0.61622 0.60262 0.61349 0.60949 0.62942 32000 0.61282 0.59419 0.60292 0.60826 0.6267 Recall@20 0 0.41377 0.41377 0.41377 0.41377 0.41377 500 0.38463 0.38752 0.38937 0.43058 0.41207 1000 0.3951 0.39427 0.39699 0.43161 0.41464 2000 0.40321 0.40246 0.4028 0.43278 0.41329 4000 0.40542 0.40033 0.40752 0.43143 0.4189 8000 0.40418 0.39583 0.39742 0.42876 0.41904 16000 0.40475 0.38942 0.3982 0.42807 0.41345 32000 0.39887 0.38136 0.38788 0.41849 0.41037 Success@20 0 0.94 0.94 0.94 0.94 0.94 500 0.935 0.935 0.93 0.945 0.93 1000 0.93 0.93 0.935 0.95 0.935 2000 0.94 0.935 0.945 0.95 0.945 4000 0.95 0.95 0.95 0.955 0.95 8000 0.95 0.95 0.955 0.95 0.955 16000 0.945 0.94 0.955 0.95 0.955 32000 0.945 0.935 0.95 0.94 0.955 NDCG@100 0 0.70963 0.70963 0.70963 0.70963 0.70963 500 0.68968 0.68743 0.69259 0.72254 0.71339 1000 0.70339 0.69928 0.70178 0.72514 0.72015 2000 0.71801 0.71431 0.71782 0.72624 0.72481 4000 0.72655 0.71896 0.72348 0.72845 0.73586 8000 0.72726 0.71366 0.7236 0.72757 0.73949 16000 0.72375 0.71325 0.72022 0.72788 0.73581 32000 0.71905 0.70656 0.70943 0.72737 0.73014 Recall@100 0 0.61225 0.61225 0.61225 0.61225 0.61225 500 0.59569 0.59606 0.60046 0.62704 0.61638 1000 0.59057 0.59225 0.59289 0.62929 0.61486 2000 0.59087 0.58942 0.58999 0.63046 0.61596 4000 0.58692 0.58056 0.58274 0.63033 0.60371 8000 0.57344 0.56642 0.5742 0.63086 0.59186 16000 0.56939 0.55861 0.5599 0.62933 0.58018 32000 0.56019 0.55254 0.55349 0.61963 0.57318 Success@100 0 0.97 0.97 0.97 0.97 0.97 500 0.97 0.975 0.965 0.975 0.98 1000 0.975 0.975 0.975 0.975 0.98 2000 0.975 0.97 0.975 0.975 0.975 4000 0.975 0.97 0.975 0.975 0.975 8000 0.975 0.97 0.975 0.975 0.975 16000 0.975 0.965 0.97 0.975 0.975 32000 0.97 0.965 0.96 0.97 0.97 Table 11: Full Results on ANTIQUE. Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.48724 0.48724 0.48724 0.48724 0.48724 500 0.48569 0.48454 0.48815 0.49358 0.49215 1000 0.48447 0.48167 0.48317 0.49497 0.49271 2000 0.48155 0.47685 0.48055 0.4958 0.49108 4000 0.47759 0.4755 0.47892 0.49768 0.49108 8000 0.47752 0.47493 0.47722 0.49818 0.48562 16000 0.48116 0.47636 0.48179 0.50124 0.49078 32000 0.48315 0.47358 0.48287 0.50933 0.49009 Recall@10 0 0.3418 0.3418 0.3418 0.3418 0.3418 500 0.35714 0.3568 0.35926 0.35052 0.35995 1000 0.35744 0.35596 0.35722 0.35049 0.3616 2000 0.35736 0.35347 0.35697 0.3521 0.36049 4000 0.35613 0.35363 0.35553 0.3541 0.36056 8000 0.3566 0.35452 0.35697 0.35376 0.35896 16000 0.3609 0.35589 0.36158 0.35759 0.36408 32000 0.36281 0.35282 0.36419 0.36243 0.36303 Success@10 0 0.81775 0.81775 0.81775 0.81775 0.81775 500 0.82485 0.82515 0.82456 0.81997 0.82751 1000 0.82219 0.82145 0.82115 0.81908 0.82751 2000 0.81893 0.81716 0.81997 0.81953 0.82485 4000 0.81834 0.81509 0.81538 0.8213 0.82352 8000 0.8176 0.81538 0.81864 0.81967 0.8213 16000 0.8216 0.81524 0.82249 0.82086 0.82263 32000 0.82234 0.81065 0.82293 0.82396 0.8213 NDCG@20 0 0.51949 0.51949 0.51949 0.51949 0.51949 500 0.51899 0.51739 0.52001 0.52728 0.52425 1000 0.51736 0.51491 0.51661 0.52742 0.52532 2000 0.51454 0.51056 0.51409 0.52841 0.52395 4000 0.51111 0.50845 0.51221 0.53023 0.52333 8000 0.5104 0.50777 0.51101 0.53049 0.51719 16000 0.51354 0.50923 0.51423 0.53244 0.52286 32000 0.51654 0.50718 0.51534 0.5389 0.52183 Recall@20 0 0.42887 0.42887 0.42887 0.42887 0.42887 500 0.45515 0.4531 0.45329 0.44183 0.4552 1000 0.45496 0.45392 0.45569 0.43807 0.45786 2000 0.45523 0.45265 0.45518 0.44009 0.45636 4000 0.45337 0.45062 0.45393 0.44354 0.45623 8000 0.45316 0.45215 0.45542 0.44278 0.4527 16000 0.45846 0.45417 0.46028 0.44532 0.4598 32000 0.46303 0.45253 0.46247 0.44889 0.4607 Success@20 0 0.85932 0.85932 0.85932 0.85932 0.85932 500 0.8645 0.86302 0.86479 0.86464 0.86686 1000 0.86361 0.86302 0.86479 0.8608 0.86672 2000 0.86154 0.86036 0.86346 0.86154 0.86627 4000 0.8605 0.85784 0.86154 0.86183 0.86405 8000 0.85962 0.85873 0.8605 0.86139 0.86065 16000 0.86124 0.85976 0.86228 0.8605 0.86405 32000 0.86686 0.85888 0.86391 0.86109 0.86391 NDCG@100 0 0.62251 0.62251 0.62251 0.62251 0.62251 500 0.62607 0.62481 0.62697 0.62901 0.62989 1000 0.62446 0.62222 0.62391 0.62902 0.63085 2000 0.62246 0.61865 0.62162 0.62995 0.62963 4000 0.61939 0.61735 0.62012 0.63217 0.62946 8000 0.62001 0.61741 0.62006 0.63178 0.62407 16000 0.62246 0.61867 0.62344 0.63372 0.62911 32000 0.62528 0.61683 0.62496 0.63913 0.62899 Recall@100 0 0.61507 0.61507 0.61507 0.61507 0.61507 500 0.65763 0.65614 0.65534 0.62793 0.65309 1000 0.65757 0.65696 0.65847 0.62328 0.6562 2000 0.65941 0.6572 0.6587 0.62496 0.65451 4000 0.65889 0.65706 0.65834 0.63125 0.65589 8000 0.66186 0.66088 0.66144 0.62854 0.65358 16000 0.66628 0.66374 0.66767 0.63196 0.66051 32000 0.67237 0.66268 0.6734 0.63364 0.66503 Success@100 0 0.91716 0.91716 0.91716 0.91716 0.91716 500 0.92604 0.92559 0.92352 0.91967 0.92382 1000 0.9247 0.92367 0.92411 0.9176 0.92485 2000 0.92441 0.92278 0.92411 0.9182 0.92337 4000 0.92367 0.92293 0.92293 0.92086 0.925 8000 0.92574 0.92337 0.92456 0.91982 0.92367 16000 0.92589 0.92322 0.92515 0.92012 0.9253 32000 0.92885 0.92204 0.92618 0.92071 0.92633 Table 12: Full Results on TriviaQA. Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.21935 0.21935 0.21935 0.21935 0.21935 500 0.24666 0.24734 0.24895 0.24686 0.25367 1000 0.25109 0.24906 0.25135 0.25058 0.25591 2000 0.25992 0.26174 0.25768 0.25393 0.26853 4000 0.28174 0.27356 0.27998 0.25811 0.28696 8000 0.29324 0.27947 0.29348 0.26045 0.30409 16000 0.30013 0.27998 0.30069 0.26549 0.30805 32000 0.29779 0.27999 0.29524 0.26966 0.30926 Recall@10 0 0.11412 0.11412 0.11412 0.11412 0.11412 500 0.13307 0.13346 0.13356 0.13029 0.13579 1000 0.13501 0.13431 0.13513 0.13227 0.13827 2000 0.13819 0.13903 0.13794 0.1331 0.14297 4000 0.14543 0.14158 0.14237 0.13445 0.14976 8000 0.15074 0.14488 0.1542 0.13591 0.15744 16000 0.15776 0.1449 0.15936 0.1378 0.1625 32000 0.15814 0.14411 0.15668 0.13863 0.16185 Success@10 0 0.63489 0.63489 0.63489 0.63489 0.63489 500 0.70638 0.70383 0.70553 0.68681 0.71319 1000 0.71489 0.71064 0.72255 0.69787 0.71915 2000 0.73277 0.73702 0.73447 0.70043 0.74128 4000 0.76255 0.75319 0.76255 0.71149 0.76766 8000 0.78638 0.75915 0.79404 0.71489 0.79064 16000 0.7966 0.75745 0.7966 0.72936 0.80085 32000 0.78894 0.7583 0.78979 0.73617 0.8 NDCG@20 0 0.26348 0.26348 0.26348 0.26348 0.26348 500 0.29366 0.29385 0.29566 0.29126 0.29826 1000 0.29637 0.29634 0.29706 0.29559 0.3002 2000 0.30455 0.30416 0.3036 0.30001 0.31348 4000 0.326 0.31997 0.32444 0.30256 0.33175 8000 0.33759 0.32329 0.33554 0.30537 0.34681 16000 0.33797 0.32148 0.33982 0.31071 0.35008 32000 0.33739 0.32248 0.33678 0.31654 0.35104 Recall@20 0 0.18949 0.18949 0.18949 0.18949 0.18949 500 0.21663 0.21695 0.21657 0.20815 0.21731 1000 0.21899 0.21913 0.22018 0.21162 0.21994 2000 0.22352 0.22182 0.22289 0.21433 0.22791 4000 0.22958 0.22733 0.22965 0.21376 0.23769 8000 0.24058 0.22914 0.23801 0.21579 0.24658 16000 0.24178 0.22593 0.24426 0.21874 0.25091 32000 0.24346 0.22538 0.2442 0.22014 0.25207 Success@20 0 0.75319 0.75319 0.75319 0.75319 0.75319 500 0.82128 0.81447 0.81872 0.79234 0.81617 1000 0.81702 0.82298 0.82128 0.8 0.81532 2000 0.82553 0.82043 0.82638 0.80426 0.84085 4000 0.84426 0.85021 0.84426 0.8017 0.85702 8000 0.86468 0.85362 0.86383 0.80936 0.87149 16000 0.86553 0.8366 0.86553 0.81702 0.86979 32000 0.86298 0.84 0.85957 0.81957 0.87064 NDCG@100 0 0.4582 0.4582 0.4582 0.4582 0.4582 500 0.49334 0.49328 0.4953 0.48779 0.49772 1000 0.49687 0.49633 0.49899 0.49213 0.50135 2000 0.50644 0.5062 0.50519 0.49567 0.51531 4000 0.52799 0.51896 0.52622 0.49817 0.53062 8000 0.53567 0.52151 0.53459 0.50174 0.54524 16000 0.53825 0.51991 0.53858 0.50578 0.5488 32000 0.53734 0.51888 0.53583 0.50892 0.54931 Recall@100 0 0.44129 0.44129 0.44129 0.44129 0.44129 500 0.48578 0.48488 0.48621 0.46503 0.48353 1000 0.49008 0.48937 0.49335 0.46952 0.49181 2000 0.49738 0.49507 0.49835 0.47295 0.50321 4000 0.50844 0.50081 0.50844 0.47397 0.51132 8000 0.51516 0.50016 0.51674 0.47688 0.52164 16000 0.5223 0.49831 0.52344 0.47718 0.53231 32000 0.52231 0.4936 0.52017 0.47535 0.53109 Success@100 0 0.91319 0.91319 0.91319 0.91319 0.91319 500 0.93617 0.93532 0.93617 0.92511 0.93362 1000 0.93702 0.93957 0.94298 0.92936 0.94128 2000 0.94468 0.94979 0.94638 0.93191 0.95404 4000 0.95149 0.95064 0.94979 0.93021 0.95404 8000 0.95149 0.94809 0.94809 0.93532 0.95234 16000 0.94894 0.94298 0.94979 0.93702 0.95574 32000 0.94894 0.94213 0.94723 0.93787 0.95234 Table 13: Full Results on TripClick (head). Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.20834 0.20834 0.20834 0.20834 0.20834 500 0.21923 0.21885 0.21742 0.2224 0.22026 1000 0.21736 0.21728 0.21675 0.22483 0.22031 2000 0.21753 0.21787 0.21744 0.22763 0.22117 4000 0.22105 0.21873 0.22282 0.22932 0.22612 8000 0.23183 0.22836 0.23209 0.22973 0.23327 16000 0.24165 0.2365 0.24048 0.23194 0.24341 32000 0.24507 0.23823 0.24798 0.23579 0.24942 Recall@10 0 0.21973 0.21973 0.21973 0.21973 0.21973 500 0.23999 0.23883 0.23861 0.23966 0.24437 1000 0.24527 0.24226 0.24388 0.24426 0.24363 2000 0.2469 0.24785 0.2479 0.24509 0.2488 4000 0.24662 0.24813 0.24984 0.24903 0.25319 8000 0.25737 0.25676 0.25413 0.25152 0.25867 16000 0.26549 0.26493 0.26218 0.25323 0.27092 32000 0.27042 0.26894 0.27346 0.2574 0.27578 Success@10 0 0.52085 0.52085 0.52085 0.52085 0.52085 500 0.54468 0.54383 0.54128 0.53787 0.54979 1000 0.54809 0.54809 0.54468 0.54723 0.54383 2000 0.55149 0.55234 0.55404 0.54809 0.55149 4000 0.55234 0.56085 0.56511 0.54979 0.56426 8000 0.58553 0.58383 0.58043 0.54979 0.57277 16000 0.59574 0.58979 0.59149 0.55745 0.59489 32000 0.59404 0.59149 0.59745 0.57277 0.61021 NDCG@20 0 0.26082 0.26082 0.26082 0.26082 0.26082 500 0.27579 0.27316 0.27365 0.2762 0.27515 1000 0.27235 0.27205 0.27208 0.27726 0.27659 2000 0.27267 0.27239 0.27311 0.28023 0.27754 4000 0.27849 0.2753 0.27812 0.28306 0.28408 8000 0.28709 0.28263 0.28792 0.28343 0.29082 16000 0.29727 0.28966 0.29574 0.28594 0.29924 32000 0.30304 0.29397 0.30349 0.28986 0.30561 Recall@20 0 0.33434 0.33434 0.33434 0.33434 0.33434 500 0.36105 0.35785 0.35804 0.35711 0.36212 1000 0.36231 0.35973 0.3617 0.35593 0.36389 2000 0.36339 0.36408 0.36735 0.35766 0.3686 4000 0.37043 0.36911 0.3716 0.36253 0.37939 8000 0.38016 0.37795 0.37853 0.36541 0.38278 16000 0.38796 0.38256 0.38589 0.36692 0.39138 32000 0.39753 0.39027 0.39605 0.37266 0.39998 Success@20 0 0.6383 0.6383 0.6383 0.6383 0.6383 500 0.67915 0.66468 0.66809 0.67149 0.67574 1000 0.67404 0.66553 0.67149 0.67319 0.6834 2000 0.67745 0.6766 0.67915 0.67404 0.6834 4000 0.69021 0.68681 0.69106 0.68 0.69872 8000 0.69447 0.69702 0.69277 0.68851 0.70043 16000 0.70468 0.70043 0.70128 0.69362 0.71064 32000 0.7183 0.71319 0.71319 0.69191 0.72 NDCG@100 0 0.36876 0.36876 0.36876 0.36876 0.36876 500 0.38618 0.38505 0.38477 0.3857 0.38506 1000 0.38433 0.38485 0.38481 0.38712 0.38806 2000 0.38651 0.38577 0.38586 0.39046 0.3905 4000 0.39201 0.38943 0.39245 0.39179 0.39496 8000 0.3995 0.39603 0.40126 0.39208 0.40289 16000 0.41015 0.40399 0.41008 0.39419 0.4117 32000 0.41662 0.40836 0.41801 0.39733 0.41867 Recall@100 0 0.60293 0.60293 0.60293 0.60293 0.60293 500 0.64261 0.64128 0.64145 0.63196 0.64077 1000 0.64984 0.64984 0.64989 0.63542 0.64843 2000 0.66019 0.65785 0.65856 0.6394 0.66177 4000 0.66304 0.66648 0.66787 0.6402 0.66628 8000 0.67083 0.67221 0.6732 0.64336 0.67385 16000 0.68717 0.68287 0.6885 0.64703 0.68699 32000 0.69987 0.68954 0.70005 0.64903 0.69874 Success@100 0 0.83915 0.83915 0.83915 0.83915 0.83915 500 0.85957 0.86128 0.85872 0.85957 0.85617 1000 0.86383 0.86553 0.86638 0.86128 0.86213 2000 0.87234 0.87234 0.87234 0.86213 0.87149 4000 0.8783 0.88085 0.88085 0.86213 0.8766 8000 0.88085 0.8834 0.8817 0.86298 0.88426 16000 0.88766 0.88681 0.89021 0.86553 0.89021 32000 0.89787 0.89362 0.89617 0.86894 0.89362 Table 14: Full Results on TripClick (torso). Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.86791 0.86791 0.86791 0.86791 0.86791 500 0.87421 0.85787 0.87533 0.89561 0.87832 1000 0.87297 0.85656 0.87007 0.89834 0.88468 2000 0.87564 0.86304 0.87542 0.90043 0.88611 4000 0.88167 0.87094 0.88168 0.90521 0.89146 8000 0.88552 0.87471 0.88762 0.90846 0.89684 16000 0.8915 0.87811 0.89261 0.911 0.90002 32000 0.892 0.87517 0.89319 0.91485 0.90247 Recall@10 0 0.93622 0.93622 0.93622 0.93622 0.93622 500 0.94158 0.93736 0.94238 0.94385 0.94226 1000 0.94305 0.93727 0.94163 0.94312 0.94523 2000 0.94305 0.9397 0.9424 0.94194 0.94457 4000 0.94484 0.9412 0.9444 0.9424 0.9459 8000 0.94635 0.94284 0.94723 0.9434 0.94892 16000 0.94806 0.94366 0.9481 0.94293 0.95087 32000 0.9486 0.94342 0.94868 0.93992 0.94965 Success@10 0 0.97735 0.97735 0.97735 0.97735 0.97735 500 0.98305 0.97705 0.9835 0.98755 0.98455 1000 0.98305 0.9772 0.98185 0.988 0.9868 2000 0.9829 0.979 0.9826 0.98785 0.98545 4000 0.9847 0.9799 0.9838 0.98875 0.9865 8000 0.985 0.9805 0.9859 0.98965 0.9883 16000 0.98515 0.9802 0.9853 0.98935 0.9892 32000 0.9838 0.9799 0.98455 0.988 0.98695 NDCG@20 0 0.8723 0.8723 0.8723 0.8723 0.8723 500 0.87815 0.86211 0.87925 0.89912 0.88211 1000 0.87689 0.86165 0.87416 0.90187 0.88805 2000 0.88005 0.86781 0.87991 0.90409 0.89001 4000 0.88609 0.87588 0.88641 0.90866 0.89527 8000 0.88992 0.87945 0.89184 0.91165 0.90086 16000 0.89561 0.88274 0.89676 0.91402 0.90385 32000 0.89564 0.87916 0.89703 0.91796 0.90634 Recall@20 0 0.95048 0.95048 0.95048 0.95048 0.95048 500 0.95453 0.95144 0.95523 0.95469 0.95459 1000 0.95569 0.95407 0.95477 0.95399 0.95601 2000 0.95721 0.95493 0.95659 0.95319 0.95708 4000 0.95903 0.95695 0.9596 0.95303 0.95791 8000 0.96049 0.95829 0.96069 0.95324 0.96156 16000 0.96127 0.95902 0.96142 0.95232 0.96278 32000 0.96026 0.95607 0.96086 0.94967 0.96195 Success@20 0 0.9859 0.9859 0.9859 0.9859 0.9859 500 0.9901 0.98635 0.9904 0.9925 0.9904 1000 0.9898 0.98755 0.9895 0.99265 0.99175 2000 0.9907 0.98755 0.9898 0.9928 0.99175 4000 0.99145 0.98845 0.99205 0.9934 0.99205 8000 0.9925 0.9892 0.9922 0.9937 0.99355 16000 0.9919 0.9895 0.99175 0.99355 0.99355 32000 0.98965 0.98605 0.9901 0.99295 0.99235 NDCG@100 0 0.87636 0.87636 0.87636 0.87636 0.87636 500 0.88261 0.86725 0.88371 0.90305 0.88639 1000 0.88132 0.8665 0.87887 0.90575 0.89229 2000 0.88435 0.87259 0.88431 0.90809 0.89427 4000 0.89035 0.88029 0.89042 0.91256 0.89958 8000 0.89399 0.88387 0.89579 0.91537 0.90469 16000 0.89971 0.88716 0.90076 0.91775 0.90758 32000 0.89989 0.88413 0.90125 0.92182 0.91042 Recall@100 0 0.96671 0.96671 0.96671 0.96671 0.96671 500 0.97215 0.97231 0.97283 0.97047 0.9714 1000 0.97325 0.97381 0.97341 0.96951 0.97267 2000 0.97417 0.97459 0.97396 0.96964 0.97374 4000 0.97595 0.97473 0.97535 0.96888 0.97511 8000 0.97648 0.97609 0.97618 0.96812 0.97659 16000 0.97727 0.97661 0.97698 0.96719 0.97709 32000 0.97751 0.9762 0.97807 0.96518 0.97812 Success@100 0 0.99205 0.99205 0.99205 0.99205 0.99205 500 0.99565 0.9943 0.9958 0.99625 0.99565 1000 0.9955 0.9949 0.99565 0.99655 0.9958 2000 0.99505 0.99475 0.99505 0.99745 0.9958 4000 0.9955 0.99445 0.9949 0.99745 0.9964 8000 0.9958 0.99505 0.9955 0.99685 0.99655 16000 0.9958 0.9949 0.9958 0.9967 0.9964 32000 0.9958 0.99505 0.9961 0.9967 0.99685 Table 15: Full Results on FEVER. Metric #iterations FT RP25 InfoBatch SP25 DP NDCG@10 0 0.78999 0.78999 0.78999 0.78999 0.78999 500 0.79112 0.78914 0.78982 0.79181 0.79469 1000 0.79348 0.7896 0.79108 0.79162 0.79549 2000 0.79611 0.79243 0.79308 0.79228 0.79771 4000 0.79654 0.79531 0.79701 0.79543 0.80125 8000 0.80141 0.79758 0.80054 0.79639 0.80721 16000 0.80386 0.79894 0.80298 0.80032 0.81139 32000 0.80585 0.80083 0.80647 0.80275 0.81208 Recall@10 0 0.76583 0.76583 0.76583 0.76583 0.76583 500 0.77434 0.77286 0.77286 0.74477 0.77056 1000 0.77576 0.77441 0.77596 0.73943 0.774 2000 0.77981 0.77873 0.7788 0.74099 0.77731 4000 0.78379 0.7815 0.78325 0.74105 0.78325 8000 0.78899 0.78379 0.78778 0.74038 0.78771 16000 0.79433 0.78656 0.79318 0.74207 0.79365 32000 0.80088 0.78623 0.80068 0.74362 0.79953 Success@10 0 0.95179 0.95179 0.95179 0.95179 0.95179 500 0.95935 0.95881 0.95895 0.95422 0.96003 1000 0.96057 0.95935 0.95989 0.95409 0.96057 2000 0.96259 0.96003 0.96084 0.95409 0.96138 4000 0.96138 0.95868 0.9603 0.95395 0.96502 8000 0.96111 0.95841 0.96016 0.95449 0.96597 16000 0.96003 0.95787 0.96003 0.95463 0.96637 32000 0.96124 0.9576 0.96084 0.95544 0.96529 NDCG@20 0 0.80366 0.80366 0.80366 0.80366 0.80366 500 0.80525 0.80333 0.80421 0.80514 0.80885 1000 0.808 0.80409 0.80541 0.80501 0.80945 2000 0.8101 0.80683 0.80703 0.80565 0.81199 4000 0.81002 0.80926 0.81084 0.80884 0.81438 8000 0.81462 0.81148 0.81433 0.80939 0.82042 16000 0.81756 0.81293 0.81682 0.81337 0.82424 32000 0.81933 0.81502 0.81977 0.81546 0.82478 Recall@20 0 0.80743 0.80743 0.80743 0.80743 0.80743 500 0.81695 0.8154 0.81614 0.78521 0.81303 1000 0.81938 0.81783 0.81924 0.78008 0.81594 2000 0.82228 0.82208 0.821 0.7819 0.82019 4000 0.82458 0.82316 0.82492 0.78217 0.82357 8000 0.82876 0.82606 0.82924 0.78015 0.82829 16000 0.83565 0.82917 0.83477 0.78143 0.83268 32000 0.84159 0.82937 0.84126 0.78204 0.83808 Success@20 0 0.96705 0.96705 0.96705 0.96705 0.96705 500 0.97434 0.97407 0.97394 0.96772 0.97556 1000 0.97596 0.97529 0.97434 0.96718 0.97556 2000 0.97623 0.97515 0.97448 0.96678 0.97637 4000 0.97556 0.97448 0.97556 0.96691 0.97623 8000 0.97529 0.97218 0.97583 0.96691 0.97826 16000 0.97637 0.97259 0.97569 0.9684 0.97893 32000 0.97691 0.97205 0.97569 0.96907 0.97812 NDCG@100 0 0.82198 0.82198 0.82198 0.82198 0.82198 500 0.82227 0.82079 0.82131 0.82394 0.82592 1000 0.82477 0.8212 0.82234 0.82389 0.82651 2000 0.8265 0.82336 0.82383 0.82444 0.82881 4000 0.82664 0.82613 0.82728 0.82724 0.83099 8000 0.83127 0.82852 0.83067 0.828 0.83651 16000 0.8334 0.82963 0.83301 0.83107 0.84023 32000 0.83481 0.83163 0.83551 0.8332 0.84056 Recall@100 0 0.88292 0.88292 0.88292 0.88292 0.88292 500 0.88785 0.88805 0.88717 0.86313 0.88386 1000 0.8892 0.88926 0.89001 0.8582 0.88724 2000 0.89061 0.89129 0.89061 0.85976 0.89041 4000 0.89318 0.89332 0.89352 0.85814 0.89271 8000 0.89757 0.89608 0.89683 0.85658 0.89534 16000 0.90095 0.89797 0.90149 0.85442 0.89878 32000 0.90554 0.89764 0.90628 0.85571 0.90365 Success@100 0 0.98825 0.98825 0.98825 0.98825 0.98825 500 0.99082 0.99095 0.99068 0.98825 0.99122 1000 0.99149 0.99122 0.99055 0.98798 0.99109 2000 0.99149 0.99109 0.99176 0.98785 0.9919 4000 0.99163 0.99149 0.99176 0.98866 0.99203 8000 0.9919 0.99217 0.99082 0.98866 0.99203 16000 0.99203 0.9919 0.99203 0.98866 0.99298 32000 0.99257 0.99109 0.99203 0.98879 0.9923 Table 16: Full Results on HotpotQA. Table 17: Qwen3-Embedding-0.6B on NFCorpus. Metric Pretrained FT InfoBatch SP DP MRR@1 0.458 0.502 0.511 0.533 0.517 MRR@5 0.543 0.572 0.580 0.595 0.587 MRR@10 0.550 0.581 0.587 0.605 0.595 MRR@20 0.555 0.584 0.590 0.607 0.598 MRR@50 0.556 0.586 0.591 0.609 0.600 MRR@100 0.557 0.586 0.592 0.609 0.600 NDCG@5 0.440 0.479 0.480 0.492 0.486 NDCG@10 0.441 0.479 0.478 0.487 0.479 NDCG@20 0.461 0.489 0.484 0.489 0.492 NDCG@50 0.517 0.539 0.540 0.545 0.541 NDCG@100 0.577 0.617 0.617 0.615 0.618 Recall@1 0.061 0.065 0.068 0.067 0.065 Recall@5 0.136 0.162 0.165 0.155 0.169 Recall@10 0.171 0.236 0.237 0.214 0.234 Recall@20 0.211 0.314 0.308 0.265 0.311 Recall@50 0.267 0.416 0.417 0.357 0.408 Recall@100 0.329 0.518 0.517 0.443 0.502 Success@1 0.458 0.502 0.511 0.533 0.517 Success@5 0.672 0.690 0.697 0.693 0.697 Success@10 0.721 0.755 0.749 0.768 0.762 Success@20 0.793 0.796 0.796 0.793 0.805 Success@50 0.836 0.842 0.845 0.851 0.864 Success@100 0.889 0.889 0.885 0.885 0.892 Table 18: Qwen3-Embedding-0.6B on FiQA. The pretrained model outperforms all finetuned methods, likely due to high-quality financial data in its pretraining corpus. Metric Pretrained FT InfoBatch SP DP MRR@1 0.469 0.392 0.394 0.390 0.384 MRR@5 0.543 0.465 0.466 0.464 0.464 MRR@10 0.555 0.474 0.473 0.473 0.471 MRR@20 0.559 0.479 0.478 0.477 0.476 MRR@50 0.561 0.480 0.480 0.480 0.478 MRR@100 0.561 0.481 0.481 0.480 0.479 NDCG@5 0.469 0.420 0.428 0.423 0.423 NDCG@10 0.511 0.454 0.455 0.456 0.450 NDCG@20 0.540 0.483 0.484 0.478 0.476 NDCG@50 0.568 0.506 0.508 0.506 0.501 NDCG@100 0.587 0.517 0.520 0.522 0.515 Recall@1 0.245 0.199 0.197 0.205 0.192 Recall@5 0.453 0.377 0.384 0.377 0.377 Recall@10 0.552 0.446 0.439 0.448 0.432 Recall@20 0.633 0.510 0.508 0.504 0.495 Recall@50 0.724 0.574 0.583 0.584 0.565 Recall@100 0.798 0.612 0.623 0.634 0.611 Success@1 0.469 0.392 0.394 0.390 0.384 Success@5 0.674 0.586 0.596 0.590 0.583 Success@10 0.761 0.657 0.644 0.656 0.634 Success@20 0.821 0.715 0.728 0.713 0.707 Success@50 0.886 0.767 0.781 0.781 0.769 Success@100 0.927 0.802 0.816 0.832 0.802 Table 19: Qwen3-Embedding-0.6B on ANTIQUE. Metric Pretrained FT InfoBatch SP DP MRR@1 0.615 0.580 0.625 0.640 0.615 MRR@5 0.718 0.682 0.707 0.738 0.696 MRR@10 0.724 0.689 0.716 0.746 0.703 MRR@20 0.727 0.692 0.718 0.747 0.706 MRR@50 0.728 0.693 0.719 0.748 0.707 MRR@100 0.728 0.693 0.719 0.748 0.707 NDCG@5 0.519 0.496 0.502 0.546 0.510 NDCG@10 0.518 0.496 0.506 0.540 0.520 NDCG@20 0.570 0.546 0.549 0.582 0.567 NDCG@50 0.646 0.617 0.624 0.658 0.636 NDCG@100 0.690 0.663 0.665 0.707 0.674 Recall@1 0.072 0.071 0.069 0.074 0.074 Recall@5 0.214 0.202 0.197 0.231 0.207 Recall@10 0.304 0.270 0.264 0.317 0.284 Recall@20 0.398 0.340 0.329 0.396 0.353 Recall@50 0.510 0.444 0.431 0.514 0.450 Recall@100 0.585 0.516 0.495 0.597 0.513 Success@1 0.615 0.580 0.625 0.640 0.615 Success@5 0.855 0.835 0.840 0.885 0.820 Success@10 0.905 0.890 0.905 0.935 0.870 Success@20 0.940 0.930 0.930 0.950 0.915 Success@50 0.980 0.955 0.950 0.975 0.950 Success@100 0.980 0.965 0.955 0.980 0.955 Table 20: Qwen3-Embedding-0.6B on TriviaQA. Metric Pretrained FT InfoBatch SP DP MRR@1 0.519 0.519 0.517 0.538 0.547 MRR@5 0.602 0.615 0.611 0.620 0.634 MRR@10 0.611 0.624 0.619 0.627 0.642 MRR@20 0.614 0.627 0.622 0.630 0.645 MRR@50 0.616 0.628 0.624 0.631 0.646 MRR@100 0.616 0.628 0.624 0.631 0.647 NDCG@5 0.461 0.483 0.478 0.489 0.501 NDCG@10 0.467 0.489 0.484 0.493 0.504 NDCG@20 0.502 0.522 0.515 0.525 0.535 NDCG@50 0.564 0.587 0.582 0.584 0.598 NDCG@100 0.605 0.632 0.626 0.623 0.640 Recall@1 0.086 0.094 0.093 0.093 0.097 Recall@5 0.236 0.267 0.263 0.253 0.271 Recall@10 0.316 0.360 0.354 0.334 0.363 Recall@20 0.403 0.462 0.453 0.421 0.461 Recall@50 0.514 0.590 0.584 0.529 0.588 Recall@100 0.591 0.677 0.669 0.603 0.669 Success@1 0.519 0.519 0.517 0.538 0.547 Success@5 0.735 0.766 0.759 0.752 0.766 Success@10 0.795 0.826 0.821 0.803 0.826 Success@20 0.844 0.871 0.864 0.848 0.867 Success@50 0.886 0.912 0.905 0.888 0.912 Success@100 0.911 0.935 0.927 0.911 0.931