MSLF: Multi-query Single-Passage Late Fusion

• MSLF is a multi-query retrieval design pattern that fuses multiple reformulations into a single retrieval score using weighted late fusion techniques.
• It reduces computational cost by collapsing diverse query rewrites or sub-queries into one consolidated query, enabling efficient sparse and dense retrieval.
• Empirical findings show significant MRR improvements and underscore the sensitivity of fusion operator choice across conversational, RL-based, and aspect-based tasks.

Multi-query Single-passage Late Fusion (MSLF) is a retrieval design pattern in which multiple reformulations, decompositions, or sub-queries derived from an input query are combined before or during ranking so that passage-level evidence can be aggregated without running a fully independent end-to-end retrieval-and-fusion pipeline for every variant. In recent literature, the acronym has been used in several non-identical but closely related senses: a conversational passage retrieval method that returns all beam-search rewrites and fuses their scores within a single first-pass retrieval stage (Kostric et al., 2024); a reinforcement-learning training-time strategy in RAG that collapses multiple sub-queries into one synthetic passage and fuses only two ranked lists (Lin et al., 8 Sep 2025); and an item-retrieval formulation that decomposes a query into aspects, scores reviews per aspect, and late-fuses at the item level (Korikov et al., 2024). This suggests that MSLF is best understood as a family of multi-query late-fusion schemes rather than a single standardized algorithm.

1. Terminological scope and recurring structure

Across the cited usages, MSLF begins with one query and replaces the single-query assumption with a set of derived units: beam-search rewrites in conversational query rewriting, reformulated sub-queries in RAG, or aspect spans in reviewed-item retrieval. The second stage computes passage- or document-level evidence for those units, and the third stage aggregates that evidence by weighted score summation, rank fusion, or aspect-wise averaging (Kostric et al., 2024, Lin et al., 8 Sep 2025, Korikov et al., 2024).

Usage	Derived units	Fusion target
Conversational passage retrieval	Top-$n$ query rewrites from beam search	One first-pass sparse or dense retrieval score
RL-based RAG training	$k$ reformulated sub-queries collapsed into one synthetic passage	Two ranked lists fused by RRF
Reviewed-item retrieval	Aspect sub-queries extracted from one query	Item score from review-level evidence

The phrase “single-passage” is therefore context-dependent. In conversational passage retrieval, it refers to issuing exactly one first-pass retrieval after combining multiple rewrites. In MoLER, it refers to synthesizing one passage from multiple sub-queries during RL training. In reviewed-item retrieval, it appears in a setting where many passages exist per item, but late fusion is still organized around passage-level evidence. A common misconception is to treat these as the same algorithm; the literature instead presents distinct instantiations that share a multi-query-plus-late-fusion motif.

2. Canonical formulation in conversational passage retrieval

In the formulation introduced for conversational passage retrieval, a pretrained encoder-decoder rewriting model generates multiple decontextualized rewrites by beam search. At turn $i$, the model takes the raw user utterance $q_i$ and history $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$, and solves

$\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$

With beam size $K=10$, the top-$n$ full sequences $\{\hat q_i^1,\dots,\hat q_i^n\}$ are returned together with their length-normalized log-probabilities

$$RS(\hat q_i^j)=\Bigl(\prod_{t=1}^{|\hat q_i^j|} P(t_t \mid t_{<t},H,q_i)\Bigr)^{1/|\hat q_i^j|}.$$

The implementation uses T5-base with 12 layers, 768-dimensional hidden states, 12 heads, maximum input length 512 tokens, and truncation of history to the last $k$0 pair; the input format is rewrite: <ĥq_1> [[SEP](https://www.emergentmind.com/topics/semantic-entropy-production-sep-metric)] <r_1> … <ĥq_{i−1}> [SEP] <r_{i−1}> [SEP] <q_i> (Kostric et al., 2024).

The paper gives a general late-fusion score

$k$1

with $k$2. For sparse retrieval, one can either issue $k$3 separate BM25 calls and sum the weighted document scores,

$k$4

or construct a single weighted bag-of-words query $k$5 via

$k$6

followed by optional normalization and one BM25-style retrieval pass. The paper states that early and late fusion are algebraically equivalent when query term frequency is linear in $k$7.

For dense retrieval, MSLF forms a single query embedding

$k$8

and then scores each document with one dot product,

$k$9

The operational claim of “no additional cost” is tied to standard beam search already maintaining the top-$i$0 hypotheses, sparse retrieval using a single weighted query instead of $i$1 calls, and dense retrieval performing one document-side nearest-neighbor search after collapsing the rewrite embeddings (Kostric et al., 2024).

3. Empirical performance and beam-size behavior

On QReCC overall, the conversational passage retrieval instantiation reports substantial MRR gains over single-rewrite baselines for both sparse and dense first-pass retrieval. With $i$2 rewrites, sparse BM25 improves from 31.03 to 37.34 with T5QR_manual, from 49.18 to 50.24 with ConvGQR, and from 46.72 to 50.73 with T5QR_LLM. Dense GTR improves from 36.08 to 40.53 with T5QR_manual, from 42.18 to 45.82 with ConvGQR, and from 42.46 to 45.98 with T5QR_LLM; all improvements are statistically significant under a $i$3-test with $i$4. The same study states that MSLF sets a new state of the art on QReCC overall, including QuAC, NQ, and CAsT (Kostric et al., 2024).

Retrieval	Rewriter	Single-Q MRR	MSLF MRR
Sparse	T5QR_manual	31.03	37.34
Sparse	ConvGQR	49.18	50.24
Sparse	T5QR_LLM	46.72	50.73
Dense	T5QR_manual	36.08	40.53
Dense	ConvGQR	42.18	45.82
Dense	T5QR_LLM	42.46	45.98

The beam-size ablation characterizes the gain curve. The baseline is $i$5, increasing $i$6 to 3–5 yields more than 50% of the full gain, and $i$7 shows diminishing returns, with $i$8 MRR points at $i$9. A full sweep over $q_i$0 showed steady gains up to 10 and saturation thereafter. In this formulation, $q_i$1 is presented as a good trade-off (Kostric et al., 2024).

These results are notable because the improvement does not require a new retriever architecture. The gains arise from exploiting beam-search diversity already present in the rewrite model and mapping that diversity into a single first-pass retrieval computation.

4. Training-time MSLF in domain-aware RAG

In the MoLER framework, MSLF is a training-time approximation used inside RL fine-tuning rather than a first-pass retrieval method for conventional conversational rewriting. The MoLER pipeline has a continual pre-training phase with a Mixture of Losses and an RL phase using Group Relative Policy Optimization. At inference time, MoLER uses full Multi-query Multi-passage Late Fusion (MMLF): it expands $q_i$2, generates $q_i$3 independent pseudo-passages $q_i$4, retrieves for each plus the original query, and fuses the resulting $q_i$5 ranked lists via Reciprocal Rank Fusion. During RL training, MSLF replaces that procedure by generating $q_i$6 reformulations, synthesizing one passage $q_i$7 from the set $q_i$8, retrieving with the original query and the synthetic passage, and fusing only two lists (Lin et al., 8 Sep 2025).

Formally, the two similarity scores are

$q_i$9

and the fused score is

$$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$0

The paper notes that one could instead use

$$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$1

but MoLER uses RRF. The fused list is evaluated for recall@K, which becomes the RL reward. Because MSLF generates $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$2 sub-queries and one passage rather than $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$3 passages, the number of retrieval calls per query is reduced from $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$4 to 2.

The complexity statement is explicit:

• MMLF training: $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$5
• MSLF training: $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$6, independent of $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$7

Under this formulation, the training cost scales as $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$8 rather than $$H=\langle \hat q_1,r_1,\dots,\hat q_{i-1},r_{i-1}\rangle$$9. The reported implementation uses $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$0, batch size $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$1, learning rate $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$2, LoRA rank 64, $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$3, and temperature 0.7. Empirically, token and latency cost per iteration in Dr.GRPO+MSLF is approximately 25–30% of that under Dr.GRPO+MMLF with $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$4, and on NFCORPUS the model achieves Recall@1k = 58.02% versus 59.72% for MMLF, described as a $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$5 absolute drop for a greater than $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$6 reduction in retrieval operations (Lin et al., 8 Sep 2025).

A plausible implication is that this variant of MSLF should be read as a surrogate objective design for RL efficiency rather than as a universal inference-time fusion rule. The paper itself switches back to MMLF at inference to recover full multi-query recall gains.

5. Formal limitations in multi-aspect reviewed-item retrieval

A different use of MSLF appears in reviewed-item retrieval, where the input query is decomposed into non-overlapping aspect spans $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$7, an item $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$8 is represented by a set of reviews $\hat q_i=\arg\max_{q'} P(q' \mid H,q_i).$9, and passage-level similarity is computed between each aspect and each review:

$K=10$0

For each item and sub-query, the top-$K=10$1 reviews are selected, and a common “max-then-mean” late-fusion score is

$K=10$2

where $K=10$3. The paper also notes an average-then-mean variant, but identifies max-aggregation as the most common (Korikov et al., 2024).

This study presents an explicit critique of MSLF under multi-aspect conditions. Two desiderata are defined: Coverage, meaning that the top-$K=10$4 reviews for each sub-query should collectively mention all relevant aspects, and Balance, meaning that each aspect should be equally represented among the fused reviews. Two failure modes are then identified: aspect popularity bias, in which more frequent aspects dominate the top-$K=10$5 pool, and embedding bias, in which a monolithic query embedding lies closer to one aspect’s reviews than another’s even when both are relevant. In fully disjoint and imbalanced datasets, the empirical manifestation is that MSLF MAP@10 stalls at approximately 0.41 and does not improve with higher $K=10$6.

The proposed remedy is Aspect Fusion (AF): first extract aspect spans with an LLM prompt, then compute per-aspect item scores

$K=10$7

and finally fuse the aspect-item scores using AMean, GMean, HMean, Min, Borda count, or round-robin interleaving. On fully overlapping balanced data, monolithic LF is approximately 0.50 MAP@10 and AF (AMean) is approximately 0.52. On fully disjoint balanced data, monolithic LF is approximately 0.41 while AF variants such as AMean, GMean, and HMean are approximately 0.56. At $K=10$8, one-popular and one-rare imbalanced settings yield LF scores of 0.36 and 0.39 respectively, while AF reaches 0.52 in both cases. The effect of $K=10$9 is also structured: AF peaks at $n$0 and then drops once $n$1 exceeds the number of available aspect-specific reviews and begins selecting irrelevant reviews. Cross-encoder and listwise reranking can improve monolithic LF at high $n$2, but at $n$3 performance worsens; for AF, reranking gives little or no gain for $n$4 (Korikov et al., 2024).

This usage is important because it demonstrates that late fusion over multiple sub-queries is not intrinsically robust. The failure is not merely one of weak embeddings; it is tied to review-level aspect distribution and to the aggregation rule itself.

6. Relation to adjacent late-fusion retrieval designs

A related retrieval-stage study, although not presented under the acronym MSLF, helps clarify why late-fusion operator choice matters in multi-query settings. In long-term conversational memory retrieval, the history is a set of past turns

$n$5

and the dense late-interaction score for a candidate session $n$6 is defined as

$n$7

The canonical late-interaction operator is turn-level cosine max-similarity,

$n$8

with comparisons against early mean-pooling, top-$n$9, and smooth-max/LSE-$\{\hat q_i^1,\dots,\hat q_i^n\}$0. The lexical score is pooled analogously,

$\{\hat q_i^1,\dots,\hat q_i^n\}$1

and dense and lexical evidence are fused after $\{\hat q_i^1,\dots,\hat q_i^n\}$2-normalization:

$\{\hat q_i^1,\dots,\hat q_i^n\}$3

The weight $\{\hat q_i^1,\dots,\hat q_i^n\}$4 is selected by leave-one-conversation-out cross-validation (Lysenstøen, 2 Jun 2026).

The reported findings are relevant to MSLF-like designs because they isolate the consequences of late interaction, max pooling over query sets, and score-level fusion. On LoCoMo with e5-large-v2, BM25 achieves Hit@1 = 0.640 and NDCG@5 = 0.746, dense early mean-pooling yields Hit@1 = 0.427 and NDCG@5 = 0.573, dense late max-sim reaches Hit@1 = 0.664 and NDCG@5 = 0.769, and fusion with $\{\hat q_i^1,\dots,\hat q_i^n\}$5 reaches Hit@1 = 0.752 and NDCG@5 = 0.829. Across six encoders, fusion adds +8.8 to +17.2 LoCoMo Hit@1 over late interaction alone, all with $\{\hat q_i^1,\dots,\hat q_i^n\}$6. The ablations further show that max-sim and top-3 track within 1–3 percentage points, while smooth-max with $\{\hat q_i^1,\dots,\hat q_i^n\}$7 catastrophically collapses for half the encoders, with Hit@1 approximately 0.13. An off-the-shelf web-search cross-encoder reranker over the fused top-10 degrades Hit@1 from 0.701 to 0.633 in the reported configuration (Lysenstøen, 2 Jun 2026).

This suggests a broader lesson for MSLF research: multi-query late fusion is sensitive not only to how queries are generated, but also to the exact pooling operator, the lexical–dense division of labor, and the mismatch between rerankers and conversational distributions. The literature therefore does not support treating “late fusion” as a single interchangeable component.

7. Synthesis and practical interpretation

Taken together, the literature supports a precise but non-uniform interpretation of MSLF. In conversational passage retrieval, it is a training-free mechanism for exploiting beam-search rewrite diversity while issuing one first-pass retrieval. In MoLER, it is an RL-stage approximation that trades a small recall loss for a substantial reduction in retrieval operations. In reviewed-item retrieval, it is a baseline late-fusion rule whose weaknesses under aspect imbalance motivate more structured aspect-aware fusion (Kostric et al., 2024, Lin et al., 8 Sep 2025, Korikov et al., 2024).

Three recurring conclusions emerge. First, multiple query views are often useful, but the benefit depends on how they are collapsed: weighted query centroids, weighted sparse terms, RRF over a small number of ranked lists, and aspect-wise score aggregation are materially different operations. Second, computational savings are central to the term’s appeal: “no additional cost” in beam-search rewriting, $\{\hat q_i^1,\dots,\hat q_i^n\}$8 RL training instead of $\{\hat q_i^1,\dots,\hat q_i^n\}$9, and single-pass retrieval after rewrite aggregation are all explicit design goals. Third, MSLF is not universally dominant. It can underperform when aspect distributions are imbalanced, when rerankers are out of distribution, or when unstable pooling operators such as smooth-max are used in related late-fusion settings.

Accordingly, the most defensible technical reading of MSLF is as a constrained multi-query retrieval strategy: retain query diversity, reduce redundant retrieval work, and defer final aggregation to a late-fusion stage whose exact form must be matched to the retrieval unit, training regime, and error model of the task.