---
title: Multi-query Multi-passage Late Fusion (MMLF)
url: https://www.emergentmind.com/topics/multi-query-multi-passage-late-fusion-mmlf
type: topic
---

# Multi-query Multi-passage Late Fusion (MMLF)

Multi-query Multi-passage Late Fusion (MMLF) is a retrieval design in which a system constructs multiple views of a query, evaluates them against multiple passage-like retrieval units or passage-conditioned representations, and delays combination until after independent scoring or ranking. In the explicit formulation used within domain-aware RAG, a user query \(q\) is expanded into sub-queries \(\mathcal{Q}=\{q_1,\dots,q_n\}\), a pseudo-document \(p_i\) is generated for each \(q_i\), and the ranking lists produced from the raw query and the pseudo-documents are fused with Reciprocal Rank Fusion (RRF) to yield the final coarse-ranking output [2509.06650]. Related conversational retrieval work places this design in a broader late-fusion family: conversational multi-query rewriting supplies weighted query variants that can feed MMLF-style systems [2406.18960], and conversational-memory retrieval demonstrates that late interaction over turn-level passages plus lexical–dense score fusion is substantially stronger than early pooling at session level [2606.04194].

## 1. Formal definition and retrieval scope

In MoLER, MMLF is defined operationally as a three-step process: instruction expansion, pre-answer guidance, and reciprocal rank fusion. Given a user query \(q\), instruction expansion produces \(n\) sub-queries,
\[
\mathcal{Q}=\{q_1,q_2,\dots,q_n\},
\]
and pre-answer guidance generates a distinct pseudo-passage \(p_i\) for each \(q_i\). Retrieval is then run independently for the original query and for each pseudo-passage, producing lists \(L_0,L_1,\dots,L_n\), which are fused by
\[
s(q,d)=\sum_{k=0}^{n}\frac{1}{\mathrm{rank}_k(d)+K},
\]
with \(K=60\) [2509.06650].

This definition is broad enough to cover several retrieval settings. In conversational passage retrieval, the underlying information need is conditioned on dialogue history \(H=\langle q_1,r_1,\dots,q_{i-1},r_{i-1}\rangle\), and the goal is to retrieve passages \(d\in\mathcal D\) relevant to the current utterance \(q_i\) [2406.18960]. In conversational-memory retrieval, the retrieval unit is a session \(S=\langle t_1,\dots,t_{|S|}\rangle\), where each turn \(t\) functions as a passage and session-level ranking is therefore a multi-passage problem [2606.04194]. A plausible implication is that MMLF is best understood not as a single model family, but as a retrieval pattern: multiple query views, multiple passage-level evidence sources, and delayed aggregation.

## 2. Multi-query construction

The multi-query component of MMLF is implemented differently across the cited systems, but the common objective is to preserve uncertainty and aspect diversity instead of collapsing everything into a single rewrite. In MoLER, the multi-query stage is called Multi Query Retriever (MQR): for a given query \(q\), the policy \(\pi_\theta\) generates \(n\) expanded sub-queries under an MQR prompt, with \(n=3\) used by default in most experiments [2509.06650].

Conversational passage retrieval provides a distinct but closely related mechanism. A T5-base sequence-to-sequence query rewriter is run with beam search of width \(k=10\), and instead of retaining only the top-1 beam, the system keeps the top \(n\) beams, usually \(n=k=10\). Each rewrite \(\hat q_i^j\) receives a length-normalized sequence score
\[
RS(\hat q_i^j)=\left(\prod_{l=1}^{|\hat q_i^j|}P(t_l\mid t_{<l},H)\right)^{\frac{1}{|\hat q_i^j|}},
\]
and these scores are later used as fusion weights [2406.18960]. The paper emphasizes that, relative to a beam-search baseline already using \(k=10\), retaining all beams incurs “no additional cost” because the beam-search computation has already been performed.

These two constructions instantiate different philosophies. MQR uses prompting to produce diverse task-oriented sub-queries [2509.06650], whereas CMQR extracts diversity from the beam structure of a trained rewriter and makes the rewrite probabilities explicit [2406.18960]. This suggests that MMLF is agnostic to the origin of query multiplicity: query views may come from prompting, sequence-generation uncertainty, or other reformulation mechanisms, provided they can be scored or fused coherently.

## 3. Multi-passage construction and late-fusion operators

The “multi-passage” component likewise admits multiple realizations. In MoLER, each expanded query \(q_i\) is paired with its own pseudo-passage,
\[
p_i\sim \pi_\theta(\cdot\mid q,q_i,\text{CQE prompt with }n=1),
\]
and retrieval is performed with a fixed embedding model, OpenAI `text-embedding-ada-002`, using cosine similarity between the embedding of \(q\) or \(p_i\) and the embedding of each document [2509.06650]. Here the passage objects are not corpus fragments but generated pseudo-documents that act as retrieval probes.

Conversational-memory retrieval studies a different multi-passage regime in which a session is the retrieval unit and individual turns are the passages. With a frozen bi-encoder \(e(\cdot)\), turn isolation retrieval scores each session by aggregating per-turn query–turn similarities. The main operators examined are
\[
s_{\text{dense}}(q,S)=\max_{t\in S}\cos(e(q),e(t))
\]
and
\[
s_{\text{dense}}(q,S)=\frac{1}{k}\sum_{t\in \mathrm{top}_k}\cos(e(q),e(t)),
\]
with max-sim and top-\(k\) both outperforming early interaction based on mean-pooled session embeddings [2606.04194]. The same work then performs a second late fusion step at score level, combining BM25 and dense late-interaction scores via query-wise \(z\)-normalization:
\[
s_{\mathrm{fuse}}=\alpha\, z(s_{\mathrm{BM25}})+(1-\alpha)\, z(s_{\mathrm{dense}}).
\]

A central technical point is that late fusion is not tied to one aggregation operator. RRF combines ranked lists in MoLER [2509.06650]; max-sim and top-\(k\) combine per-passage dense scores in conversational memory retrieval [2606.04194]. By contrast, fixed-parameter smooth-max was shown to be brittle: with \(\beta=10\), log-sum-exp collapsed for half of the tested encoders on LoCoMo [2606.04194]. The evidence therefore favors scale-free passage aggregators such as max or top-\(k\), or rank-based fusion such as RRF, over uncalibrated smooth pooling.

## 4. Variants, neighboring formulations, and architectural relations

The phrase MMLF is used most explicitly in MoLER, but several adjacent formulations occupy nearby points in the same design space.

| Formulation | Multi-query component | Fusion locus |
|---|---|---|
| CMQR | Top-\(n\) query rewrites from beam search | Term weights or query embeddings |
| Conversational-memory late interaction | One query per question | Turn-to-session aggregation, then lexical–dense score fusion |
| MoLER MMLF | MQR sub-queries plus one pseudo-passage per sub-query | Rank-level RRF over \(L_0,\dots,L_n\) |

CMQR is conceptually similar to MMLF but not identical. In its sparse form, all rewrites are merged into a single weighted bag-of-words query, with raw term weights
\[
w'_{t,q_i}=\sum_{j=1}^{n}RS(\hat q_i^j)\,c(t,\hat q_i^j),
\]
followed by normalization across terms. In its dense form, rewrite embeddings are merged into a weighted centroid,
\[
h_{q_i}=\sum_{j=1}^{n} encode_q(\hat q_i^j)\cdot RS(\hat q_i^j),
\]
and retrieval proceeds with a single query vector [2406.18960]. The paper explicitly states that there is no rank-based fusion stage; fusion occurs earlier, at the term or embedding level. A common misconception is therefore that “late fusion” in all MMLF-adjacent work means merging ranked lists. The conversational rewriting paper shows that the same multi-query signal can be fused before retrieval rather than after it.

MoLER introduces another distinction through Multi-query Single-passage Late Fusion (MSLF), its training-time surrogate for MMLF. In MSLF, the system still generates multiple sub-queries \(q_1,\dots,q_n\), but CQE is called only once with all queries to produce a single pseudo-passage \(p\), and RRF is then applied to two rank lists, from \(q\) and \(p\). This reduces the number of model interactions from \(n+1\) to \(2\) during policy rollouts. At inference, the same policy \(\pi_\theta\) switches to full MMLF, generating one pseudo-passage per sub-query and fusing all resulting lists [2509.06650]. This training–inference asymmetry is central to MoLER’s efficiency claims.

## 5. Empirical behavior

The empirical literature around MMLF and closely related late-fusion systems shows three recurring patterns: multi-query evidence improves retrieval, multi-passage late interaction is materially better than early pooling, and lexical–dense complementarity is substantial but domain-dependent.

In conversational passage retrieval on QReCC, CMQR improved sparse BM25 overall MRR from 31.03 to 37.34 for T5QR\(_{Manual}\), from 49.18 to 50.24 for ConvGQR, and from 46.72 to 50.73 for T5QR\(_{LLM}\); in dense GTR retrieval, the corresponding MRR improvements were from 36.08 to 40.53, from 42.18 to 45.82, and from 42.46 to 45.98. The reported gains versus the single-query counterparts were statistically significant at \(p<0.05\) [2406.18960]. These are not full MMLF results, but they show that retaining multiple rewrite views reliably improves first-pass retrieval.

In conversational-memory retrieval on LoCoMo, the late-minus-early gap was large for all six tested encoders. For e5-large-v2, dense early interaction achieved Hit@1 \(0.427\), dense late max-sim achieved \(0.664\), BM25 achieved \(0.640\), and BM25 plus late dense fusion achieved Hit@1 \(0.752\) and NDCG@5 \(0.829\). Across six encoders, score-level fusion of BM25 with late interaction improved LoCoMo Hit@1 by \(+8.8\) to \(+17.2\) points over late interaction alone, all with \(p<10^{-4}\) [2606.04194]. The same paper also found that reranking the fused top-10 with `ms-marco-MiniLM-L-6-v2` degraded Hit@1 from \(0.701\) to \(0.633\), a drop of \(6.88\) points, indicating that a generic web-search cross-encoder can be harmful in this domain.

The gains are not uniform across datasets. On LongMemEval-S, BM25 already reached R@5 \(0.948\) and NDCG@5 \(0.916\); dense late interaction gave R@1 \(0.568\), and BM25 plus late fusion gave R@1 \(0.594\), only \(+0.67\) over BM25, with a confidence interval including zero and \(p=0.43\) [2606.04194]. This suggests that when lexical overlap saturates the task, sophisticated dense multi-passage fusion adds comparatively little.

MoLER reports that MMLF consistently outperforms its cheaper MSLF training-time analogue at inference. For Qwen3-1.7B with MoL and Dr.GRPO on SCIFACT, MSLF obtained Recall@10 \(75.16\) and nDCG@10 \(57.45\), whereas MMLF reached Recall@10 \(77.47\) and nDCG@10 \(60.90\). In the main results table, Qwen3-1.7B+MoL+GRPO achieved NFCORPUS Recall@1k \(61.42\) and SCIFACT Recall@10 \(79.69\), compared with \(60.87\) and \(79.26\) for Qwen3-32B+MMLF [2509.06650]. The paper further reports nearly logarithmic scaling of recall with the number of query expansions in MMLF, whereas MSLF scales poorly and plateaus quickly.

## 6. Limitations, misconceptions, and open problems

One misconception is that MMLF necessarily requires independent retrieval for every query variant followed by rank fusion. The CMQR results show a different possibility: multi-query evidence can be fused earlier, either as sparse term weights or as a dense centroid embedding, while still preserving the underlying rationale of combining multiple query perspectives [2406.18960]. Another misconception is that adding a reranker is automatically beneficial. The conversational-memory evidence shows that at least one off-the-shelf cross-encoder reranker can degrade a strong fused first stage by \(6.88\) points of Hit@1 [2606.04194].

The current literature also imposes clear scope limits. CMQR is confined to first-pass retrieval and explicitly identifies multi-query use in re-ranking as future work [2406.18960]. The conversational-memory study is a retrieval-stage account rather than a complete memory architecture, and it does not test multi-query generation per question, even though its equations are compatible with that extension [2606.04194]. MoLER depends on domain corpora for continual pre-training, relevant-document labels for RL reward construction, and a multi-step pipeline with multiple LLM calls, multiple retrievals, and RRF fusion; the paper also notes diminishing returns as \(n\) grows and acknowledges the risk of off-topic expansions or hallucinated pseudo-passages [2509.06650].

The open research directions are correspondingly structured. The cited works propose or motivate adaptive selection of the number of rewrites, multi-query use in re-ranking components, query-type-dependent lexical–dense weights \(\alpha(q)\), and better-calibrated smooth pooling operators [2406.18960; 2606.04194]. MoLER points toward training regimes in which an efficient surrogate such as MSLF is used during RL, while full MMLF is reserved for inference, and toward broader integration of domain-aware continual pre-training, GRPO-style optimization, and scalable late-fusion retrieval [2509.06650]. Taken together, these results position MMLF less as a single fixed algorithm than as a family of retrieval architectures organized around three principles: multiplicity of query views, preservation of passage-level evidence, and deferred combination of heterogeneous retrieval signals.

Source: https://www.emergentmind.com/topics/multi-query-multi-passage-late-fusion-mmlf