Large language models (LLMs) are now a standard source of query expansion terms but they hallucinate. They inject non existent entities and off-topic terms that add ranking noise and can hurt strong retrievers. Existing remedies such as corpus grounding, mutual verification and preference alignment treat hallucinated terms as an undifferentiated nuisance to be filtered by agreement heuristics, without a mechanistic account of why a given term appears or a principled criterion for how many terms to keep. We propose Subsequence-Association Filtered, breadth-aware query expansion (SAFE-QE), a training-free, retriever agnostic method that draws on the subsequence-association account of hallucination. We score each candidate expansion term by its corpus conditioned cross-context reproducibility, terms that reappear under randomised query contexts yet lack support in the pseudo-relevant set are flagged as products of dominant hallucinatory associations and down-weighted. Drawing on the characterisation of language generation as a trade-off between consistency (no hallucination) and breadth (coverage), we cast term selection as constrained coverage maximisation over the pseudo-relevant set, keeping a set that is approximately broad but consistent and stable across resampling. We also introduce the Hallucinated Expansion Term Rate, a query side faithfulness metric that counts injected expansion terms no relevant document supports. We evaluate our approach on benchmarked TREC and BEIR collections. Our SAFE-QE is statistically indistinguishable from generative and corpus-steered expansion on nDCG@10 while injecting fewer unsupported terms 4.3 per query against 27.8 for Query2doc and 57.5 for HyDE and on a strong learned sparse retriever, where every expansion method regresses. Faithfulness is therefore available at no measurable cost in ranking quality.
Figures & tables
Figure 1: A schematic pipeline of a dominant hallucinated subsequence association makes the LLM emit context-free, ungrounded expansion terms that inject false positives into the ranking, and these terms hurt stronger retrievers.
nDCG@10
HETR
Baseline
SAFE-QE
base
Δ
p
SAFE-QE
base
Δ
p
No expansion
0.404
0.410
-0.006
0.152
–
–
–
–
Query2doc
0.403
0.411
-0.008 ∗
0.021
0.440
0.582
-0.142 ∗∗∗
< 0.001
HyDE
0.403
0.399
+0.004
1.000
0.440
0.593
-0.153 ∗∗∗
< 0.001
CSQE
0.404
0.407
-0.004
0.683
0.369
0.416
-0.047 ∗∗∗
< 0.001
MILL
0.404
0.400
+0.004
0.562
0.369
0.435
-0.066 ∗∗∗
< 0.001
Table 1: Paired per-query tests of SAFE-QE with each baseline, pooled over the four BEIR collections with the gemma-2-9b generator. Δ is SAFE-QE baseline. p is a paired t -test with Bonferroni correction across baselines, ∗p<0.05 , ∗∗p<0.01 , ∗∗∗p<0.001 . On effectiveness SAFE-QE is statistically indistinguishable from every generative baseline, on faithfulness it is better than rest of the methods. The HETR of 0.440 here is the BEIR-pooled per-query value; the all-collection macro-average appears in Table 5 .
Collection
Retriever
None
Query2doc
HyDE
CSQE
MILL
SAFE-QE
DL’19
BM25
0.5058
0.6324
0.5255
0.5611
0.5174
0.5876
SPLADE
0.7308
0.5848
0.6160
n/a
n/a
0.6950
Contriever
0.5812
†
†
0.5844
†
0.6381
DL’20
BM25
0.4796
0.6044
0.5597
0.5057
0.4622
0.5336
SPLADE
0.7197
0.6409
0.5936
n/a
n/a
0.6127
Contriever
0.5251
0.6731
†
0.5469
†
0.5775
Table 2: Evaluation across six collections and three retrievers, where generator is gemma-2-9b. The best nDCG@10 scores are in bold. n/a represents the baseline’s injected no terms at all and is slightly identical to no expansion, CSQE and MILL under SPLADE. These are excluded from every aggregate. † marks Contriever cells not included in this comparison; they are omitted from all aggregates. Δ is the mean gain over no expansion a method covers.
Faithfulness
Query-time cost
Method
HETR
∣E(q)∣
load
cut
s/query
tok/query
gen. calls
Query2doc
0.656
43.0
27.83
85%
4.06
78
1.00
HyDE
0.663
87.2
57.47
93%
1.10
231
0.19
CSQE
0.531
14.8
7.90
45%
5.23
758
1.00
MILL
0.546
13.8
7.52
43%
2.91
757
0.50
SAFE-QE
0.465
10.3
4.79
–
10.97
1516
2.00
Table 3: Faithfulness and query time cost on the collection, retriever, where generator is gemma-2-9b, macro-averaged over all six collections and three retrievers. HETR here is the micro-rate over injected terms, so it differs from the BEIR-pooled per-query value in Table 1 . ∣E(q)∣ is the number of terms a method injects into the query. load is the absolute number of those terms that no judged relevant document supports, HETR ×∣E(q)∣ , and cut is SAFE-QE’s reduction in that load. Lower is better in the first three columns. SAFE-QE buys its faithfulness with generation cost, two sampled generations plus P perturbed prompts.
Figure 2: Results for decomposing what a retriever actually receives, per retriever, over the collections. On the left, how many terms a method injects. In middle, what fraction of them no judged relevant document supports (HETR). On right, their product, the hallucinated-term load. The advantage of SAFE-QE is largest on the dense retriever, where free generation is least grounded.
Collection
Retriever
Query2doc
HyDE
CSQE
MILL
SAFE-QE
DL’19
BM25
0.194
0.206
0.042
0.065
0.041
SPLADE
0.194
0.206
n/a
n/a
0.310
Contriever
†
†
0.274
†
0.125
DL’20
BM25
0.262
0.288
0.077
0.106
0.083
SPLADE
0.262
0.288
n/a
n/a
0.370
Contriever
0.747
†
0.347
†
0.197
Table 4: HETR across all six collections and three retrievers, and generator is gemma-2-9b. HETR is retriever-independent for Query2doc and HyDE, whose injected set does not depend on the first stage, and retriever-dependent for the grounded methods, whose selection is computed against the retriever’s own pseudo-relevant set. n/a and † are as in Table 2 .
Figure 3: The faithfulness effectiveness plane, per retriever, macro averaged over the collections. Up and to the left is better. SAFE-QE sits on the frontier under BM25 and Contriever. Under SPLADE its rate is higher than the generative baselines’ even though its load is a third of theirs (Fig. 2 ), because grounding is computed against SPLADE’s own pseudo-relevant set and that set admits more candidates.
nDCG@10
HETR
Method
Qwen
Gemma
Qwen
Gemma
Qwen
Gemma
Qwen
Gemma
0.5B
2B
7B
9B
0.5B
2B
7B
9B
HyDE
0.3951
0.4641
0.4697
0.4788
0.640
0.597
0.590
0.570
MILL
0.4414
0.4535
0.4584
0.4620
0.480
0.447
0.420
0.443
SAFE-QE
0.4648
0.4784
0.4750
0.4845
0.398
0.386
0.344
0.375
Table 5: nDCG@10 and HETR as the expansion LLM grows from 0.5B to 9B parameters, macro-averaged over all collections and retrievers. SAFE-QE’s faithfulness advantage is present at every scale and without dependence on a large generator; the 9B HETR ( 0.375 ) therefore differs from the BEIR-pooled 0.440 in Table 1 .