CeQe: Grounding Lexical Retrieval in Semantic Evidence

Lexical retrieval (BM25) captures exact keyword matches and weights terms by corpus-wide significance, but it is blind to the semantic vocabulary gap: when a relevant document phrases an answer differently from the query, BM25 never retrieves it, and no amount of downstream reranking or fusion can recover a document that was never in the candidate set. We present Cross-Encoder Query Expansion (CE-QE), which reads the per-token relevance attributions of a cross-encoder applied to top semantic search results, selects the terms the cross-encoder treats as decisive, and appends them to the BM25 query. Unlike classical pseudo-relevance feedback, which reuses BM25's own (possibly wrong) top results, CE-QE seeds expansion from the semantic retriever's results, avoiding self-reinforcing query drift. Unlike recent generative query expansion (HyDE, Query2doc), which prompts a large language model to hallucinate text from its parametric knowledge, every CE-QE expansion term is copied verbatim from a retrieved passage, so it cannot introduce vocabulary the corpus does not contain, and its only added cost is attribution extraction on a cross-encoder a hybrid pipeline already runs for reranking. On seven BEIR datasets, CE-QE improves lexical recall substantially where query and answer vocabulary diverge (e.g., NQ Recall@100 from 0.32 to 0.47), and its score-fusion variant (SESF) beats cross-encoder score fusion by 2.5% on Recall@100 and beats SPLADEv2 and ColBERTv2 by 5.3% and 4.6% on nDCG@10, while leaving the underlying BM25 index completely unmodified.

Hierarchical BM25: Lexical Search at Billion-Document Scale

A flat BM25 index over one billion documents occupies about 400 GB. Holding it in memory requires DRAM proportional to corpus size. Serving it from disk takes 4-12 seconds per query. Exact top-k lexical retrieval at this scale is therefore impractical within an interactive latency budget. Hierarchical BM25 gives up exact ranking in exchange for fixed bounds on memory and latency. A resident coarse index selects which of ~1K topical, size-balanced document groups a query visits, using two signals: the total frequency of each query term within a group, and, for informative terms spread too thinly across groups for frequency totals to reflect, whether several of them appear together in one document. Selected groups are then searched exhaustively and scored against ~100 KB of global statistics. Every returned score therefore equals the flat index's score, and the approximation is confined to selection alone. The resident footprint is ~4.4 GB, independent of corpus size. Sixteen-term queries over one billion documents return in ~300 ms (4.7x to 5.6x the throughput of a flat multi-threaded index), and a warmed cache sustains ~32 queries per second versus under 3 for flat indexing. At a 500K-document configuration, visiting 5-10% of clusters recovers 0.83-0.92 of the exhaustive result score. Billion-scale recall and a direct comparison against document-reordered BlockMax-WAND remain open.