BoundaryMORPH: Budgeted Reranking via Active Set Selection for Diffuse Retrieval
Eylon Caplan, Shamik Roy, Shib Sankar Dasgupta, Yingfan Wang, Rashmi Gangadharaiah
cs.IR
2026-09-23
A MIPS-prior Gaussian process spends scarce CE calls on the RAG top-k cutoff, gaining up to 5.4 nCG@100 over the strongest baseline.
Open-ended RAG queries are often diffuse: dozens or hundreds of relevant documents sit scattered through a dual-encoder candidate list. The generator's context capacity \(k\) is fixed in advance, say 100 slots, while the cross-encoder (CE) budget \(B\) is capped by latency and is often smaller than \(k\). One figure in the paper has 144 gold-relevant documents, \(k=100\), and \(B=25\).
The default policy scores the dual-encoder top-\(B\) with the CE and fills the remaining slots from the original ranking. That wastes calls on documents already safely inside the top-\(k\), and it never looks at documents further down that could still enter the window. When \(B<k\), \(k-B\) slots get no CE signal at all.
The job is therefore allocation: which \(B\) documents to score so that the \(k\) documents handed to the generator are as relevant as possible.
BoundaryMORPH treats this as budgeted top-\(k\) set selection, using a Gaussian process as a surrogate for the CE.
The prior is the dual-encoder MIPS percentile rank inside the pool, near 1 at the head and near 0 in the tail. The GP models the residual of CE scores against that prior. Unscored regions fall back to the dual encoder; each CE call only bends the surface. A von Mises–Fisher kernel on unit embeddings lets an observation update nearby documents. The query vector is entered as a free observation at score 1, shrinking variance near the query before any budget is spent.
Acquisition does not hunt the global maximum. The current posterior mean splits the pool into incumbents (the estimated top-\(k\)) and challengers. The pair with the smallest standardized boundary gap is the most likely to sit on the wrong side of the cutoff; the CE call goes to whichever of the two has larger variance. Documents already safely in or out are skipped. Standard GP-UCB is the \(k=1\) special case.
The candidate pool is the Qwen3-Embedding-4B top-10,000. The selector has no extra hyperparameters. The kernel is \(O(N^2)\) once; posterior updates are \(O(B^3 N)\). Wall-clock time is still dominated by CE inference.
Queries are filtered to those with at least 20 relevant documents: NeuCLIR (85 queries, median 51 relevant), Robust04 (187, median 62), TravelDest (99, median 462). The main encoder–CE pair is multilingual-e5-large with zerank-2. The metrics are nCG@\(k\) against human labels and CE-nCG@\(k\) against the CE's own ranking, because the object of interest is the set, not the order inside it.
BoundaryMORPH wins every dataset \(\times B \times k\) cell. BAGEL, another GP method with a zero prior and max-seeking UCB, is a clear second.
| Dataset | Setting | BoundaryMORPH | BAGEL | Single-stage |
| NeuCLIR | B=25, nCG@100 | 55.1 | 51.4 | 46.2 |
| Robust04 | B=25, nCG@100 | 46.4 | 41.0 | 37.1 |
| TravelDest | B=25, nCG@100 | 39.8 | 35.5 | 28.4 |
| NeuCLIR | B=50, nCG@100 | 59.2 | 55.7 | 46.2 |
The abstract's peak of +5.4 nCG@100 over the strongest baseline is Robust04 at \(B=25\), \(k=100\). Averaged, nCG@100 is +3.8 points over the runner-up and CE-nCG@200 is +7.3. The gap holds across other embedder–CE pairs.
Both pieces matter: dropping boundary acquisition costs 1.5–2.6 nCG points; dropping the MIPS prior costs 2.1–3.8. Performance peaks when the \(k\) given to the algorithm matches the \(k\) used at evaluation.
The gain comes from not scoring obvious winners. A large share of final top-\(k\) relevance comes from never-scored documents. Multimodal mass (prominence-weighted relevance outside the tallest peak) predicts the per-query edge over BAGEL at Spearman \(\rho=+0.59\). Max-seekers spend the budget on the primary mode; BoundaryMORPH reaches a second semantic peak.
Deep-research RAG often really has \(B<k\). Using the CE to polish the dual-encoder head is the wrong objective. The right one is set membership. The method needs no training and no hyperparameter sweep, and it plugs into a stock dual-encoder plus CE stack. Twenty-five CE calls can cover a wider set of semantic peaks than single-stage reranking at the same budget.
It is a selection policy, not a new encoder. Documents absent from the pool stay absent.
The GP updates after every CE call, so the loop is sequential; a batched single-stage reranker can hide latency on large GPUs. Exact posterior updates grow as \(B^3\); they stay cheap at \(B\le 200\) and can exceed 30 seconds at \(B=500\). Capacity is a document count \(k\), while real windows are token-limited. Chunking makes that a fair proxy when lengths are similar; variable-length chunks are unsolved. Evaluation keeps only queries with at least 20 relevant documents, so factoid queries are out of scope.
The pool is already an embedding top-10,000, so the comparison is how to spend the budget, not how to retrieve from the full corpus. If the CE is systematically biased, the selected set follows that bias.