Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming

Retrieval diversification is widely available in retrieval-augmented generation (RAG) frameworks, yet prior studies disagree on whether it improves retrieval and answer quality. We show that its effectiveness varies primarily with candidate-pool redundancy, in a pattern consistent with the number of distinct evidence pieces a query requires. Using controlled near-duplicate injection and production-style overlapping chunking, we find that diversification harms relevance, evidence coverage and answer quality on clean pools, but becomes beneficial on multi-evidence tasks when redundancy causes nearest-neighbor retrieval to select repeated passages. We therefore introduce a query-adaptive rule that diversifies only when the effective number of distinct documents in the nearest-neighbor top-$k$ selection falls below the query's evidence requirement. Computed from existing embeddings, the rule captures most of the achievable gain, transfers across datasets and encoders and automatically reduces to nearest-neighbor retrieval for single-evidence queries. We also introduce RNG-Score, a geometric reranker with an exact nearest-neighbor fallback whose margin indicates duplicate structure. Overall, we conclude that diversification should be used selectively, based on observable redundancy and evidence requirements.

Retrieval-augmented generation (RAG) systems typically rely on a single retriever and a single set of hyperparameters, despite facing highly heterogeneous queries that range from simple factoid questions to complex multi-hop reasoning. We propose a method that automatically selects a small, diverse subset of retrievers (a portfolio) from a large pool of candidates, to cover different regions of the target query distribution. We formalize this setting via an expected best-of-$k$ objective over the query distribution and show that it admits an efficient portfolio construction algorithm with near-optimal guarantees. Across multiple QA benchmarks, our learned portfolios and router pipeline consistently outperform single-retriever and naive multi-retriever baselines on both retrieval metrics and answer quality. In addition, compared to inference-time hyperparameter tuning approaches, fixed portfolios enable parallel retrieval and LLM calls, achieving comparable (and sometimes better) accuracy with substantially lower latency and token cost.

Retrieval-augmented generation (RAG) typically retrieves a fixed number of passages for every query. This is wasteful when the reader already knows the answer, and it can be harmful when irrelevant or partially relevant passages distract the reader. We formulate adaptive RAG as calibrated retrieval-budget allocation: given a query, decide whether to answer closed-book, retrieve a compact context (k=1), retrieve a full context (k=5), or abstain. The contribution is a probability interface rather than a new raw uncertainty signal. We calibrate sequence log-probability and prefix-logit uncertainty signals into probabilities of correctness, then use these probabilities for graded context selection, selective abstention, and explicit latency/token trade-offs. Across core QA experiments on TriviaQA, Natural Questions, and MS MARCO, with auxiliary PopQA motivation and Qwen/Llama family checks, diagnostic out-of-fold calibration improves probability quality dramatically: for sequence log-probability, ECE drops from 0.275 to 0.062 on TriviaQA, 0.643 to 0.009 on NQ, and 0.711 to 0.031 on MS MARCO. Graded retrieval improves full-context and passage-budget frontiers for both our signal and TARG-style prefix entropy/margin, while retrieval-call AUC remains essentially tied with binary gating because k=1 is still a retrieval call. Held-out train/validation/test threshold experiments report deployable operating points. At matched-accuracy frontier operating points, a measured cost model reveals that gating is not universally faster: it increases latency by about 27% on Qwen3-8B but saves about 8% on Qwen3-32B. These results support a nuanced view of adaptive RAG: calibrated confidence is best understood as a reusable interface for allocating retrieval budget under task and system constraints.