# BoundaryMORPH: Budgeted Reranking via Active Set Selection for Diffuse Retrieval

arXiv: https://arxiv.org/abs/2609.27213 · HTML: https://mlsanity.com/paper/2609.27213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 43 of its 65 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- Retrieval-augmented generation / [Generation and context integration](https://mlsanity.com/rag/generation-and-context-integration/)

## Builds on (most cited first, 30 of 43)

- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [Active Retrieval Augmented Generation](https://mlsanity.com/paper/2305.06983/) (2023)
- [A Survey on RAG Meeting LLMs: Towards Retrieval-Augmented Large Language Models](https://mlsanity.com/paper/2405.06211/) (2024)
- [Adaptive-RAG: Learning to Adapt Retrieval-Augmented Large Language Models through Question Complexity](https://mlsanity.com/paper/2403.14403/) (2024)
- [Multilingual E5 Text Embeddings: A Technical Report](https://mlsanity.com/paper/2402.05672/) (2024)
- [Demonstrate-Search-Predict: Composing retrieval and language models for knowledge-intensive NLP](https://mlsanity.com/paper/2212.14024/) (2022)
- [The Power of Noise: Redefining Retrieval for RAG Systems](https://mlsanity.com/paper/2401.14887/) (2024)
- [Dense Text Retrieval based on Pretrained Language Models: A Survey](https://mlsanity.com/paper/2211.14876/) (2022)
- [Deep Research Agents: A Systematic Examination And Roadmap](https://mlsanity.com/paper/2506.18096/) (2025)
- [A Survey on Retrieval-Augmented Text Generation for Large Language Models](https://mlsanity.com/paper/2404.10981/) (2024)
- [DeepResearchGym: A Free, Transparent, and Reproducible Evaluation Sandbox for Deep Research](https://mlsanity.com/paper/2505.19253/) (2025)
- [Information Retrieval: Recent Advances and Beyond](https://mlsanity.com/paper/2301.08801/) (2023)
- [Adaptive Re-Ranking with a Corpus Graph](https://mlsanity.com/paper/2208.08942/) (2022)
- [Ranked List Truncation for Large Language Model-based Re-Ranking](https://mlsanity.com/paper/2404.18185/) (2024)
- [PISCO: Pretty Simple Compression for Retrieval-Augmented Generation](https://mlsanity.com/paper/2501.16075/) (2025)
- [The Use of Generative Search Engines for Knowledge Work and Complex Tasks](https://mlsanity.com/paper/2404.04268/) (2024)
- [Guiding Retrieval using LLM-based Listwise Rankers](https://mlsanity.com/paper/2501.09186/) (2025)
- [Do RAG Systems Really Suffer From Positional Bias?](https://mlsanity.com/paper/2505.15561/) (2025)
- [Elaborative Subtopic Query Reformulation for Broad and Indirect Queries in Travel Destination Recommendation](https://mlsanity.com/paper/2410.01598/) (2024)
- [Multimodal Item Scoring for Natural Language Recommendation via Gaussian Process Regression with LLM Relevance Judgments](https://mlsanity.com/paper/2510.22023/) (2025)
- [AcuRank: Uncertainty-Aware Adaptive Computation for Listwise Reranking](https://mlsanity.com/paper/2505.18512/) (2025)
- [NeuCLIRBench: A Modern Evaluation Collection for Monolingual, Cross-Language, and Multilingual Information Retrieval](https://mlsanity.com/paper/2511.14758/) (2025)
- [Rerank Before You Reason: Analyzing Reranking Tradeoffs through Effective Token Cost in Deep Search Agents](https://mlsanity.com/paper/2601.14224/) (2026)

## Abstract (arXiv)

Open-ended queries in modern Retrieval-Augmented Generation (RAG) are increasingly "diffuse," requiring a large set of documents to be assembled into a finite LLM context window. To ensure retrieval quality, systems use fast dual-encoders and more expensive cross-encoders (CEs) to score candidates. However, the CE budget B is strictly bounded by latency and is often smaller than the context window capacity k. This mismatch makes standard reranking structurally flawed: it wastes compute verifying obvious top candidates while ignoring relevant documents further down the initial ranking. To address this, we introduce BoundaryMORPH, a novel algorithm that allocates CE budget specifically for the LLM's context capacity k. Using a Gaussian Process, BoundaryMORPH treats the initial dual-encoder ranking as a structural prior and intelligently spends CE calls on resolving top-k set membership at the boundary, rather than seeking a single most-relevant document. Information from each CE call propagates to unscored documents, maximizing the utility of the budget. We demonstrate that BoundaryMORPH achieves state-of-the-art set retrieval quality across multiple models and datasets with open-ended queries (+5.4 nCG@100 over the strongest baseline).