# QUBO-Optimized Evidence Selection for Retrieval-Augmented Question Answering with Unconventional Solvers

arXiv: https://arxiv.org/abs/2607.12334 · HTML: https://mlsanity.com/paper/2607.12334/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge-graph and structured-knowledge RAG, one of 15 directions in Retrieval-augmented generation.
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Placed in

- Retrieval-augmented generation / [Knowledge-graph and structured-knowledge RAG](https://mlsanity.com/rag/knowledge-graph-and-structured-knowledge-rag/)

## Builds on (most cited first, 8 of 8)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Seven Failure Points When Engineering a Retrieval Augmented Generation System](https://mlsanity.com/paper/2401.05856/) (2024)
- [HAVEN: High-Bandwidth Flash Augmented Vector Engine for Large-Scale Approximate Nearest-Neighbor Search Acceleration](https://mlsanity.com/paper/2603.01175/) (2026)
- [Digital Annealer for quadratic unconstrained binary optimization: a comparative performance analysis](https://mlsanity.com/paper/2012.12264/) (2020)

## Built on by (most cited first, 1 of 1)

- [Recall What Is Missing: Composing Evidence from Long-Term Agent Memory](https://mlsanity.com/paper/2610.15642/) (2026)

## Abstract (arXiv)

Retrieval-augmented question answering depends on selecting evidence passages that jointly support answer generation. However, many RAG pipelines rely on top-(k) ranking, where passages are selected mainly by individual relevance scores, even though multi-hop questions often require complementary evidence satisfying multiple information requirements. Recent LLM-based selectors address this by treating retrieval as set selection, but using an LLM for this intermediate stage can be costly and difficult to scale. In this work, we formulate evidence selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Given a question, candidate passages, and decomposed information requirements, our method constructs an energy function that balances relevance, requirement coverage, support strength, redundancy, complementarity, and compactness. Low-energy solutions correspond to compact evidence subsets that cover the needed requirements while avoiding unnecessary or repetitive context. The selected passages are then passed to a downstream language model for answer generation, separating combinatorial evidence selection from semantic answer generation. We evaluate the proposed QUBO selector on HotpotQA and compare it with LLM-based set selectors and non-LLM baselines including BM25, relevance top-(k), maximal marginal relevance, hybrid lexical--semantic ranking, greedy coverage, and random selection. The QUBO selector achieves competitive exact-match and token-F1 performance relative to LLM-based selectors while providing a solver-compatible formulation for structured evidence selection. These results suggest that multi-hop evidence selection can be cast as discrete optimization, opening a path toward RAG pipelines where LLMs are reserved for semantic processing and answer generation, while context selection is handled by Ising/QUBO-compatible solvers.