# WARP: Wasserstein-Aligned RAG for Population Opinions

arXiv: https://arxiv.org/abs/2608.22859 · HTML: https://mlsanity.com/paper/2608.22859/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RAG robustness and adaptive retrieval, one of 15 directions in Retrieval-augmented generation.
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Placed in

- Retrieval-augmented generation / [RAG robustness and adaptive retrieval](https://mlsanity.com/rag/rag-robustness-and-adaptive-retrieval/)

## Builds on (most cited first, 23 of 23)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Judging the Judges: A Systematic Study of Position Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2406.07791/) (2024)
- [Judging the Judges: Evaluating Alignment and Vulnerabilities in LLMs-as-Judges](https://mlsanity.com/paper/2406.12624/) (2024)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [FA*IR: A Fair Top-k Ranking Algorithm](https://mlsanity.com/paper/1706.06368/) (2017)
- [Summarizing Opinions: Aspect Extraction Meets Sentiment Prediction and They Are Both Weakly Supervised](https://mlsanity.com/paper/1808.08858/) (2018)
- [The Amazon Nova Family of Models: Technical Report and Model Card](https://mlsanity.com/paper/2506.12103/) (2025)
- [Result Diversification in Search and Recommendation: A Survey](https://mlsanity.com/paper/2212.14464/) (2022)
- [Wasserstein Measure Coresets](https://mlsanity.com/paper/1805.07412/) (2018)
- [Large-Scale and Multi-Perspective Opinion Summarization with Diverse Review Subsets](https://mlsanity.com/paper/2310.13340/) (2023)
- [OTExtSum: Extractive Text Summarisation with Optimal Transport](https://mlsanity.com/paper/2204.10086/) (2022)
- [AdaGReS:Adaptive Greedy Context Selection via Redundancy-Aware Scoring for Token-Budgeted RAG](https://mlsanity.com/paper/2512.25052/) (2025)
- [OpinioRAG: Towards Generating User-Centric Opinion Highlights from Large-scale Online Reviews](https://mlsanity.com/paper/2509.00285/) (2025)
- [Multi-Group Proportional Representation in Retrieval](https://mlsanity.com/paper/2407.08571/) (2024)
- [MUSS: Multilevel Subset Selection for Relevance and Diversity](https://mlsanity.com/paper/2503.11126/) (2025)
- [Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming](https://mlsanity.com/paper/2604.02554/) (2026)
- [Retrieval-Augmented Generation Must Move Beyond Factual Grounding to Represent Diverse Opinions](https://mlsanity.com/paper/2604.12138/) (2026)

## Abstract (arXiv)

RAG systems are increasingly used to summarize what large collections of documents say. A user asks "What do people think about X?" and receives an answer that reads as consensus. But standard top-k retrieval ranks documents by query similarity, not by how faithfully they represent the population, so minority views quietly disappear. Existing fixes fall short. Diversity re-rankers like MMR and DPP spread retrieved documents apart, but with no target distribution to aim for. Calibration methods based on KL or JS divergence do target one, yet treat opinion bins as unordered: confusing strong positive with strong negative costs no more than an adjacent-bin miss. We introduce WARP, a family of post-retrieval algorithms that calibrate retrieved evidence to the population's opinion distribution. WARP first recovers underrepresented opinions that cosine ranking may bury, then uses Wasserstein-1 distance to select documents whose sentiment-intensity distribution matches the population target, capturing the ordinal structure ignored by KL and JS divergence. We develop three variants for dense, sparse, and variable candidate pools, trading off calibration quality and speed. Across three review domains spanning 35K documents, 156 queries, and 26 entities, WARP's domain-matched variants reduce distributional error by at least 43% with sub-second latency. These gains carry through to generation: a five-judge LLM panel prefers WARP-generated answers in 86% of decided comparisons at k <= 5.