WARP: Wasserstein-Aligned RAG for Population Opinions
2026-08-24 • Information Retrieval
Information RetrievalComputation and Language
AI summaryⓘ
The authors point out that current systems summarizing opinions from many documents tend to miss minority views because they only pick top documents most similar to the question. They introduce WARP, a new method that better matches the overall distribution of opinions by adjusting which documents to include based on both the strength and order of sentiments. WARP uses a special math tool called Wasserstein-1 distance to ensure the summary truly reflects the mix of opinions in the population. Tests across various domains show WARP reduces errors significantly, and summaries created with it are preferred by expert judges.
RAG systemstop-k retrievalopinion distributionWasserstein-1 distanceKL divergenceJS divergencediversity re-rankingcosine similaritysentiment analysisdocument retrieval
Authors
Aman Singh Thakur, Aditya Agrawal, Alwarappan Nakkiran, Alex Karlsson
Abstract
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.