# Beyond Perplexity: Let the Reader Select Retrieval Summaries via Spectrum Projection Score

arXiv: https://arxiv.org/abs/2508.05909 · HTML: https://mlsanity.com/paper/2508.05909/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RAG pipeline design and evaluation, one of 15 directions in Retrieval-augmented generation.
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Placed in

- Retrieval-augmented generation / [RAG pipeline design and evaluation](https://mlsanity.com/rag/rag-pipeline-design-and-evaluation/)

## Builds on (most cited first, 21 of 21)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [xRAG: Extreme Context Compression for Retrieval-augmented Generation with One Token](https://mlsanity.com/paper/2405.13792/) (2024)
- [RLPR: Extrapolating RLVR to General Domains without Verifiers](https://mlsanity.com/paper/2506.18254/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [SuRe: Summarizing Retrievals using Answer Candidates for Open-domain QA of LLMs](https://mlsanity.com/paper/2404.13081/) (2024)
- [SePer: Measure Retrieval Utility Through The Lens Of Semantic Perplexity Reduction](https://mlsanity.com/paper/2503.01478/) (2025)
- [Refiner: Restructure Retrieval Content Efficiently to Advance Question-Answering Capabilities](https://mlsanity.com/paper/2406.11357/) (2024)
- [Soft Reasoning: Navigating Solution Spaces in Large Language Models through Controlled Embedding Exploration](https://mlsanity.com/paper/2505.24688/) (2025)
- [EEE-QA: Exploring Effective and Efficient Question-Answer Representations](https://mlsanity.com/paper/2403.02176/) (2024)

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

- [LODESTAR: Robust Entropy-Based Answer Selection in Retrieval-Augmented Generation for Question Answering -- Directing Frozen-LLM Entropy with a Reinforcement-Learned Prompt Polarizer under Misleading Passages](https://mlsanity.com/paper/2608.11922/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have shown improved generation performance through retrieval-augmented generation (RAG) following the retriever-reader paradigm, which supplements model inputs with externally retrieved knowledge. However, prior work often evaluates RAG holistically, assessing the retriever and reader jointly, making it difficult to isolate the true contribution of retrieval, particularly given the prompt sensitivity of LLMs used as readers. We move beyond perplexity and introduce Spectrum Projection Score (SPS), a lightweight and supervision-free metric that allows the reader to gauge the semantic alignment of a retrieved summary with its hidden representation by comparing the area formed by generated tokens from the summary, and the principal directions of subspace in the reader and to measure the relevance. Building on SPS we present xCompress, an inference-time controller framework that dynamically samples, ranks, and compresses retrieval summary candidates. Extensive experiments on five QA benchmarks with four open-sourced LLMs show that SPS not only enhances performance across a range of tasks but also provides a principled perspective on the interaction between retrieval and generation.