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

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 introduce Spectrum Projection Score (SPS), a lightweight, supervision‑free metric that lets the reader gauge the semantic alignment of a retrieved summary with its hidden representation. SPS projects the passage summary embeddings onto the reader’s principal subspace and uses the residual as an immediate quality signal: the smaller the residual, the more the reader “expects” the passage summary. 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 source 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.