Retrieval-augmented generation (RAG) utilizes retrieved texts to enhance large language models (LLMs). However, studies show that RAG is not consistently effective and can even mislead LLMs due to noisy or incorrect retrieved texts. This suggests that RAG possesses a duality including both benefit and detriment. Although many existing methods attempt to address this issue, they lack a theoretical explanation for the duality in RAG. The benefit and detriment within this duality remain a black box that cannot be quantified or compared in an explainable manner. This paper takes the first step in theoretically giving the essential explanation of benefit and detriment in RAG by: (1) decoupling and formalizing them from RAG prediction, (2) approximating the gap between their values by representation similarity and (3) establishing the trade-off mechanism between them, to make them explainable, quantifiable, and comparable. We demonstrate that the distribution difference between retrieved texts and LLMs' knowledge acts as double-edged sword, bringing both benefit and detriment. We also prove that the actual effect of RAG can be predicted at token level. Based on our theory, we propose a practical novel method, X-RAG, which achieves collaborative generation between pure LLM and RAG at token level to preserve benefit and avoid detriment. Experiments in real-world tasks based on LLMs including OPT, LLaMA-2, and Mistral show the effectiveness of our method and support our theoretical results.

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