In-Context Optimization for Retrieval-Augmented Generation: A Gradient-Descent Perspective

• URL: http://arxiv.org/abs/2605.26356v1
• Date: Mon, 25 May 2026 22:04:54 GMT
• Title: In-Context Optimization for Retrieval-Augmented Generation: A Gradient-Descent Perspective
• Abstract summary: We study RAG as an in-context optimization process.<n>We show that one linear self-attention layer can implement one gradient-descent step on a unified linearized RAG objective.<n>We turn this view into a lightweight method for frozen RAG LLMs.
• Score: 39.37659538213411
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In-context learning has recently been linked to implicit gradient descent in linear self-attention models, suggesting that context can induce a forward-pass update. Retrieval-augmented generation (RAG) also relies on context, but retrieved documents are usually treated as static evidence rather than signals for adaptation. We study RAG as an in-context optimization process. First, we show that one linear self-attention layer can implement one gradient-descent step on a unified linearized RAG objective covering both projection-based and dot-product retrieval interfaces. This gives an exact regime where retrieval-augmented prediction and in-context optimization coincide. We use this result not as a literal model of LLM computation, but as a guide for adapting the interaction between queries and retrieved evidence. We then test the boundary of this correspondence: it remains stable under controlled linear extensions, but becomes feature-distribution dependent under nonlinear architectures. Finally, we turn this view into a lightweight method for frozen RAG LLMs. The method keeps the retriever and backbone fixed, and predicts a context-conditioned update to a generator-side evidence-use interface. Across seven QA benchmarks, two retrievers, and two frozen LLM backbones, this forward-only update improves a shared-interface baseline, transfers to held-out tasks, and approaches test-time gradient adaptation at much lower per-query cost.

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