X-Router: Decoupling Knowledge and Reasoning for Cost-Effective LLM Inference

Large Language Models (LLMs) are often augmented with Retrieval-Augmented Generation (RAG) and Chain-of-Thought (CoT) prompting, yet static "always-on" use is computationally wasteful. Existing adaptive methods typically optimize a single axis, overlooking that evidence need and reasoning depth are only partially correlated. We present X-ROUTER, a dual-axis routing framework that separates retrieval necessity from reasoning necessity under a user-defined cost-quality trade-off. Offline, X-ROUTER profiles four pipelines (DIRECT, RAG, COT, RAG+COT) and derives supervision by selecting the utilitymaximizing strategy that trades answer quality against token usage and latency. Online, a compact dual-head router, conditioned on cost weights, uses lightweight probesretrieval-score dispersion (NQC) and singlepass draft negative log-likelihood (NLL)-to decide whether to invoke RAG and/or CoT without sampling or model internals. Across six QA benchmarks, X-ROUTER reduces token usage by up to 86% and latency by up to 84% while improving answer quality over strong baselines.