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 , a dual-axis routing framework that separates retrieval necessity from reasoning necessity under a user-defined cost–quality trade-off. Offline, profiles four pipelines (Direct, RAG, CoT, RAG+CoT) and derives supervision by selecting the utility-maximizing strategy that trades answer quality against token usage and latency. Online, a compact dual-head router, conditioned on cost weights, uses lightweight probes—retrieval-score dispersion (NQC) and single-pass draft negative log-likelihood (NLL)—to decide whether to invoke RAG and/or CoT without sampling or model internals. Across six QA benchmarks, reduces token usage by up to 86% and latency by up to 84% while improving answer quality over strong baselines.

Graph-based Retrieval-Augmented Generation (GraphRAG) can fail in interdisciplinary medicine where evidence comes from incommensurable knowledge systems, e.g., Traditional Chinese Medicine (TCM) and Western Medicine (WM). Similarity-driven retrieval in a shared latent space may over-unify heterogeneous concepts, causing semantic collapse (spurious alignments, provenance-blind mixing, and broken multi-hop chains). We propose Xonto-RAG, a cross-ontology GraphRAG framework that avoids ontological unification by constructing a dual-ontology graph with typed bridges induced via LLM-assisted verify-and-vote. A query-aware Relational Graph Attention Network (RGAT) then assembles compact, provenance-tracked multi-hop evidence subgraphs for grounded generation. Across TCM–WM benchmarks, Xonto-RAG outperforms strong RAG/GraphRAG baselines, seeing up to +22.2% accuracy on MLEC-QA TCWM (vs. OG-RAG), 77.0% accuracy with a 7B backbone, and 85.1% faithfulness on MLEC-TCM, while reducing semantic-collapse failures and yielding interpretable reasoning chains.