Large Language Models (LLMs) promise impressive capabilities, yet their multi-billion parameter scale makes on-device or low-resource deployment prohibitive. Mixed precision quantization offers a compelling solution, but existing methods struggle when the average precision drops below four bits, as they rely on isolated, layer-specific metrics that overlook critical inter-layer interactions affecting overall performance. To address these limitations, we first frame the mixed-precision quantization problem as a cooperative game among layers and introduce Shapley-based Progressive Quantization Estimation (SPQE) to efficiently obtain accurate Shapley estimates of layer sensitivities and inter-layer interactions. Leveraging the SPQE estimates, we propose Cooperative Game Inspired Mixed-Precision Quantization (CoopQ) which translates these Shapley estimates into a binary quadratic optimization formulation, assigning either 2 or 4-bit precision to layers under strict memory constraints. Comprehensive experiments conducted on Llama-3, Gemma-2, and Qwen models across three independent PTQ backends (Quanto, HQQ, GPTQ) demonstrate CoopQ’s scalability and consistently superior performance compared to methods relying solely on isolated metrics. Across average precisions spanning 4 bit down to 2 bit, CoopQ cuts Perplexity by 20 – 80 % relative to the best baseline, with the margin growing as the bit-width tightens.

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.