# CR^2: Cost-Aware Risk-Controlled Routing for Wireless Device-Edge LLM Inference

arXiv: https://arxiv.org/abs/2605.12001 · HTML: https://mlsanity.com/paper/2605.12001/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 30 of 40)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [Mobile Edge Intelligence for Large Language Models: A Contemporary Survey](https://mlsanity.com/paper/2407.18921/) (2024)
- [SPINN: Synergistic Progressive Inference of Neural Networks over Device and Cloud](https://mlsanity.com/paper/2008.06402/) (2020)
- [Sequoia: Scalable, Robust, and Hardware-aware Speculative Decoding](https://mlsanity.com/paper/2402.12374/) (2024)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [EdgeBERT: Sentence-Level Energy Optimizations for Latency-Aware Multi-Task NLP Inference](https://mlsanity.com/paper/2011.14203/) (2020)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [TensorOpera Router: A Multi-Model Router for Efficient LLM Inference](https://mlsanity.com/paper/2408.12320/) (2024)
- [Edge Intelligence: On-Demand Deep Learning Model Co-Inference with Device-Edge Synergy](https://mlsanity.com/paper/1806.07840/) (2018)
- [Smoothie: Label Free Language Model Routing](https://mlsanity.com/paper/2412.04692/) (2024)
- [CE-CoLLM: Efficient and Adaptive Large Language Models Through Cloud-Edge Collaboration](https://mlsanity.com/paper/2411.02829/) (2024)
- [WDMoE: Wireless Distributed Mixture of Experts for Large Language Models](https://mlsanity.com/paper/2411.06681/) (2024)
- [R2-T2: Re-Routing in Test-Time for Multimodal Mixture-of-Experts](https://mlsanity.com/paper/2502.20395/) (2025)

## Built on by (most cited first, 1 of 1)

- [CopRoute: Dependence-Aware Conformal Routing for Language Models](https://mlsanity.com/paper/2610.13276/) (2026)

## Abstract (arXiv)

As large language models (LLMs) move from centralized clouds to mobile edge environments, efficient serving must balance latency, energy consumption, and accuracy under constrained device-edge resources. Query-level routing between lightweight on-device models and stronger edge models provides a flexible mechanism to navigate this trade-off. However, existing routers are designed for centralized cloud settings and optimize token-level costs, failing to capture the dynamic latency and energy overheads in wireless edge deployments. In this paper, we formulate mobile edge LLM routing as a deployment-constrained, cost-aware decision problem, and propose CR^2, a two-stage device-edge routing framework. CR^2 decouples a lightweight on-device margin gate from an edge-side utility selector for deferred queries. The margin gate operates on frozen query embeddings and a user-specified cost weight to predict whether local execution is utility-optimal relative to the best edge alternative under the target operating point. We further introduce a conformal risk control (CRC) calibration procedure that maps each operating point to an acceptance threshold, enabling explicit control of the marginal false-acceptance risk under the full-information utility reference. Experiments on the routing task show that CR^2 closely matches a full-information reference router using only device-side signals before deferral. Compared with strong query-level baselines, CR^2 consistently improves the deployable accuracy-cost Pareto frontier and reduces normalized deployment cost by up to 16.9% at matched accuracy.