# Federate the Router: Learning Language Model Routers with Sparse and Decentralized Evaluations

arXiv: https://arxiv.org/abs/2601.22318 · HTML: https://mlsanity.com/paper/2601.22318/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 76 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 54)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [MPNet: Masked and Permuted Pre-training for Language Understanding](https://mlsanity.com/paper/2004.09297/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Asynchronous Federated Optimization](https://mlsanity.com/paper/1903.03934/) (2019)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Towards Building the Federated GPT: Federated Instruction Tuning](https://mlsanity.com/paper/2305.05644/) (2023)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [FLoRA: Federated Fine-Tuning Large Language Models with Heterogeneous Low-Rank Adaptations](https://mlsanity.com/paper/2409.05976/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [AutoMix: Automatically Mixing Language Models](https://mlsanity.com/paper/2310.12963/) (2023)
- [A Review on Edge Large Language Models: Design, Execution, and Applications](https://mlsanity.com/paper/2410.11845/) (2024)
- [Fly-Swat or Cannon? Cost-Effective Language Model Choice via Meta-Modeling](https://mlsanity.com/paper/2308.06077/) (2023)
- [Heterogeneity for the Win: One-Shot Federated Clustering](https://mlsanity.com/paper/2103.00697/) (2021)
- [FedNLP: Benchmarking Federated Learning Methods for Natural Language Processing Tasks](https://mlsanity.com/paper/2104.08815/) (2021)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning](https://mlsanity.com/paper/2506.09033/) (2025)

## Built on by (most cited first, 3 of 3)

- [Typed Federated Artifacts for the Agentic Web:Sharing Tool-Routing Knowledge Across Frozen,Heterogeneous LLM Agents](https://mlsanity.com/paper/2609.06815/) (2026)
- [Mind the Delay: Latency-aware Query Routing for Heterogeneous LLM pools](https://mlsanity.com/paper/2607.18253/) (2026)
- [Synapse: Federated Tool Routing via Typed Compendium Artifacts](https://mlsanity.com/paper/2602.00911/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly accessed as remotely hosted services by edge and enterprise clients that cannot run frontier models locally. Since models vary widely in capability and price, routing queries to models that balance quality and inference cost is essential. Existing router approaches assume access to centralized query-model evaluation data. However, these data are often fragmented across clients, such as end users and organizations, and are privacy-sensitive, which makes centralizing data infeasible. Additionally, per-client router training is ineffective since local evaluation data is limited and covers only a restricted query distribution and a biased subset of model evaluations. We introduce the first federated framework for LLM routing, enabling clients to learn a shared routing policy from local offline query-model evaluation data. Our framework supports both parametric multilayer perceptron router and nonparametric K-means router under heterogeneous client query distributions and non-uniform model coverage. Across three benchmarks, federated collaboration improves the accuracy-cost frontier over client-local routers, both via increased effective model coverage and better query generalization. Our theoretical results also validate that federated training reduces routing suboptimality.