# IR3DE: A Linear Router for Large Language Models

arXiv: https://arxiv.org/abs/2606.06098 · HTML: https://mlsanity.com/paper/2606.06098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 4 Jun 2026.

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Okapi: Instruction-tuned Large Language Models in Multiple Languages with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.16039/) (2023)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Pile of Law: Learning Responsible Data Filtering from the Law and a 256GB Open-Source Legal Dataset](https://mlsanity.com/paper/2207.00220/) (2022)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [IRT-Router: Effective and Interpretable Multi-LLM Routing via Item Response Theory](https://mlsanity.com/paper/2506.01048/) (2025)
- [MergeBench: A Benchmark for Merging Domain-Specialized LLMs](https://mlsanity.com/paper/2505.10833/) (2025)
- [Towards Model Agnostic Federated Learning Using Knowledge Distillation](https://mlsanity.com/paper/2110.15210/) (2021)
- [ICL-Router: In-Context Learned Model Representations for LLM Routing](https://mlsanity.com/paper/2510.09719/) (2025)
- [M2D2: A Massively Multi-domain Language Modeling Dataset](https://mlsanity.com/paper/2210.07370/) (2022)
- [Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering](https://mlsanity.com/paper/2210.14664/) (2022)
- [R2-Router: A New Paradigm for LLM Routing with Reasoning](https://mlsanity.com/paper/2602.02823/) (2026)
- [Accelerating Heterogeneous Federated Learning with Closed-form Classifiers](https://mlsanity.com/paper/2406.01116/) (2024)
- [Task-Aware LLM Routing with Multi-Level Task-Profile-Guided Data Synthesis for Cold-Start Scenarios](https://mlsanity.com/paper/2604.09377/) (2026)
- [MoDEM: Mixture of Domain Expert Models](https://mlsanity.com/paper/2410.07490/) (2024)
- [DiSRouter: Distributed Self-Routing for LLM Selections](https://mlsanity.com/paper/2510.19208/) (2025)
- [HDEE: Heterogeneous Domain Expert Ensemble](https://mlsanity.com/paper/2502.19385/) (2025)
- [HierRouter: Coordinated Routing of Specialized Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2511.09873/) (2025)
- [Training-Free Dynamic Upcycling of Expert Language Models](https://mlsanity.com/paper/2603.29765/) (2026)

## Abstract (arXiv)

Foundational Large Language Models (LLMs) demonstrate proficiency on a wide range of general tasks, and achieve remarkable results on various specialized tasks via domain-expert LLMs. With the ever-growing list of available LLMs, inference routers are being proposed to select the most appropriate LLM for each prompt. However, existing routing methods either optimize cost across weak-to-strong generalist LLMs or require substantial training to support domain-expertise routing. In this paper, we propose IR3DE, a Ridge Regression-based Router for Domain Experts that provides cheap and fast routing decisions for each prompt. We evaluate IR3DE in two Causal Language Modeling (CLM) settings where the tasks are next-token prediction for all domains, and one reasoning setting where each domain has its own distinct reasoning task. Despite being a linear router, IR3DE achieves performance comparable to the other baselines in both CLM settings, and surpassing them in the reasoning setting, with a normalized performance of 98.4%. Moreover, IR3DE enables the addition or removal of new domain experts without requiring the router to be retrained from scratch, allowing a dynamic set of LLMs to be served with minimal disruption to the router itself. Our code is available at: github.com/gensyn-ai/IR3DE.