# MedRouter: Demystifying Knowledge Differences Across Medical LLMs for Routing-Based Reasoning

arXiv: https://arxiv.org/abs/2609.33119 · HTML: https://mlsanity.com/paper/2609.33119/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Clinical and biomedical applications, one of 17 directions in LLM reasoning.
- Builds on 27 of its 61 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Placed in

- LLM reasoning / [Clinical and biomedical applications](https://mlsanity.com/lr/clinical-and-biomedical-applications/)

## Builds on (most cited first, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [PathVQA: 30000+ Questions for Medical Visual Question Answering](https://mlsanity.com/paper/2003.10286/) (2020)
- [MedGemma Technical Report](https://mlsanity.com/paper/2507.05201/) (2025)
- [PMC-VQA: Visual Instruction Tuning for Medical Visual Question Answering](https://mlsanity.com/paper/2305.10415/) (2023)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [Qwen3-VL-Embedding and Qwen3-VL-Reranker: A Unified Framework for State-of-the-Art Multimodal Retrieval and Ranking](https://mlsanity.com/paper/2601.04720/) (2026)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [HuaTuo: Tuning LLaMA Model with Chinese Medical Knowledge](https://mlsanity.com/paper/2304.06975/) (2023)
- [DeepRetrieval: Hacking Real Search Engines and Retrievers with Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2503.00223/) (2025)
- [Cost-Effective Online Multi-LLM Selection with Versatile Reward Models](https://mlsanity.com/paper/2405.16587/) (2024)
- [SuperRL: Reinforcement Learning with Supervision to Boost Language Model Reasoning](https://mlsanity.com/paper/2506.01096/) (2025)
- [xRouter: Training Cost-Aware LLMs Orchestration System via Reinforcement Learning](https://mlsanity.com/paper/2510.08439/) (2025)
- [Accelerating Clinical Evidence Synthesis with Large Language Models](https://mlsanity.com/paper/2406.17755/) (2024)
- [A foundation model for human-AI collaboration in medical literature mining](https://mlsanity.com/paper/2501.16255/) (2025)
- [Not All Tokens Matter: Towards Efficient LLM Reasoning via Token Significance in Reinforcement Learning](https://mlsanity.com/paper/2506.08125/) (2025)
- [EHR-RAG: Bridging Long-Horizon Structured Electronic Health Records and Large Language Models via Enhanced Retrieval-Augmented Generation](https://mlsanity.com/paper/2601.21340/) (2026)
- [MedGuideX: Internalizing Decision Logic from Executable Guidelines into Large Language Models for Clinical Reasoning](https://mlsanity.com/paper/2605.26567/) (2026)
- [Formula-R1: Incentivizing LLM Reasoning over Complex Tables with Numerical Computation via Formula-Driven Reinforcement Learning](https://mlsanity.com/paper/2505.23667/) (2025)
- [GuideSkill: Evolving Executable LLM Agent Skills for Guideline-Grounded Clinical Reasoning](https://mlsanity.com/paper/2607.26160/) (2026)

## Abstract (arXiv)

Medical question answering spans diverse specialties and modalities, and individual medical large language models (LLMs) exhibit distinct strengths across tasks and domains. This heterogeneity suggests that combining specialists may enable broader coverage of medical questions than relying on any single model. However, existing LLM routing methods primarily seek to balance answer quality and inference cost, leaving open how to exploit differences in specialist competence to improve medical reasoning. In this paper, we introduce MedRouter, an agentic system that uses an embedding-based multi-label router to select and query specialist LLMs, then passes their responses to a generator to produce the final answer. We further propose SCALE (Specialist Competence-Aware Learning), a two-stage training framework that first trains the Router with specialist correctness supervision and then optimizes its selections through reinforcement learning. The second stage uses a Performance Gain Reward (PGR) that measures how specialist information affects the generator's answer correctness relative to answering without that information. Experiments on eight text-based and multimodal medical QA benchmarks show that MedRouter outperforms the strongest routing baseline by 8% in average accuracy. Our analysis of specialist outputs further reveals distinct strengths and complementary question-level coverage, motivating learned routing to combine these capabilities for more comprehensive medical reasoning.