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

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.