# EntroRouter: Learning Efficient Model Routing via Entropy Regulation

arXiv: https://arxiv.org/abs/2606.29424 · HTML: https://mlsanity.com/paper/2606.29424/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [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)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Fly-Swat or Cannon? Cost-Effective Language Model Choice via Meta-Modeling](https://mlsanity.com/paper/2308.06077/) (2023)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)

## Abstract (arXiv)

Model routing balances solution accuracy and computational cost by selecting among models of varying capabilities. While recent multi-round frameworks interleave reasoning and planning, we identify a structural failure mode termed Trust Region Collapse. We demonstrate that the deep coupling of reasoning and routing, exacerbated by the dominance of strong pre-training priors under sparse supervision, leads to degenerate local optima where capable experts are systematically suppressed. To decouple these processes, we propose EntroRouter, a single-round routing framework that treats entropy regulation as a core objective. We first initialize the policy via Soft Supervision, fitting a distribution of suitable models to establish a high-entropy prior for exploration. Subsequently, we stabilize Reinforcement Learning using a Soft Anchor, which utilizes offline capability estimates to orchestrate controlled entropy contraction within a safe trust region. Extensive experiments demonstrate that EntroRouter retains 98.3% of the strongest expert's accuracy while reducing computational costs by 48.25%.