# Route-and-Reason: Scaling Large Language Model Reasoning with Reinforced Model Router

arXiv: https://arxiv.org/abs/2506.05901 · HTML: https://mlsanity.com/paper/2506.05901/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 29 of its 89 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 29 of 29)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Take a Step Back: Evoking Reasoning via Abstraction in Large Language Models](https://mlsanity.com/paper/2310.06117/) (2023)
- [Edge AI: On-Demand Accelerating Deep Neural Network Inference via Edge Computing](https://mlsanity.com/paper/1910.05316/) (2019)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [CHAMP: A Competition-level Dataset for Fine-Grained Analyses of LLMs' Mathematical Reasoning Capabilities](https://mlsanity.com/paper/2401.06961/) (2024)
- [Sub-Task Decomposition Enables Learning in Sequence to Sequence Tasks](https://mlsanity.com/paper/2204.02892/) (2022)
- [OpenCity: A Scalable Platform to Simulate Urban Activities with Massive LLM Agents](https://mlsanity.com/paper/2410.21286/) (2024)
- [Programming Puzzles](https://mlsanity.com/paper/2106.05784/) (2021)
- [Division-of-Thoughts: Harnessing Hybrid Language Model Synergy for Efficient On-Device Agents](https://mlsanity.com/paper/2502.04392/) (2025)
- [Large Language Model-driven Meta-structure Discovery in Heterogeneous Information Network](https://mlsanity.com/paper/2402.11518/) (2024)
- [HLM-Cite: Hybrid Language Model Workflow for Text-based Scientific Citation Prediction](https://mlsanity.com/paper/2410.09112/) (2024)
- [Chain-of-Questions Training with Latent Answers for Robust Multistep Question Answering](https://mlsanity.com/paper/2305.14901/) (2023)

## Built on by (most cited first, 13 of 13)

- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Dynamic Model Routing and Cascading for Efficient LLM Inference: A Survey](https://mlsanity.com/paper/2603.04445/) (2026)
- [R2-Router: A New Paradigm for LLM Routing with Reasoning](https://mlsanity.com/paper/2602.02823/) (2026)
- [GraphPlanner: Graph Memory-Augmented Agentic Routing for Multi-Agent LLMs](https://mlsanity.com/paper/2604.23626/) (2026)
- [SWE-Router: Routing in Multi-turn Agentic Software Engineering Tasks](https://mlsanity.com/paper/2607.00053/) (2026)
- [Uno-Orchestra: Parsimonious Agent Routing via Selective Delegation](https://mlsanity.com/paper/2605.05007/) (2026)
- [Bridging On-Device and Cloud LLMs for Collaborative Reasoning: A Unified Methodology for Local Routing and Post-Training](https://mlsanity.com/paper/2509.24050/) (2025)
- [When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions](https://mlsanity.com/paper/2605.22873/) (2026)
- [SALMONN-duo: Adaptive Dual-System Coordination for Full-Duplex Voice Agents](https://mlsanity.com/paper/2609.34247/) (2026)
- [RouteGoT: Node-Adaptive Routing for Cost-Efficient Graph of Thoughts Reasoning](https://mlsanity.com/paper/2603.05818/) (2026)
- [Iterative Critique-and-Routing Controller for Multi-Agent Systems with Heterogeneous LLMs](https://mlsanity.com/paper/2605.08686/) (2026)
- [RLCascadeRouter: Quality-Estimator-Free Cascade Routing via Reinforcement Learning](https://mlsanity.com/paper/2608.15817/) (2026)
- [Mo' Models, Mo' Problems: How to best select model pools when designing Multi-Agent Systems](https://mlsanity.com/paper/2609.17306/) (2026)

## Abstract (arXiv)

Chain-of-thought has been proven essential for enhancing the complex reasoning abilities of Large Language Models (LLMs), but it also leads to high computational costs. Recent advances have explored the method to route queries among multiple models and proved it as a promising approach. However, previous works directly operate at the task level, i.e., assigning user queries to suitable LLMs, which does not allow hybrid LLMs to truly collaborate on finer-grained sub-tasks. Collaboration at the level of intermediate reasoning steps (thoughts) could enable more efficient coordination, but it also poses significant challenges for router scheduling, placing immense demands on the quality of task decomposition and the precision of the router. To address this, we propose R2-Reasoner, a novel framework centered around a Reinforced Model Router designed to efficiently scale LLM reasoning. This router orchestrates collaboration across nine heterogeneous models, whose parameter scales range from less than 1B to hundreds of billions, by first breaking down a complex query into subtasks with a decomposer, and then assigning each subtask to the optimal model with a subtask allocator, balancing performance with cost. Training this router involves a two-stage alternating process for the decomposer and the allocator, integrating supervised fine-tuning with reinforcement learning to enable effective self-supervised refinement. Extensive experiments across six challenging reasoning benchmarks demonstrate that R2-Reasoner reduces API costs by 84.46% compared with state-of-the-art baselines while maintaining competitive reasoning accuracy. Our framework paves the way for the development of more scalable and efficient reasoning systems. Our code is open-source at https://anonymous.4open.science/r/R2_Reasoner.