# Learning from Diverse Reasoning Paths with Routing and Collaboration

arXiv: https://arxiv.org/abs/2508.16861 · HTML: https://mlsanity.com/paper/2508.16861/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 64 of its 97 references that are in the map.
- First posted on arXiv 23 Aug 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 64)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Multi-Agent Collaboration Mechanisms: A Survey of LLMs](https://mlsanity.com/paper/2501.06322/) (2025)
- [Multi-Agent Collaboration: Harnessing the Power of Intelligent LLM Agents](https://mlsanity.com/paper/2306.03314/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Symbolic Knowledge Distillation: from General Language Models to Commonsense Models](https://mlsanity.com/paper/2110.07178/) (2021)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Exploring the Reasoning Abilities of Multimodal Large Language Models (MLLMs): A Comprehensive Survey on Emerging Trends in Multimodal Reasoning](https://mlsanity.com/paper/2401.06805/) (2024)

## Built on by (most cited first, 12 of 12)

- [Multi-Agent Debate for LLM Judges with Adaptive Stability Detection](https://mlsanity.com/paper/2510.12697/) (2025)
- [Distribution-Aligned Sequence Distillation for Superior Long-CoT Reasoning](https://mlsanity.com/paper/2601.09088/) (2026)
- [Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation](https://mlsanity.com/paper/2605.19433/) (2026)
- [Metacognitive Self-Correction for Multi-Agent System via Prototype-Guided Next-Execution Reconstruction](https://mlsanity.com/paper/2510.14319/) (2025)
- [CoT-Evo: Evolutionary Distillation of Chain-of-Thought for Scientific Reasoning](https://mlsanity.com/paper/2510.13166/) (2025)
- [The Single-Multi Evolution Loop for Self-Improving Model Collaboration Systems](https://mlsanity.com/paper/2602.05182/) (2026)
- [From Cross-Task Examples to In-Task Prompts: A Graph-Based Pseudo-Labeling Framework for In-context Learning](https://mlsanity.com/paper/2510.24528/) (2025)
- [Reforming the Mechanism: Editing Reasoning Patterns in LLMs with Circuit Reshaping](https://mlsanity.com/paper/2603.06923/) (2026)
- [Probing to Refine: Reinforcement Distillation of LLMs via Explanatory Inversion](https://mlsanity.com/paper/2603.19266/) (2026)
- [Are Rationales Necessary and Sufficient? Tuning LLMs for Explainable Misinformation Detection](https://mlsanity.com/paper/2605.19285/) (2026)
- [Separate the Wheat from the Chaff: Winnowing Down Divergent Views in Retrieval Augmented Generation](https://mlsanity.com/paper/2511.04700/) (2025)
- [Structural Rationale Distillation via Reasoning Space Compression](https://mlsanity.com/paper/2605.07139/) (2026)

## Abstract (arXiv)

Advances in large language models (LLMs) significantly enhance reasoning capabilities but their deployment is restricted in resource-constrained scenarios. Knowledge distillation addresses this by transferring knowledge from powerful teacher models to compact and transparent students. However, effectively capturing the teacher's comprehensive reasoning is challenging due to conventional token-level supervision's limited scope. Using multiple reasoning paths per query alleviates this problem, but treating each path identically is suboptimal as paths vary widely in quality and suitability across tasks and models. We propose Quality-filtered Routing with Cooperative Distillation (QR-Distill), combining path quality filtering, conditional routing, and cooperative peer teaching. First, quality filtering retains only correct reasoning paths scored by an LLM-based evaluation. Second, conditional routing dynamically assigns paths tailored to each student's current learning state. Finally, cooperative peer teaching enables students to mutually distill diverse insights, addressing knowledge gaps and biases toward specific reasoning styles. Experiments demonstrate QR-Distill's superiority over traditional single- and multi-path distillation methods. Ablation studies further highlight the importance of each component including quality filtering, conditional routing, and peer teaching in effective knowledge transfer. Our code is available at https://github.com/LzyFischer/Distill.