# MAgICoRe: Multi-Agent, Iterative, Coarse-to-Fine Refinement for Reasoning

arXiv: https://arxiv.org/abs/2409.12147 · HTML: https://mlsanity.com/paper/2409.12147/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 39 of its 59 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 39)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration](https://mlsanity.com/paper/2307.05300/) (2023)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [More Agents Is All You Need](https://mlsanity.com/paper/2402.05120/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [GLoRe: When, Where, and How to Improve LLM Reasoning via Global and Local Refinements](https://mlsanity.com/paper/2402.10963/) (2024)

## Built on by (most cited first, 30 of 41)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning](https://mlsanity.com/paper/2502.12853/) (2025)
- [Harnessing the Reasoning Economy: A Survey of Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.24377/) (2025)
- [ReSo: A Reward-driven Self-organizing LLM-based Multi-Agent System for Reasoning Tasks](https://mlsanity.com/paper/2503.02390/) (2025)
- [The LLM Already Knows: Estimating LLM-Perceived Question Difficulty via Hidden Representations](https://mlsanity.com/paper/2509.12886/) (2025)
- [AI Agentic Programming: A Survey of Techniques, Challenges, and Opportunities](https://mlsanity.com/paper/2508.11126/) (2025)
- [Model Swarms: Collaborative Search to Adapt LLM Experts via Swarm Intelligence](https://mlsanity.com/paper/2410.11163/) (2024)
- [Reinforce LLM Reasoning through Multi-Agent Reflection](https://mlsanity.com/paper/2506.08379/) (2025)
- [nvAgent: Automated Data Visualization from Natural Language via Collaborative Agent Workflow](https://mlsanity.com/paper/2502.05036/) (2025)
- [Learning to Generate Unit Tests for Automated Debugging](https://mlsanity.com/paper/2502.01619/) (2025)
- [TimeRefine: Temporal Grounding with Time Refining Video LLM](https://mlsanity.com/paper/2412.09601/) (2024)
- [Anthropomimetic Uncertainty: What Verbalized Uncertainty in Language Models is Missing](https://mlsanity.com/paper/2507.10587/) (2025)
- [Not All Queries Need Deep Thought: CoFiCot for Adaptive Coarse-to-fine Stateful Refinement](https://mlsanity.com/paper/2603.08251/) (2026)
- [ARAG: Agentic Retrieval Augmented Generation for Personalized Recommendation](https://mlsanity.com/paper/2506.21931/) (2025)
- [The Hidden Strength of Disagreement: Unraveling the Consensus-Diversity Tradeoff in Adaptive Multi-Agent Systems](https://mlsanity.com/paper/2502.16565/) (2025)
- [SPARTA ALIGNMENT: Collectively Aligning Multiple Language Models through Combat](https://mlsanity.com/paper/2506.04721/) (2025)
- [Training Language Model to Critique for Better Refinement](https://mlsanity.com/paper/2506.22157/) (2025)
- [PRInTS: Reward Modeling for Long-Horizon Information Seeking](https://mlsanity.com/paper/2511.19314/) (2025)
- [The Interaction Tax: When Communication Erases Diversity in Multi-Agent Teams](https://mlsanity.com/paper/2608.23541/) (2026)
- [Everyone Contributes! Incentivizing Strategic Cooperation in Multi-LLM Systems via Sequential Public Goods Games](https://mlsanity.com/paper/2508.02076/) (2025)
- [LATTS: Locally Adaptive Test-Time Scaling](https://mlsanity.com/paper/2509.20368/) (2025)
- [More Rounds, More Noise: Why Multi-Turn Review Fails to Improve Cross-Context Verification](https://mlsanity.com/paper/2603.16244/) (2026)
- [Another Turn, Better Output? A Turn-Wise Analysis of Iterative LLM Prompting](https://mlsanity.com/paper/2509.06770/) (2025)
- [Self-Correction as Feedback Control: Error Dynamics, Stability Thresholds, and Prompt Interventions in LLMs](https://mlsanity.com/paper/2604.22273/) (2026)
- [Ecdysis: Efficient and Effective Training of Runtime Harnesses for LLM Agents](https://mlsanity.com/paper/2609.11677/) (2026)
- [Adaptive Multi-Agent Response Refinement in Conversational Systems](https://mlsanity.com/paper/2511.08319/) (2025)
- [Certifiable Boolean Reasoning Is Universal](https://mlsanity.com/paper/2602.05120/) (2026)
- [Guided Collaboration in Heterogeneous LLM-Based Multi-Agent Systems via Entropy-Based Understanding Assessment and Experience Retrieval](https://mlsanity.com/paper/2602.13639/) (2026)

## Abstract (arXiv)

Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point. Refinement offers an alternative by using LLM-generated feedback to improve solution quality. However, refinement introduces 3 key challenges: (1) Excessive refinement: Uniformly refining all instances can over-correct and reduce the overall performance. (2) Inability to localize and address errors: LLMs have a limited ability to self-correct and struggle to identify and correct their own mistakes. (3) Insufficient refinement: Deciding how many iterations of refinement are needed is non-trivial, and stopping too soon could leave errors unaddressed. To tackle these issues, we propose MAgICoRe, which avoids excessive refinement by categorizing problem difficulty as easy or hard, solving easy problems with coarse-grained aggregation and hard ones with fine-grained and iterative multi-agent refinement. To improve error localization, we incorporate external step-wise reward model (RM) scores. Moreover, to ensure effective refinement, we employ a multi-agent loop with three agents: Solver, Reviewer (which generates targeted feedback based on step-wise RM scores), and the Refiner (which incorporates feedback). To ensure sufficient refinement, we re-evaluate updated solutions, iteratively initiating further rounds of refinement. We evaluate MAgICoRe on Llama-3-8B and GPT-3.5 and show its effectiveness across 5 math datasets. Even one iteration of MAgICoRe beats Self-Consistency by 3.4%, Best-of-k by 3.2%, and Self-Refine by 4.0% while using less than half the samples. Unlike iterative refinement with baselines, MAgICoRe continues to improve with more iterations. Finally, our ablations highlight the importance of MAgICoRe's RMs and multi-agent communication.