# MOC: Multi-Order Communication in LLM-based Multi-Agent Systems

arXiv: https://arxiv.org/abs/2606.02359 · HTML: https://mlsanity.com/paper/2606.02359/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 42 of its 48 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

- 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 42)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [LongLLMLingua: Accelerating and Enhancing LLMs in Long Context Scenarios via Prompt Compression](https://mlsanity.com/paper/2310.06839/) (2023)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Multi-Agent Collaboration Mechanisms: A Survey of LLMs](https://mlsanity.com/paper/2501.06322/) (2025)

## Built on by (most cited first, 4 of 4)

- [Social Circuits behind Multi-agent Echo Chambers](https://mlsanity.com/paper/2609.34444/) (2026)
- [Self-Adapting Group of Experts for Multi-Agent Reasoning](https://mlsanity.com/paper/2609.35412/) (2026)
- [CollabFlow: Recursive Self-Improvement of Agent Collaboration](https://mlsanity.com/paper/2609.38662/) (2026)
- [BRIDGE: Selective Boundary Repair with Dependency Graph Evidence in Multi-Agent Systems](https://mlsanity.com/paper/2610.17805/) (2026)

## Abstract (arXiv)

Despite the remarkable progress of Large Language Model (LLM) based Multi-Agent Systems, most research focuses on optimizing coordination topology while largely underexploring the equally critical problem: how to transmit and optimize messages among agents effectively? Current communication schemes typically rely on the direct concatenation of first-order neighbor responses, which induces a restricted evidence receptive field and leads to the dilution of crucial insights over multi-hop paths. To address these limitations, we propose the Multi-Order Communication (MOC) scheme, which reconstructs the inter-agent communication to capture multi-hop dependencies and incorporates a structural message consolidation strategy to ensure efficiency. Specifically, we formalize the communication mechanism to construct a structured multi-order evidence stream, and subsequently design a Semantic-Topological Merging algorithm to optimize semantic fidelity within token constraints. Extensive experiments across six diverse datasets and LLM backbones of varying parameter scales demonstrate that MOC consistently improves task performance and reduces communication costs. The code is available at https://github.com/yao-guan/MOC.