Benefits and Limitations of Communication in Multi-Agent Reasoning

TL;DR

The paper addresses how multi-agent reasoning with Transformers can extend reasoning over long contexts by decomposing problems into subproblems processed by multiple agents. It introduces a formal framework for MAS expressivity based on decoder-only UHAT Transformers and derives bounds on the number of agents, inter-agent communication, and speedups for three task families: associative recall, state tracking, and k-hop reasoning. The authors prove three distinct depth–communication regimes and provide optimality results, complemented by synthetic experiments showing alignment with theory on pretrained LLMs. The work offers principled guidelines for designing scalable multi-agent reasoning systems that balance context size, bandwidth, and wall-clock time, with implications for long-context tasks and distributed reasoning pipelines.

Abstract

Chain-of-thought prompting has popularized step-by-step reasoning in large language models, yet model performance still degrades as problem complexity and context length grow. By decomposing difficult tasks with long contexts into shorter, manageable ones, recent multi-agent paradigms offer a promising near-term solution to this problem. However, the fundamental capacities of such systems are poorly understood. In this work, we propose a theoretical framework to analyze the expressivity of multi-agent systems. We apply our framework to three algorithmic families: state tracking, recall, and $k$-hop reasoning. We derive bounds on (i) the number of agents required to solve the task exactly, (ii) the quantity and structure of inter-agent communication, and (iii) the achievable speedups as problem size and context scale. Our results identify regimes where communication is provably beneficial, delineate tradeoffs between agent count and bandwidth, and expose intrinsic limitations when either resource is constrained. We complement our theoretical analysis with a set of experiments on pretrained LLMs using controlled synthetic benchmarks. Empirical outcomes confirm the tradeoffs between key quantities predicted by our theory. Collectively, our analysis offers principled guidance for designing scalable multi-agent reasoning systems.

Figures (14)

• Figure 1: Graphical representations of the protocols analyzed in Section \ref{['sec:results']}.
• Figure 2: Three possible and one impossible regimes for depth-communication tradeoffs.
• Figure 3: Llama-70B accuracy on Recall across sequence lengths. CoA is the theoretically optimal protocol.
• Figure 4: Empirical validation for Parity.
• Figure 5: Empirical validation for $k$-hop reasoning.

Theorems & Definitions (34)

• Definition 3.1: Multi-agent system
• Definition 3.2: Complexity of Multi-Agent System
• Definition 3.3: Agent computation
• Proposition 4.1: Conservation of size
• proof
• Proposition 4.2
• Proposition 4.3
• Definition 4.1: State tracking problem
• Proposition 4.4
• Proposition 4.5