Hyperbolic Graph-of-Agents: A Training-Free Framework for LLM-Based Multi-Agent Collaboration in Hyperbolic Space

With the continuous advancement of agents, the need to orchestrate multi-agent collaboration to enhance task performance has become increasingly urgent. Existing multi-agent collaboration methods typically use natural language text as the collaboration medium for multiple rounds of message passing, causing inference costs to grow rapidly with the number of collaboration rounds and agents, and introducing semantic drift through multiple rounds of comprehension and restatement. To this end, we propose Hyperbolic Graph-of-Agents (HGoA), a training-free framework for large language model-based multi-agent collaboration in hyperbolic space. Specifically, a novel hyperbolic-aware dual-channel graph construction method is proposed to adaptively construct an agent graph from observable outputs in a training-free manner. Next, a novel hyperbolic collaboration method based on consensus energy is proposed, which uses representation vectors instead of natural language text as the collaboration medium, thereby mitigating semantic drift while reducing inference costs. Furthermore, we leverage hyperbolic space to overcome the limitation of Euclidean space in failing to capture the hierarchical structures that exist among agent responses. Finally, experiments on six benchmarks demonstrate that, compared with mainstream methods, HGoA can improve the efficiency of multi-agent collaboration on various complex tasks.