How do LLM agents interact on large networks?
An invariance principle based concentration result for large-scale stochastic pairwise interaction network systems
This paper studies how the stable states of large populations of interacting agents (like in a social network or epidemic model) concentrate around specific behaviors as the population size increases. It uses Lyapunov functions to show this concentration happens not just for fully-connected networks, but also for sparser networks with sufficient mixing properties, including randomly generated Erdös-Rényi graphs.
For LLM-based multi-agent systems, this research suggests that as the number of LLMs in a system grows and they interact on a sufficiently connected network, their combined behavior might become more predictable and concentrate around certain equilibrium states, even if the individual LLMs are stochastic. This could be crucial for understanding emergent behavior and designing robust multi-agent LLM applications.