Variational Bayes Naming Game: Decentralized Multi-Agent Inference for Symbol Emergence

Emergent communication in multi-agent systems poses scalability challenges, as conventional models are typically limited to dyadic interactions. This study introduces the Variational Bayes Naming Game (VBNG), a decentralized Bayesian inference framework for modeling symbol emergence among three or more agents. Based on the Collective Predictive Coding (CPC) hypothesis, VBNG enables agents to infer shared signs by minimizing free energy using their individual observations. In our experiment, we evaluated the proposed method against a conventional sampling-based approach (RMHNG) and a centralized topline model (VB) using both synthetic and patched MNIST image datasets. VBNG achieved accuracy comparable to the topline model. Although the conventional method failed under conditions where individual agents' observations were insufficient for identification, VBNG demonstrated high robustness (ARI > 0.6). The proposed method demonstrated significantly improved computational efficiency, converging 2-4 times faster than the conventional method in experiments with up to 10 agents. This performance was achieved while attaining high classification accuracy and high inter-agent agreement (kappa = 0.94) on the MNIST task. This study presents a robust, scalable, and theoretically coherent framework for symbol emergence research, demonstrating variational inference as an effective mechanism for consensus formation in decentralized multi-agent systems.