Recursive Metropolis-Hastings Naming Game: Symbol Emergence in a
  Multi-agent System based on Probabilistic Generative Models
Jun Inukai Tadahiro Taniguchi Akira Taniguchi Yoshinobu Hagiwara
In the studies on symbol emergence and emergent communication in a population
of agents, a computational model was employed in which agents participate in
various language games. Among these, the Metropolis-Hastings naming game (MHNG)
possesses a notable mathematical property: symbol emergence through MHNG is
proven to be a decentralized Bayesian inference of representations shared by
the agents. However, the previously proposed MHNG is limited to a two-agent
scenario. This paper extends MHNG to an N-agent scenario. The main
contributions of this paper are twofold: (1) we propose the recursive
Metropolis-Hastings naming game (RMHNG) as an N-agent version of MHNG and
demonstrate that RMHNG is an approximate Bayesian inference method for the
posterior distribution over a latent variable shared by agents, similar to
MHNG; and (2) we empirically evaluate the performance of RMHNG on synthetic and
real image data, enabling multiple agents to develop and share a symbol system.
Furthermore, we introduce two types of approximations -- one-sample and
limited-length -- to reduce computational complexity while maintaining the
ability to explain communication in a population of agents. The experimental
findings showcased the efficacy of RMHNG as a decentralized Bayesian inference
for approximating the posterior distribution concerning latent variables, which
are jointly shared among agents, akin to MHNG. Moreover, the utilization of
RMHNG elucidated the agents' capacity to exchange symbols. Furthermore, the
study discovered that even the computationally simplified version of RMHNG
could enable symbols to emerge among the agents.