  Constructive studies on symbol emergence systems seek to investigate
computational models that can better explain human language evolution, the
creation of symbol systems, and the construction of internal representations.
This study provides a new model for emergent communication, which is based on a
probabilistic generative model (PGM) instead of a discriminative model based on
deep reinforcement learning. We define the Metropolis-Hastings (MH) naming game
by generalizing previously proposed models. It is not a referential game with
explicit feedback, as assumed by many emergent communication studies. Instead,
it is a game based on joint attention without explicit feedback.
Mathematically, the MH naming game is proved to be a type of MH algorithm for
an integrative PGM that combines two agents that play the naming game. From
this viewpoint, symbol emergence is regarded as decentralized Bayesian
inference, and semiotic communication is regarded as inter-personal cross-modal
inference. This notion leads to the collective predictive coding hypothesis}
regarding language evolution and, in general, the emergence of symbols. We also
propose the inter-Gaussian mixture model (GMM)+ variational autoencoder (VAE),
a deep generative model for emergent communication based on the MH naming game.
The model has been validated on MNIST and Fruits 360 datasets. Experimental
findings demonstrate that categories are formed from real images observed by
agents, and signs are correctly shared across agents by successfully utilizing
both of the observations of agents via the MH naming game. Furthermore,
scholars verified that visual images were recalled from signs uttered by
agents. Notably, emergent communication without supervision and reward feedback
improved the performance of the unsupervised representation learning of agents.
