# Recursive Metropolis-Hastings Naming Game: Symbol Emergence in a Multi-agent System based on Probabilistic Generative Models

arXiv: https://arxiv.org/abs/2305.19761 · HTML: https://mlsanity.com/paper/2305.19761/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Multi-Agent Cooperation and the Emergence of (Natural) Language](https://mlsanity.com/paper/1612.07182/) (2016)
- [Emergence of Language with Multi-agent Games: Learning to Communicate with Sequences of Symbols](https://mlsanity.com/paper/1705.11192/) (2017)
- [Emergence of Linguistic Communication from Referential Games with Symbolic and Pixel Input](https://mlsanity.com/paper/1804.03984/) (2018)
- [How agents see things: On visual representations in an emergent language game](https://mlsanity.com/paper/1808.10696/) (2018)
- [Emergent Communication of Generalizations](https://mlsanity.com/paper/2106.02668/) (2021)
- [Symbol Emergence in Cognitive Developmental Systems: a Survey](https://mlsanity.com/paper/1801.08829/) (2018)
- [Learning to Ground Multi-Agent Communication with Autoencoders](https://mlsanity.com/paper/2110.15349/) (2021)
- [Symbol Emergence in Robotics: A Survey](https://mlsanity.com/paper/1509.08973/) (2015)
- [Compositional Obverter Communication Learning From Raw Visual Input](https://mlsanity.com/paper/1804.02341/) (2018)
- [Neuro-SERKET: Development of Integrative Cognitive System through the Composition of Deep Probabilistic Generative Models](https://mlsanity.com/paper/1910.08918/) (2019)
- [Emergent Communication under Competition](https://mlsanity.com/paper/2101.10276/) (2021)
- [Emergent Communication through Metropolis-Hastings Naming Game with Deep Generative Models](https://mlsanity.com/paper/2205.12392/) (2022)
- [SERKET: An Architecture for Connecting Stochastic Models to Realize a Large-Scale Cognitive Model](https://mlsanity.com/paper/1712.00929/) (2017)
- [Symbol Emergence as an Interpersonal Multimodal Categorization](https://mlsanity.com/paper/1905.13443/) (2019)
- [Multiagent Multimodal Categorization for Symbol Emergence: Emergent Communication via Interpersonal Cross-modal Inference](https://mlsanity.com/paper/2109.07194/) (2021)
- [Dynamic population-based meta-learning for multi-agent communication with natural language](https://mlsanity.com/paper/2110.14241/) (2021)

## Built on by (most cited first, 8 of 8)

- [LLM-Based Agent Society Investigation: Collaboration and Confrontation in Avalon Gameplay](https://mlsanity.com/paper/2310.14985/) (2023)
- [Generative Emergent Communication: Large Language Model is a Collective World Model](https://mlsanity.com/paper/2501.00226/) (2024)
- [Lewis's Signaling Game as beta-VAE For Natural Word Lengths and Segments](https://mlsanity.com/paper/2311.04453/) (2023)
- [Constructive Approach to Bidirectional Influence between Qualia Structure and Language Emergence](https://mlsanity.com/paper/2409.09413/) (2024)
- [System 0/1/2/3: Quad-process theory for multi-timescale embodied collective cognitive systems](https://mlsanity.com/paper/2503.06138/) (2025)
- [Metropolis-Hastings Captioning Game: Knowledge Fusion of Vision Language Models via Decentralized Bayesian Inference](https://mlsanity.com/paper/2504.09620/) (2025)
- [Co-Creative Learning via Metropolis-Hastings Interaction between Humans and AI](https://mlsanity.com/paper/2506.15468/) (2025)
- [Emergent Communication between Heterogeneous Visual Agents through Decentralized Learning](https://mlsanity.com/paper/2605.11695/) (2026)

## Abstract (arXiv)

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.