# The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents

arXiv: https://arxiv.org/abs/1910.05291 · HTML: https://mlsanity.com/paper/1910.05291/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2019.

## Built on by (most cited first, 26 of 26)

- [Emergent Communication for Understanding Human Language Evolution: What's Missing?](https://mlsanity.com/paper/2204.10590/) (2022)
- [Iterated learning for emergent systematicity in VQA](https://mlsanity.com/paper/2105.01119/) (2021)
- [Multi-label Iterated Learning for Image Classification with Label Ambiguity](https://mlsanity.com/paper/2111.12172/) (2021)
- [Linking Emergent and Natural Languages via Corpus Transfer](https://mlsanity.com/paper/2203.13344/) (2022)
- [Iterated Learning Improves Compositionality in Large Vision-Language Models](https://mlsanity.com/paper/2404.02145/) (2024)
- [Bias Amplification in Language Model Evolution: An Iterated Learning Perspective](https://mlsanity.com/paper/2404.04286/) (2024)
- [A Review of the Applications of Deep Learning-Based Emergent Communication](https://mlsanity.com/paper/2407.03302/) (2024)
- [Towards More Human-like AI Communication: A Review of Emergent Communication Research](https://mlsanity.com/paper/2308.02541/) (2023)
- [Expressivity of Emergent Language is a Trade-off between Contextual Complexity and Unpredictability](https://mlsanity.com/paper/2106.03982/) (2021)
- [Emergent Quantized Communication](https://mlsanity.com/paper/2211.02412/) (2022)
- [The Curious Case of Representational Alignment: Unravelling Visio-Linguistic Tasks in Emergent Communication](https://mlsanity.com/paper/2407.17960/) (2024)
- [lpNTK: Better Generalisation with Less Data via Sample Interaction During Learning](https://mlsanity.com/paper/2401.08808/) (2024)
- [Visual Referential Games Further the Emergence of Disentangled Representations](https://mlsanity.com/paper/2304.14511/) (2023)
- [Learning Multi-Object Positional Relationships via Emergent Communication](https://mlsanity.com/paper/2302.08084/) (2023)
- [Unsupervised Translation of Emergent Communication](https://mlsanity.com/paper/2502.07552/) (2025)
- [Meta-Referential Games to Learn Compositional Learning Behaviours](https://mlsanity.com/paper/2207.08012/) (2022)
- [ELCC: the Emergent Language Corpus Collection](https://mlsanity.com/paper/2407.04158/) (2024)
- [Implicit Repair with Reinforcement Learning in Emergent Communication](https://mlsanity.com/paper/2502.12624/) (2025)
- [Discrete Messages Improve Communication Efficiency among Isolated Intelligent Agents](https://mlsanity.com/paper/2312.15985/) (2023)
- [Learning Efficient Recursive Numeral Systems via Reinforcement Learning](https://mlsanity.com/paper/2409.07170/) (2024)
- [Learning to Communicate Across Modalities: Perceptual Heterogeneity in Multi-Agent Systems](https://mlsanity.com/paper/2601.22041/) (2026)
- [Using Representation Expressiveness and Learnability to Evaluate Self-Supervised Learning Methods](https://mlsanity.com/paper/2206.01251/) (2022)
- [ETHER: Aligning Emergent Communication for Hindsight Experience Replay](https://mlsanity.com/paper/2307.15494/) (2023)
- [Cognitively-Inspired Emergent Communication via Knowledge Graphs for Assisting the Visually Impaired](https://mlsanity.com/paper/2505.22087/) (2025)
- [Evaluating the relationship between regularity and learnability in recursive numeral systems using Reinforcement Learning](https://mlsanity.com/paper/2602.21720/) (2026)
- [Math Takes Two: A test for emergent mathematical reasoning in communication](https://mlsanity.com/paper/2604.21935/) (2026)

## Abstract (arXiv)

Since first introduced, computer simulation has been an increasingly important tool in evolutionary linguistics. Recently, with the development of deep learning techniques, research in grounded language learning has also started to focus on facilitating the emergence of compositional languages without pre-defined elementary linguistic knowledge. In this work, we explore the emergence of compositional languages for numeric concepts in multi-agent communication systems. We demonstrate that compositional language for encoding numeric concepts can emerge through iterated learning in populations of deep neural network agents. However, language properties greatly depend on the input representations given to agents. We found that compositional languages only emerge if they require less iterations to be fully learnt than other non-degenerate languages for agents on a given input representation.