[Paper Review] The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents

Shangmin Guo, Yi Ren+4 more|arXiv (Cornell University)|Oct 11, 2019

Language and cultural evolution18 references17 citations

TL;DR

This paper demonstrates that compositional languages for numeric concepts can emerge through iterated learning in deep neural network agents, but only when input representations (e.g., concatenated one-hot vectors or images of object counts) enable faster learning by listeners. Compositional languages dominate only when they are more learnable than holistic alternatives, highlighting learnability as a key driver of compositional structure in emergent communication.

ABSTRACT

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.

Motivation & Objective

• To investigate whether compositional languages for numeric concepts can emerge in multi-agent communication systems without predefined linguistic elements.
• To examine how input representation (concatenation, image, or bag of vectors) affects the emergence of compositional language through iterated learning.
• To determine whether learnability—specifically, the number of training iterations required for listeners to master a language—drives the emergence of compositional structure.
• To test the hypothesis that compositionality arises from a trade-off between expressivity and learnability in iterated learning settings.

Proposed method

• Designed a referential game called 'Bag-Select' where a speaker observes a bag with a specific number of two object types (A and B), produces a message, and a listener selects the correct bag from 15 candidates.
• Used three distinct input representations: (1) concatenation of one-hot vectors (e.g., '2A3B' → [001000; 000100]), (2) images of scenes with varying numbers of objects, and (3) bags of one-hot vectors representing quantities.
• Employed distinct neural encoders: multilayer perceptron (MLP) for concatenations, LeNet-5-style CNN for images, and a set-encoder with sigmoid activation for bags to preserve permutation invariance.
• Implemented iterated learning by chaining dyads (speaker-listener pairs) across generations, where each listener becomes a new speaker in the next generation, simulating cultural transmission.
• Trained agents using cross-entropy loss and stochastic gradient descent (SGD), with performance measured by message accuracy (speaker) and correct bag selection (listener).
• Tracked language evolution via topological similarity of emergent languages and posterior probability of languages with varying compositionality (ρ), using smoothed metrics over generations.

Experimental results

Research questions

• RQ1 Does iterated learning in neural agents lead to the emergence of compositional languages for numeric concepts?
• RQ2 How do different input representations (concatenation, image, bag) influence the emergence of compositional structure in emergent languages?
• RQ3 Is the learnability of a language—measured by the number of training iterations required for listeners to master it—a determining factor in whether compositional languages dominate?
• RQ4 Why do compositional languages fail to emerge under bag-based input representations despite similar expressivity?

Key findings

• Compositional languages (ρ > 0.6) emerged and dominated over generations when inputs were represented as concatenated one-hot vectors or images, with posterior probability of high-compositionality languages increasing steadily.
• In the concatenation and image conditions, the final emergent language showed clear compositional structure, such as distinct message tokens corresponding to counts of A and B objects.
• Under bag-based input representation, no compositional language emerged; the final language was non-compositional, with no clear mapping between message tokens and object counts.
• The topological similarity of emergent languages was significantly lower in the bag condition compared to concatenation and image conditions, indicating less structural consistency across generations.
• Compositional languages were more learnable by listeners—requiring fewer training iterations—than holistic or emergent languages in the same input condition, explaining their dominance in iterated learning.
• The results support the hypothesis that compositionality emerges under pressure from both expressivity and learnability, with the bag representation favoring non-compositional languages due to higher listener learnability despite lower structural regularity.