Communicating artificial neural networks develop efficient color-naming systems

Abstract

Words categorize the semantic fields they refer to in ways that maximize communication accuracy while minimizing complexity. Focusing on the well-studied color domain, we show that artificial neural networks trained with deep-learning techniques to play a discrimination game develop communication systems whose distribution on the accuracy/complexity plane closely matches that of human languages. The observed variation among emergent color-naming systems is explained by different degrees of discriminative need, of the sort that might also characterize different human communities. Like human languages, emergent systems show a preference for relatively low-complexity solutions, even at the cost of imperfect communication. We demonstrate next that the nature of the emergent systems crucially depends on communication being discrete (as is human word usage). When continuous message passing is allowed, emergent systems become more complex and eventually less efficient. Our study suggests that efficient semantic categorization is a general property of discrete communication systems, not limited to human language. It suggests moreover that it is exactly the discrete nature of such systems that, acting as a bottleneck, pushes them toward low complexity and optimal efficiency.

Keywords: color-naming systems; efficiency of human language; language emergence in artificial neural networks.

Fig. 1.

The 330 WCS color chips. Rows correspond to equally spaced lightness values and columns to equally spaced Munsell hues. Each stimulus is at the maximum available saturation for that hue/lightness combination.

Fig. 2.

A successful round of the discrimination game. A chip $c$ is drawn from a uniform distribution and fed to Speaker. Speaker outputs a probability distribution $p\left(W|c\right)$ over its vocabulary of size $\left|V\right|$. Here, a probability is mapped to a color according to a gray gradient (with darker colors representing higher probabilities). A word $w$ is sampled from $p\left(W|c\right)$ and fed to Listener. Finally, Listener—given $w$, the target chip (in position 1 in this illustration), and a distractor chip (in position 2 in this illustration)—assigns a probability to both positions, representing its guess about the position of the target (in this illustration, Listener correctly assigns a higher probability to the target position).

Fig. 3.

Human (blue circles) and NN (orange circles) color-naming systems on the information plane. English (light blue circle) is not in WCS, but it is approximated relying on Zaslavsky et al. (SI Appendix, figure S7 in ref. 7). The IB curve (black line) defines the theoretical limit on accuracy given complexity. All color-naming systems achieve near-optimal efficiency.

Fig. 4.

Complexity distributions of NN systems across different discriminative needs (human distribution included for comparison). There is a decreasing trend in complexity when increasing percentile (P = 0.004; Kruskal–Wallis). Pairwise differences are not significant when evaluated with Bonferroni-corrected Mann–Whitney–Wilcoxon.

Fig. 5.

Complexity and inefficiency of NN color-naming systems trained with REINFORCE or GS with different $\tau$s. Pairwise differences evaluated with Bonferroni-corrected Mann–Whitney–Wilcoxon. *P < 0.05; **P < 0.01; ***P < 0.001; ****P < 0.0001. Differences that are not significant are not marked.