On the Optimality of Discrete Object Naming: a Kinship Case Study

TL;DR

This work addresses how discrete object naming can achieve an optimal trade-off between informativeness and complexity. It introduces an information-theoretic framework with information loss $L$ and complexity $C$, proves that optimality is attained only when the Listener's decoder equals the Speaker's Bayesian decoder, and applies this to kinship naming in both human data and emergent neural speakers. Through a need-agnostic reformulation, it enables cross-linguistic comparison independent of communicative need distributions, and demonstrates that neural emergent systems can approach the theoretical frontier while maintaining tractable complexity. The findings highlight a robust link between Bayesian decoding and efficiency in discrete naming, with practical implications for modeling language evolution and designing efficient emergent communication systems.

Abstract

The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Prior work capitalizes on information theory to formalize these notions; however, these studies generally rely on two simplifications: (i) optimal listeners, and (ii) universal communicative need across languages. Here, we address these limitations by introducing an information-theoretic framework for discrete object naming systems, and we use it to prove that an optimal trade-off is achievable if and only if the listener's decoder is equivalent to the Bayesian decoder of the speaker. Adopting a referential game setup from emergent communication, and focusing on the semantic domain of kinship, we show that our notion of optimality is not only theoretically achievable but also emerges empirically in learned communication systems.

Figures (10)

• Figure 1: Illustration of two English-speaking agents playing the kinship naming game. The Speaker (left) selects a family member and produces a name. The Listener (right) receives the name and infers which member is being referred to.
• Figure 2: Visualization of the optimal trade-off curve (red line) and the feasible region (white area) encompassing all valid communication systems.
• Figure 3: The kinship graph is adapted from the familial structures described by Kemp2012. Nodes are labeled using abbreviations, where "F", "M", "B", "Z", "S", "D", "y", and "e" stand for "father", "mother", "brother", "sister", "son", "daughter", "younger", and "elder", respectively. For example, MBe denotes the "mother's elder brother". Each edge in the graph is bidirectional, labeled parent-of when traversing top-down and child-of when traversing bottom-up.
• Figure 4: (Top) Trade-offs for HP systems with Bayesian (B) and Non-Bayesian (NB) listeners, and neural network (NN) systems (averaged over 50 runs; standard deviations shown as light gray ellipses). Trade-offs under Non-Bayesian HP-Listener conditions collectively (denoted as NB-mean) form lines that are approximately parallel to the optimal curve. Each line is annotated with the flip rate $r_e$ and its distance $d$ to the optimal curve. For visual clarity, only 100 randomly selected Non-Bayesian listeners are shown per language. (Bottom) Accuracy of NN and human systems when paired with the Bayesian HP-Listener.
• Figure 5: Trajectories of NN systems over time, recorded every 10 epochs, under the English communicative need distribution. Results are averaged over 50 runs, with standard deviation represented by ellipses.