Self-Sustaining Iterated Learning

TL;DR

This paper demonstrates how slight modifications to the iterated learning process can achieve self-sustainability in language learning, including discrete and linear regression cases, with implications for natural algorithms.

Contribution

It introduces a geometric characterization of iterated learnability and proposes a method to ensure self-sustainability in both discrete and nondiscrete language classes.

Findings

Steady increase in training session lengths guarantees self-sustainability for discrete languages.

Self-sustainability can be achieved in linear regression models.

Implications for non-equilibrium dynamics in natural algorithms.

Abstract

An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve self-sustainability. Our work is in two parts. First, we characterize iterated learnability in geometric terms and show how a slight, steady increase in the lengths of the training sessions ensures self-sustainability for any discrete language class. In the second part, we tackle the nondiscrete case and investigate self-sustainability for iterated linear regression. We discuss the implications of our findings to issues of non-equilibrium dynamics in natural algorithms.