Modelling the development of counting with memory-augmented neural networks

TL;DR

This paper models the development of counting in humans using a memory-augmented neural network, demonstrating an inflection point in learning and the ability to extrapolate beyond trained ranges, akin to child development.

Contribution

It introduces a memory-augmented neural network architecture that mimics human counting development and exhibits systematic extrapolation beyond training data.

Findings

Model shows an inflection point similar to human development.

Capable of extrapolating to higher counts outside training range.

Resembles systematic generalization observed in children.

Abstract

Learning to count is an important example of the broader human capacity for systematic generalization, and the development of counting is often characterized by an inflection point when children rapidly acquire proficiency with the procedures that support this ability. We aimed to model this process by training a reinforcement learning agent to select N items from a binary vector when instructed (known as the give-$N$ task). We found that a memory-augmented modular network architecture based on the recently proposed Emergent Symbol Binding Network (ESBN) exhibited an inflection during learning that resembled human development. This model was also capable of systematic extrapolation outside the range of its training set - for example, trained only to select between 1 and 10 items, it could succeed at selecting 11 to 15 items as long as it could make use of an arbitrary count sequence of at least that length. The close parallels to child development and the capacity for extrapolation suggest that our model could shed light on the emergence of systematicity in humans.