  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.
