  Understanding the features of and mechanisms behind language learning can
provide insights into the general process of knowledge acquisition. Recent
methods from network science applied to language learning have advanced the
field, particularly by noting associations between densely connected words and
acquisition. However, the importance of sparse areas of the network, or
knowledge gaps, remains unexplored. Here we create a semantic feature network
in which words correspond to nodes and in which connections correspond to
semantic similarity. We develop a new analytical approach built on principles
of applied topology to query the prevalence of knowledge gaps, which we propose
manifest as cavities within the network. We detect topological cavities of
multiple dimensions in the growing semantic feature network of children ages 16
to 30 months. The pattern of cavity appearance matches that of a constrained
null model, created by predefining the affinity of each node for connections.
Furthermore, when word acquisition time is computed from children of mothers
with differing levels of education, we find that despite variation at the word
level, the global organization as measured by persistent homology remains
comparable. We show that topological properties of a node correlate with
filling in cavities better than simple lexical properties such as the length
and frequency of the corresponding word. Finally, we show that the large-scale
architecture of the semantic feature network is topologically accommodating to
many node orders. We discuss the importance of topology in language learning,
and we speculate that the formation and filling of knowledge gaps may be a
robust feature of knowledge acquisition.
