  Humans are constantly exposed to sequences of events in the environment.
Those sequences frequently evince statistical regularities, such as the
probabilities with which one event transitions to another. Collectively,
inter-event transition probabilities can be modeled as a graph or network. Many
real-world networks are organized hierarchically and understanding how humans
learn these networks is an ongoing aim of current investigations. While much is
known about how humans learn basic transition graph topology, whether and to
what degree humans can learn hierarchical structures in such graphs remains
unknown. We investigate how humans learn hierarchical graphs of the
Sierpi\'nski family using computer simulations and behavioral laboratory
experiments. We probe the mental estimates of transition probabilities via the
surprisal effect: a phenomenon in which humans react more slowly to less
expected transitions, such as those between communities or modules in the
network. Using mean-field predictions and numerical simulations, we show that
surprisal effects are stronger for finer-level than coarser-level hierarchical
transitions. Surprisal effects at coarser levels of the hierarchy are difficult
to detect for limited learning times or in small samples. Using a serial
response experiment with human participants (n=$100$), we replicate our
predictions by detecting a surprisal effect at the finer-level of the hierarchy
but not at the coarser-level of the hierarchy. To further explain our findings,
we evaluate the presence of a trade-off in learning, whereby humans who learned
the finer-level of the hierarchy better tended to learn the coarser-level
worse, and vice versa. Our study elucidates the processes by which humans learn
hierarchical sequential events. Our work charts a road map for future
investigation of the neural underpinnings and behavioral manifestations of
graph learning.
