  Transformer models underpin many recent advances in practical machine
learning applications, yet understanding their internal behavior continues to
elude researchers. Given the size and complexity of these models, forming a
comprehensive picture of their inner workings remains a significant challenge.
To this end, we set out to understand small transformer models in a more
tractable setting: that of solving mazes. In this work, we focus on the
abstractions formed by these models and find evidence for the consistent
emergence of structured internal representations of maze topology and valid
paths. We demonstrate this by showing that the residual stream of only a single
token can be linearly decoded to faithfully reconstruct the entire maze. We
also find that the learned embeddings of individual tokens have spatial
structure. Furthermore, we take steps towards deciphering the circuity of
path-following by identifying attention heads (dubbed $\textit{adjacency
heads}$), which are implicated in finding valid subsequent tokens.
