  There has been growing excitement over the possibility of employing
artificial neural networks (ANNs) to gain new theoretical insight into the
physics of quantum many-body problems. ``Interpretability'' remains a concern:
can we understand the basis for the ANN's decision-making criteria in order to
inform our theoretical understanding? ``Interpretable'' machine learning in
quantum matter has to date been restricted to linear models, such as support
vector machines, due to the greater difficulty of interpreting non-linear ANNs.
Here we consider topological quantum phase transitions in models of Chern
insulator, $\mathbb{Z}_2$ topological insulator, and $\mathbb{Z}_2$ quantum
spin liquid, each using a shallow fully connected feed-forward ANN. The use of
quantum loop topography, a ``domain knowledge''-guided approach to feature
selection, facilitates the construction of faithful phase diagrams and
semi-quantitative interpretation of the criteria in certain cases. To identify
the topological phases, the ANNs learn physically meaningful features, such as
topological invariants and deconfinement of loops. The interpretability in
these cases suggests hope for theoretical progress based on future uses of
ANN-based machine learning on quantum many-body problems.
