  Machine learning has been widely applied to clearly defined problems of
astronomy and astrophysics. However, deep learning and its conceptual
differences to classical machine learning have been largely overlooked in these
fields. The broad hypothesis behind our work is that letting the abundant real
astrophysical data speak for itself, with minimal supervision and no labels,
can reveal interesting patterns which may facilitate discovery of novel
physical relationships. Here as the first step, we seek to interpret the
representations a deep convolutional neural network chooses to learn, and find
correlations in them with current physical understanding. We train an
encoder-decoder architecture on the self-supervised auxiliary task of
reconstruction to allow it to learn general representations without bias
towards any specific task. By exerting weak disentanglement at the information
bottleneck of the network, we implicitly enforce interpretability in the
learned features. We develop two independent statistical and
information-theoretical methods for finding the number of learned informative
features, as well as measuring their true correlation with astrophysical
validation labels. As a case study, we apply this method to a dataset of
~270000 stellar spectra, each of which comprising ~300000 dimensions. We find
that the network clearly assigns specific nodes to estimate (notions of)
parameters such as radial velocity and effective temperature without being
asked to do so, all in a completely physics-agnostic process. This supports the
first part of our hypothesis. Moreover, we find with high confidence that there
are ~4 more independently informative dimensions that do not show a direct
correlation with our validation parameters, presenting potential room for
future studies.
