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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.