  We have recently seen great progress in learning interpretable music
representations, ranging from basic factors, such as pitch and timbre, to
high-level concepts, such as chord and texture. However, most methods rely
heavily on music domain knowledge. It remains an open question what general
computational principles give rise to interpretable representations, especially
low-dim factors that agree with human perception. In this study, we take
inspiration from modern physics and use physical symmetry as a self consistency
constraint for the latent space of time-series data. Specifically, it requires
the prior model that characterises the dynamics of the latent states to be
equivariant with respect to certain group transformations. We show that
physical symmetry leads the model to learn a linear pitch factor from
unlabelled monophonic music audio in a self-supervised fashion. In addition,
the same methodology can be applied to computer vision, learning a 3D Cartesian
space from videos of a simple moving object without labels. Furthermore,
physical symmetry naturally leads to counterfactual representation
augmentation, a new technique which improves sample efficiency.
