I would recommend this paper for acceptance. The paper considers the (relatively new) idea of finding symmetry-based disentangled representations and provides a fresh perspective on the settings where such representations may be learned. As such, this paper stands apart from the numerous paper investigated in the last year that propose marginal improvements to existing disentanglement metrics and methods. While reviewers have brought up that the exposition can be improved, the authors have responded to these concerns in the author response and are encouraged to further polish their submission for the camera-ready version.