  Learning disentangled representations with variational autoencoders (VAEs) is
often attributed to the regularisation component of the loss. In this work, we
highlight the interaction between data and the reconstruction term of the loss
as the main contributor to disentanglement in VAEs. We show that standard
benchmark datasets have unintended correlations between their subjective
ground-truth factors and perceived axes in the data according to typical VAE
reconstruction losses. Our work exploits this relationship to provide a theory
for what constitutes an adversarial dataset under a given reconstruction loss.
We verify this by constructing an example dataset that prevents disentanglement
in state-of-the-art frameworks while maintaining human-intuitive ground-truth
factors. Finally, we re-enable disentanglement by designing an example
reconstruction loss that is once again able to perceive the ground-truth
factors. Our findings demonstrate the subjective nature of disentanglement and
the importance of considering the interaction between the ground-truth factors,
data and notably, the reconstruction loss, which is under-recognised in the
literature.
