  In representation learning and non-linear dimension reduction, there is a
huge interest to learn the 'disentangled' latent variables, where each
sub-coordinate almost uniquely controls a facet of the observed data. While
many regularization approaches have been proposed on variational autoencoders,
heuristic tuning is required to balance between disentanglement and loss in
reconstruction accuracy -- due to the unsupervised nature, there is no
principled way to find an optimal weight for regularization. Motivated to
completely bypass regularization, we consider a projection strategy: modifying
the canonical Gaussian encoder, we add a layer of scaling and rotation to the
Gaussian mean, such that the marginal correlations among latent sub-coordinates
become exactly zero. This achieves a theoretically maximal disentanglement, as
guaranteed by zero cross-correlation between one latent sub-coordinate and the
observed varying with the rest. Unlike regularizations, the extra projection
layer does not impact the flexibility of the previous encoder layers, leading
to almost no loss in expressiveness. This approach is simple to implement in
practice. Our numerical experiments demonstrate very good performance, with no
tuning required.
