  Variational autoencoders (VAEs) have recently been used for unsupervised
disentanglement learning of complex density distributions. Numerous variants
exist to encourage disentanglement in latent space while improving
reconstruction. However, none have simultaneously managed the trade-off between
attaining extremely low reconstruction error and a high disentanglement score.
We present a generalized framework to handle this challenge under constrained
optimization and demonstrate that it outperforms state-of-the-art existing
models as regards disentanglement while balancing reconstruction. We introduce
three controllable Lagrangian hyperparameters to control reconstruction loss,
KL divergence loss and correlation measure. We prove that maximizing
information in the reconstruction network is equivalent to information
maximization during amortized inference under reasonable assumptions and
constraint relaxation.
